Meeting Archive

May 6, 2023

Discovery Learning: Beginner Group (in Pre-Algebra and below)

Speaker: Dr. Nick Treuer, Texas A&M University

Title: River Crossings

Abstract: We will consider variations of the ancient river crossing problem including the wolf/goat cabbage version, the human/zombies variation and the hungry monsters version.  Factorization will be discussed.

Discovery Learning: Intermediate Group (in Algebra I or above)

Speaker: Logan Knudsen, Texas A&M University

Title: Colored Loops

Abstract: In this activity we will use arrows to create colorful loops that cycle back to the starting arrow. Based on the Julia Robinson Mathematics Festival activity, Colored Loops, this activity will secretly explore modular arithmetic and cyclic groups.

Discovery Learning: Advanced Group (in Algebra II or above)

Speaker: Dr. Frank Lin, Texas A&M University

Title: Gauss-Jordan Reduction and Matrix Inversion

Abstract: In matrix algebra, one can draw further analogies with the algebra of ordinary numbers.  For example, the identity matrix is analogous to the number 1 in the multiplication of ordinary numbers.  Matrix inversion can be thought of as taking the "reciprocal" of a matrix, and multiplying by the inverse of a matrix is like "dividing" by that matrix.    We will introduce one method of finding the inverse of a matrix - via elementary matrices and Gauss-Jordan elimination, which is an extension of Gaussian elimination, which itself has been previously seen to be useful for solving a system of equations.  

Problem-Solving: Beginner Group

Instructors: Dr. Kun Wang (Texas A&M), Dr. Irina Bobkova  (Texas A&M), and Dr. Guangbo Xu (Texas A&M)

Problem-Solving: Intermediate Group

Instructors: Xiaoyu Su (Texas A&M), Dr. Jinmin Wang (Texas A&M), and Dr. Bo Zhu (Texas A&M)

Problem-Solving: Advanced Group

Instructors: Andrew Yu (Phillips Academy), Dr. Sherry Gong (Texas A&M), and Dr. Zhizhang Xie (Texas A&M)

April 29, 2023

SPECIAL ACTIVITY

On April 29, we will have a visit from an NSF Research group in the School of Architecture at Texas A&M developing Augmented Reality (AR) for learning. You will get to hold a model car or boat or airplane in front of the computer. A picture of the vehicle will appear on the screen and as you move the vehicle, the math equations to describe that motion will also appear on the screen. We hope that you will learn some of those formulas. You can see a promotional video (at the college level) for the AR Classroom App at https://multiplex.videohall.com/presentations/2284.

This visit will last up to 3 hours and replace both the Discovery Learning and Problem Solving sessions. So please plan to arrive at 1:00 and stay until 4:00. We certainly understand if you cannot stay the whole time. If you have a laptop and can install software on your machine (as administrator), please bring it on April 29. 

(If you are attending virtually, please log in at 1:00. We will have someone working the computer visible to the remote students. Unfortunately, you will not have the model vehicle in your hands to move.)

April 22, 2023

Discovery Learning: Beginner Group (Pre-Algebra and below) and Intermediate Group (in Algebra I or above)

Speaker: Dr. Philip Yasskin, Texas A&M University

Title: Matrices in Manufacturing

Abstract: A bakery can make brownies and cookies. Each brownie takes 2 oz of sugar and 5 oz of flour. Each cookie takes 1 oz of sugar and 4 oz of flour. If they want to make 100 brownies and 200 cookies, how much sugar and flour will it take? Conversely, if they have 1000 oz of sugar and 550 oz of flour, how many brownies and cookies can they make assuming they use up the sugar and flour? We will study this and similar problems using 2D matrices.

Discovery Learning: Advanced Group (in Algebra II or above)

Speaker: Dr. John Weeks, Texas A&M University

Title: Matrices in Manufacturing

Abstract: A matrix is an array of numbers arranged in a rectangular grid. The use of matrices pops up in anything from engineering to baking to giving mathematical solutions to systems of equations. We will cover some of the myriad applications and tools that matrices give us, including calculating inverse matrices to solve systems of equations in 2-by-2 and 3-by-3 settings.

Problem-Solving: Beginner Group

Instructors: Dr. Kun Wang (Texas A&M), Dr. Irina Bobkova  (Texas A&M), and Dr. Guangbo Xu (Texas A&M)

Problem-Solving: Intermediate Group

Instructors: Xiaoyu Su (Texas A&M), Dr. Jinmin Wang (Texas A&M), and Dr. Bo Zhu (Texas A&M)

Problem-Solving: Advanced Group

Instructors: Andrew Yu (Phillips Academy), Dr. Sherry Gong (Texas A&M), and Dr. Zhizhang Xie (Texas A&M)

March 25, 2023

Discovery Learning: Beginner Group (Pre-Algebra and below)

Speaker: Arpan Pal, Texas A&M University

Title: Polydrons

Abstract: Polydrons are Legos for three-dimensional shapes! We will build many different structures of all shapes and sizes in an interactive discussion that will introduce students to key geometry concepts.

Discovery Learning: Intermediate Group (in Algebra I or above)

Speaker: Youngho Yoo, Texas A&M University

Title: Mondrian Art Puzzles

Abstract: We will play with some mathematical puzzles inspired by the paintings of Piet Mondrian. Specifically, we will look for ways to divide a square canvas into rectangles of different dimensions. Can we find such a division minimizing the differences in the areas of the rectangles used? And if we want to color the rectangles so that no two of the same color touch each other, how many colors do we need?

Discovery Learning: Advanced Group (in Algebra II or above)

Speaker: Hannah Solomon, Texas A&M University

Title: How (Not) to Hang a Picture

Abstract: We will discuss how to hang a picture on the wall using two nails in such a way that removing either of the nails will make the picture fall down to the foor. We will see how one can come up with a solution without experimentation. In fact, the same statement holds for any number of nails, and we will find a way to compute the solutions.

Problem-Solving: Beginner Group

Instructors:  Dr. Kun Wang (Texas A&M), Dr. Irina Bobkova  (Texas A&M), and Dr. Guangbo Xu (Texas A&M)

Problem-Solving: Intermediate Group

Instructors: Xiaoyu Su (Texas A&M), Dr. Jinmin Wang (Texas A&M),  and Dr. Bo Zhu(Texas A&M)

Problem-Solving: Advanced Group

Instructors:  Andrew Yu (Phillips Academy), Dr. Sherry Gong (Texas A&M), and  Dr. Zhizhang Xie (Texas A&M)

March 4, 2023

Discovery Learning: Beginner Group (Pre-Algebra and below)

Speaker: Dr. Nick Treuer, Texas A&M University

Title: Prime Cubes

Abstract: Can you place the numbers 1 through 8 on the vertices of a cube so that adjacent vertices sum to a prime number?  How about the numbers 1 through 4 on a tetrahedron?  We will explore these questions and others related to prime numbers on Saturday.

Discovery Learning: Intermediate Group (in Algebra I or above)

Speaker: Kyle Murphy, Texas A&M University

Title: Lights Out - Dimensions!

Abstract: We will be exploring the classic game Lights Out, how it changes when extended to three or even four dimensions, and how this relates to modular arithmetic and group theory.

Discovery Learning: Advanced Group (in Algebra II or above)

Speaker: Dr. Matthias Hofmann, Texas A&M University

Title: Inversion in the Circle

Abstract: Inversion in the circle is a useful tool for solving geometric problems. We will review properties of the inversion of the circle and discuss strategies in its usage for problem solving. In this context, we will show Ptolemy's theorem, which characterizes all cyclic quadrilaterals, i.e. quadrilaterals for which all corners lie on the same circle. Finally, we will introduce the arbelos of Pappus, which is a type of ring of circles each tangent to two tangent circles, and consider in this context geometric problems as they appeared in math competitions to apply the learned concepts.

February 25, 2023

Discovery Learning: Beginner Group (Pre-Algebra and below)

Speaker: Erika Gonzalez Brizuela, Texas A&M University

Title: Sprigs

Abstract: In this activity, students will try to be the last to draw a curve (sprig) by  joining a set of dots. Based on the Julia Robinson Mathematics Festival activity, Sprigs, students will develop their own strategies to always win the round. As new rules are introduced, students will have to modify their strategy and discover what determines the winner in any scenario.   

Discovery Learning: Intermediate Group (in Algebra I or above)

Speaker: Agniva Dasgupta, Texas A&M University

Title: De Brujin Sequences

Abstract: De Bruijn sequences are fun combinatorial objects that have some nice applications in biology, cryptography and graph theory. A De Bruijn sequence of window length k is a zero/one sequence of length 2^k such that every k consecutive digits appear only once (we are allowed to cycle around the corner). It is not at all obvious that these exist. We will discuss a simple way to see explicitly how they exist, via some elegant graph theory. If there is time, (and enough people!) we can discuss a simple (but impressive) card trick based off these sequences.  

Discovery Learning: Advanced Group (in Algebra II or above)

Speaker: Dr. Phil Yasskin, Texas A&M University

Title: The a+b+ab Problem

Abstract: Write down the numbers from 1 to 100. Randomly select 2 numbers from the list, say a and b, and cross them off, but add to the list the number a+b+ab. You now have 99 numbers. Repeat this process until you have only 1 number left. What are all possible final numbers?

Problem-Solving: Beginner Group

Instructors:  Dr. Kun Wang (Texas A&M), Dr. Irina Bobkova  (Texas A&M), and Dr. Guangbo Xu (Texas A&M)

Problem-Solving: Intermediate Group

Instructors: Xiaoyu Su (Texas A&M), Dr. Jinmin Wang (Texas A&M),  and Dr. Bo Zhu(Texas A&M)

Problem-Solving: Advanced Group

Instructors:  Andrew Yu (Phillips Academy), Dr. Sherry Gong (Texas A&M), and  Dr. Zhizhang Xie (Texas A&M)

February 18, 2023

Discovery Learning: Beginner Group (Pre-Algebra and below)

Speaker: Nick Treuer, Texas A&M University

Title: Colored Loops

Abstract: In this activity we will use arrows to create colorful loops that cycle back to the starting arrow. Based on the Julia Robinson Mathematics Festival activity, Colored Loops, this activity will secretly explore modular arithmetic and cyclic groups.

Discovery Learning: Intermediate Group (in Algebra I or above)

Speaker: Shuqin Zhou, Texas A&M University

Title: Queen's Move

Abstract: Move a Queen on a chessboard. The goal is to move the Queen to the bottom left square, and every move must get them to that square. This means each turn the player can move the Queen in any of the following ways: any numbers of spaces straight down, straight to the left, or on the downward-left diagonal.

The game can start with the Queen on any square. We will discuss how to find a winning strategy from multiple different starting positions.

Discovery Learning: Advanced Group (in Algebra II or above)

Speaker: Agniva Dasgupta, Texas A&M University

Title: De Brujin Sequences

Abstract: De Bruijn sequences are fun combinatorial objects that have some nice applications in biology, cryptography and graph theory. A De Bruijn sequence of window length k is a zero/one sequence of length 2^k such that every k consecutive digits appear only once (we are allowed to cycle around the corner). It is not at all obvious that these exist. We will discuss a simple way to see explicitly how they exist, via some elegant graph theory. If there is time, (and enough people!) we can discuss a simple (but impressive) card trick based off these sequences.

Problem-Solving: Beginner Group

Instructors:  Dr. Kun Wang (Texas A&M), Dr. Irina Bobkova  (Texas A&M), and Dr. Guangbo Xu (Texas A&M)

Problem-Solving: Intermediate Group

Instructors: Xiaoyu Su (Texas A&M), Dr. Jinmin Wang (Texas A&M),  and Dr. Bo Zhu(Texas A&M)

Problem-Solving: Advanced Group

Instructors:  Andrew Yu (Phillips Academy), Dr. Sherry Gong (Texas A&M), and  Dr. Zhizhang Xie (Texas A&M)

February 11, 2023

Discovery Learning: Beginner Group (Pre-Algebra and below)

Speaker: Shuqin Zhou, Texas A&M University

Title: Queen's Move

Abstract: Move a Queen on a chessboard. The goal is to move the Queen to the bottom left square, and every move must get them to that square. This means each turn the player can move the Queen in any of the following ways: any numbers of spaces straight down, straight to the left, or on the downward-left diagonal.

The game can start with the Queen on any square. We will discuss how to find a winning strategy from multiple different starting positions.

Discovery Learning: Intermediate Group (in Algebra I or above)

Speaker: Logan Knudsen, Texas A&M University

Title: The Candy Conundrum

Abstract: Students will figure out the number of different combinations of different candies (represented using pebbles) they  can make. Further, students will practice using ratios to decide how many different flavors can be made from different candies, and attempt to find a geometric representation of these flavors.

Discovery Learning: Advanced Group (in Algebra II or above)

Speaker: Kyle Murphy, Texas A&M University

Title: Lights Out - Dimensions!

Abstract: We will be exploring the classic game Lights Out, how it changes when extended to three or even four dimensions, and how this relates to modular arithmetic and group theory.

Problem-Solving: Beginner Group

Instructors:  Dr. Kun Wang (Texas A&M), Dr. Irina Bobkova  (Texas A&M), and Dr. Guangbo Xu (Texas A&M)

Problem-Solving: Intermediate Group

Instructors: Xiaoyu Su (Texas A&M), Dr. Jinmin Wang (Texas A&M),  and Dr. Bo Zhu(Texas A&M)

Problem-Solving: Advanced Group

Instructors:  Andrew Yu (Phillips Academy), Dr. Sherry Gong (Texas A&M), and  Dr. Zhizhang Xie (Texas A&M)

February 4, 2023

Discovery Learning: Beginner Group (Pre-Algebra and below)

Speaker: Matthew Atanas, Texas A&M University

Title: Gossip

Abstract: We will be exploring the mathematics of Gossip and how it relates to combinatorics and graph theory.

Discovery Learning: Intermediate Group (in Algebra I or above)

Speaker: Tanuj Gupta, Texas A&M University

Title: Hexaflexagons

Abstract: A flexagon is a flat model made by folding and gluing a strip of paper which can be "flexed" or folded in certain ways to reveal faces that were at first hidden. If the folded paper looks like a hexagon (a six sided polygon), then we call it a "hexaflexagon". In this session, we will create this funny sounding thing (hexaflexagon) from a piece of paper and try to find the patterns hidden in it. 

Discovery Learning: Advanced Group (in Algebra II or above)

Speaker: David Cates, Texas A&M University

Title: TBA - Games, continued

Abstract: TBA - We will continue studying games from a combinatorial point of view.

Problem-Solving: Beginner Group

Instructors:  Dr. Kun Wang (Texas A&M), Dr. Irina Bobkova  (Texas A&M), and Dr. Guangbo Xu (Texas A&M)

Problem-Solving: Intermediate Group

Instructors: Xiaoyu Su (Texas A&M), Dr. Jinmin Wang (Texas A&M),  and Dr. Bo Zhu(Texas A&M)

Problem-Solving: Advanced Group

Instructors:  Andrew Yu (Phillips Academy), Dr. Sherry Gong (Texas A&M), and  Dr. Zhizhang Xie (Texas A&M)

January 28, 2023

Discovery Learning: Beginner Group (Pre-Algebra and below)

Speaker: Logan Knudsen, Texas A&M University

Title: The Candy Conundrum

Abstract: Students will figure out the number of different combinations of different candies (represented using pebbles) they  can make. Further, students will practice using ratios to decide how many different flavors can be made from different candies, and attempt to find a geometric representation of these flavors.

Discovery Learning: Intermediate Group (in Algebra I or above)

Speaker: Matthew Atanas, Texas A&M University

Title: Gossip

Abstract: We will be exploring the mathematics of Gossip and how it relates to combinatorics and graph theory.

Discovery Learning: Advanced Group (in Algebra II or above)

Speaker: David Cates, Texas A&M University

Title: The Game of Hackenbush

Abstract: The game of Hackenbush is a two-player so-called “combinatorial game.” Students will play various rounds of the game, analyze the game, and begin to learn the basics of the field of Combinatorial Game Theory.

Problem-Solving: Beginner Group

Instructors:  Dr. Kun Wang (Texas A&M), Dr. Irina Bobkova  (Texas A&M), and Dr. Guangbo Xu (Texas A&M)

Problem-Solving: Intermediate Group

Instructors: Xiaoyu Su (Texas A&M), Dr. Jinmin Wang (Texas A&M),  and Dr. Bo Zhu(Texas A&M)

Problem-Solving: Advanced Group

Instructors:  Andrew Yu (Phillips Academy), Dr. Sherry Gong (Texas A&M), and  Dr. Zhizhang Xie (Texas A&M)

December 10, 2022

Discovery Learning: Beginner Group (Pre-Algebra and below)

Speaker: Hannah Solomon, Texas A&M University

Title: How do we know we live on a sphere?

Abstract: We will start by brainstorming ways to know we live on a sphere versus a torus (surface of a donut.

What is a torus?  We will construct a torus out of paper and learn a little more about this surface. How could we make a surface with 2 donut holes?

What is a Möbius strip?  We will construct one from paper and learn about non orientability.  We will also learn what a Klein bottle is.

We will play games (such as chess and checkers) as if we were playing them on a torus or Klein bottle.

Discovery Learning: Intermediate Group (in Algebra I or above)

Speaker: Ajay Karri, Texas A&M University

Title: The a+b+ab problem

Abstract: Write down the numbers from 1 to 100. Randomly select 2 numbers from the list, say a and b, and cross them off, but add to the list the number a+b+ab. You now have 99 numbers. Repeat this process until you have only 1 number left. What are all possible final numbers?

Discovery Learning: Advanced Group (in Algebra II or above)

Speaker: Shuqin Zhou, Texas A&M University

Title: Switching Light Bulbs

Abstract: Say 100 people numbered 1 through 100 walk past 100 light bulbs with pull strings. Initially, the lights are all off. When the string is pulled the light changes from off to on or from on to off. Each person, when they walk down the hallway, will pull the string of every light bulb whose number is a multiple of theirs. (So, for example, person 1 will pull every string; person 2 will pull the strings of bulb number 2, 4, 6, 8, 10, …, and person 17 will pull the strings of bulb number 17, 34, 51, 68, ….) Which light bulbs are on after all the 100 people are done walking? We will discuss this problem and generalizations. 

Problem-Solving: Beginner Group

Instructors:  Dr. Kun Wang (Texas A&M), Dr. Irina Bobkova  (Texas A&M), and Dr. Guangbo Xu (Texas A&M)

Problem-Solving: Intermediate Group

Instructors: Xiaoyu Su (Texas A&M), Dr. Jinmin Wang (Texas A&M),  and Dr. Bo Zhu (Texas A&M)

Problem-Solving: Advanced Group

Instructors:  Andrew Yu (Phillips Academy), Dr. Sherry Gong (Texas A&M), and  Dr. Zhizhang Xie (Texas A&M)

December 3, 2022

Discovery Learning: Beginner Group (Pre-Algebra and below)

Speaker: Youngho Yoo, Texas A&M University

Title: Mondrian Art Puzzles

Abstract: We will play with some mathematical puzzles inspired by the paintings of Piet Mondrian. Specifically, we will look for ways to divide a square canvas into rectangles of different dimensions. Can we find such a division minimizing the differences in the areas of the rectangles used? And if we want to color the rectangles so that no two of the same color touch each other, how many colors do we need?

Discovery Learning: Intermediate Group (in Algebra I or above)

Speaker: Hannah Solomon, Texas A&M University

Title: How do we know we live on a sphere?

Abstract: We will start by brainstorming ways to know we live on a sphere versus a torus (surface of a donut.

What is a torus?  We will construct a torus out of paper and learn a little more about this surface. How could we make a surface with 2 donut holes?

What is a Möbius strip?  We will construct one from paper and learn about non orientability.  We will also learn what a Klein bottle is.

We will play games (such as chess and checkers) as if we were playing them on a torus or Klein bottle.

Discovery Learning: Advanced Group (in Algebra II or above)

Speaker: Matthias Hofmann, Texas A&M University

Title: Apollonius' Problem - Construct a Circle Tangent to Three Circles in the Plane

Abstract: The problem of Apollonius is a simple construction problem that is closely related to finding the incircle and excircle in the triangle. The earliest consideration of the problem goes back to Apollonius of Perge who considered the problem around 2200 years ago. However, only several centuries later the problem was solved, and an elegant and elementary solution of the problem was discovered towards the end of the 19th century via inversions in the circle. We will discuss simple variants of the problem and learn how to construct the circular inversion for different geometric objects in the plane. Ultimately, we discuss how circular inversion can be used to simplify the problem.

Problem-Solving: Beginner Group

Instructors:  Dr. Kun Wang (Texas A&M), Dr. Irina Bobkova  (Texas A&M), and Dr. Guangbo Xu (Texas A&M)

Problem-Solving: Intermediate Group

Instructors: Xiaoyu Su (Texas A&M), Dr. Jinmin Wang (Texas A&M),  and Dr. Bo Zhu(Texas A&M)

Problem-Solving: Advanced Group

Instructors:  Andrew Yu (Phillips Academy), Dr. Sherry Gong (Texas A&M), and  Dr. Zhizhang Xie (Texas A&M)

November 19, 2022

Discovery Learning: Beginner Group (Pre-Algebra and below)

Speaker: Daniel Perales Anaya, Texas A&M University

Title: Covering a chess board with dominoes

Abstract: We will discuss the following classic problems: Is it possible to cover an 8x8 board with 2x1 dominoes? Is it possible to do it if we remove one corner of the board? What if we remove two corners? What if we remove some random squares?

Turns out that we can solve all these questions with the same technique, by looking at the colors of the chess board.

Then we will discuss a similar problem, where now we cover the board with checkers, and add or remove checkers to the board according to certain rules, with the final objective of clearing the whole board. This is sometimes possible and sometimes impossible, to check when is impossible we can again color the board and find an invariant. This is probably one of the nicest ways to learn the invariance principle, a very useful heuristic to solve math problems.

Discovery Learning: Intermediate Group (in Algebra I or above)

Speaker: Philip Yasskin, Texas A&M University

Title: Pile Splitting, Handshakes, & Diagonals

Abstract: We will look at three problems:

Hand Shaking: If N people all shake hands, how many handshakes will happen?

Pile Splitting: Start with 10 poker chips. Split them into two piles, say 4 and 6. Multiply those numbers to get 24.

Now pick one of those piles, split it and multiply the numbers. Keep going until all the piles have 1 chip.

Finally add up all the products. What is this sum?

We will find these two problems are closely related.

If we have time, we will count the number of non-touching diagonals which can be drawn in an NxN grid of squares.

The answer is related to the other two problems.

Discovery Learning: Advanced Group (in Algebra II or above)

Speaker: Igor Zelenko, Texas A&M University

Title: Method of center of mass in geometry

Abstract: Center mass is not only a very useful notion in mechanics but can be used as an effective method to solve problems in geometry and clarifies the meaning of the geometric results. In this activity, we will try together to solve several geometric problems using this method.

Problem-Solving: Beginner Group

Instructors:  Dr. Kun Wang (Texas A&M), Dr. Irina Bobkova  (Texas A&M), and Dr. Guangbo Xu (Texas A&M)

Problem-Solving: Intermediate Group

Instructors: Xiaoyu Su (Texas A&M), Dr. Jinmin Wang (Texas A&M),  and Dr. Bo Zhu(Texas A&M)

Problem-Solving: Advanced Group

Instructors:  Andrew Yu (Phillips Academy), Dr. Sherry Gong (Texas A&M), and  Dr. Zhizhang Xie (Texas A&M)

November 5, 2022

Discovery Learning: Beginner Group (Pre-Algebra and below)

Speaker: Frank Lin, Texas A&M University

Title: Rook's Move

Abstract: In Rook's Move, two players start with a single rook on a chess board. Players take turns moving the rook down or to the left on a chess board. The player to place the rook in the bottom left hand corner wins. We will investigate properties of symmetry and optimal game play in this activity. Variations of this activity will also be explored.

Discovery Learning: Intermediate Group (in Algebra I or above)

Speaker: Matthew Atanas, Texas A&M University

Title: Subtraction, NIM, and Tip the Die Games

Abstract: We will be playing Subtraction, NIM, and Tip the Die games and finding strategies for them to provably always win!

Discovery Learning: Advanced Group (in Algebra II or above)

Speaker: Marshall King, Texas A&M University

Title: Pick's Theorem

Abstract: Suppose we have a pegboard with a grid of pegs and we make a polygon by wrapping a band around some collection of these pegs. How would we calculate the area of this polygon? One way is to split the polygon into smaller polygons and add up all their areas, but we could also use Pick's Theorem to easily find the total area. We will discover how Pick's Theorem arises from this problem, and construct an explanation of why it must be true.

Problem-Solving: Beginner Group

Instructor:  Dr. Kun Wang (Texas A&M), Dr. Irina Bobkova  (Texas A&M), and Dr. Guangbo Xu (Texas A&M)

Problem-Solving: Intermediate Group

Instructor: Xiaoyu Su (Texas A&M), Dr. Jinmin Wang (Texas A&M),  and Dr. Bo Zhu(Texas A&M)

Problem-Solving: Advanced Group

Instructors:  Andrew Yu (Phillips Academy), Dr. Sherry Gong (Texas A&M), and  Dr. Zhizhang Xie (Texas A&M)

October 29, 2022

Discovery Learning: Beginner Group (Pre-Algebra and below)

Speaker: Tanuj Gupta, Texas A&M University

Title: Hexahexaflexagons

Abstract: A flexagon is a flat model made by folding and gluing a strip of paper which can be "flexed" or folded in certain ways to reveal faces that were at first hidden. If the folded paper looks like a hexagon (a six sided polygon), then we call it a "hexaflexagon". In this session, we will create this funny sounding thing (hexaflexagon) from a piece of paper and try to find the patterns hidden in it.

Discovery Learning: Intermediate Group (in Algebra I or above)

Speaker: Marshall King, Texas A&M University

Title: Pick's Theorem

Abstract: Suppose we have a pegboard with a grid of pegs and we make a polygon by wrapping a band around some collection of these pegs. How would we calculate the area of this polygon? One way is to split the polygon into smaller polygons and add up all their areas, but we could also use Pick's Theorem to easily find the total area. We will discover how Pick's Theorem arises from this problem, and construct an explanation of why it must be true.

Discovery Learning: Advanced Group (in Algebra II or above)

Speaker: Matthew Atanas, Texas A&M University

Title: Subtraction, NIM, and Tip the Die Games

Abstract: We will be playing Subtraction, NIM, and Tip the Die games and finding strategies for them to provably always win!

Problem-Solving: Beginner Group

Instructor:  Dr. Kun Wang (Texas A&M), Dr. Irina Bobkova  (Texas A&M), and Dr. Guangbo Xu (Texas A&M)

Problem-Solving: Intermediate Group

Instructor: Xiaoyu Su (Texas A&M), Dr. Jinmin Wang (Texas A&M),  and Dr. Bo Zhu(Texas A&M)

Problem-Solving: Advanced Group

Instructors:  Andrew Yu (Phillips Academy), Dr. Sherry Gong (Texas A&M), and  Dr. Zhizhang Xie (Texas A&M)

October 22, 2022

Discovery Learning: Beginner Group (Pre-Algebra and below)

Speaker: Shuqin Zhou, Texas A&M University

Title: Switching Light Bulbs

Abstract: Say 100 people numbered 1 through 100 walk past 100 light bulbs with pull strings. Initially, the lights are all off. When the string is pulled the light changes from off to on or from on to off. Each person, when they walk down the hallway, will pull the string of every light bulb whose number is a multiple of theirs. (So, for example, person 1 will pull every string; person 2 will pull the strings of bulb number 2, 4, 6, 8, 10, …, and person 17 will pull the strings of bulb number 17, 34, 51, 68, ….)  Which light bulbs are on after all the 100 people are done walking? We will discuss this problem and generalizations.  

Discovery Learning: Intermediate Group (in Algebra I or above)

Speaker: Erika Gonzalez, Texas A&M University

Title: Balance Beams

Abstract: We will use a meter stick as a balance beam. We will put a few weights on each side to investigate how the distances from the pivot affect the balance. Then we will develop equations to predict this.

Discovery Learning: Advanced Group (in Algebra II or above)

Speaker: David Cates, Texas A&M University

Title: Stones on an Infinite Chessboard

Abstract: The game works as follows: You have n stones that may be placed anywhere on an infinite chessboard, each worth value 1. After you have placed the stones, place markers worth 2, 3, … next to the stones according to the following rule: To place the stone k, the surrounding 8 squares must have values summing to k.

Students will investigate maximal configurations of stones and markers, and potential upper and lower bounds for how large k can be for given values of n.

Problem-Solving: Beginner Group

Instructor:  Dr. Kun Wang (Texas A&M), Dr.  Irina Bobkova  (Texas A&M), and Dr. Guangbo Xu (Texas A&M)

Problem-Solving: Intermediate Group

Instructor: Xiaoyu Su (Texas A&M), Dr. Jinmin Wang (Texas A&M),  and Dr. Bo Zhu(Texas A&M)

Problem-Solving: Advanced Group

Instructors:  Andrew Yu (Phillips Academy), Dr. Sherry Gong (Texas A&M), and  Dr. Zhizhang Xie (Texas A&M)

October 8, 2022

Discovery Learning: Beginner Group (Pre-Algebra and below)

Speaker:  Matthew Atanas, Texas A&M University

Title:  Subtraction and Nim

Abstract:  We will play several two-person games starting with the Subtraction Game and then Nim. 

That will be followed by variations of them.

Discovery Learning: Intermediate Group (in Algebra I or above)

Speaker:  Logan Knudsen, Texas A&M University

Title:  Towers of Hanoi

Abstract:  Based on a children's toy, the Tower of Hanoi problem asks how many moves it takes to move a stack of disks from one post to another while keeping the disks in decreasing order of size. We will find the algorithm for how to do this as fast as possible as well as the number of steps when there are N disks. Further, we will explore number of steps when there are N disks for more pegs, and introduce the concept of induction.

Discovery Learning: Advanced Group (in Algebra II or above)

Speaker: Dr. Philip Yasskin, Texas A&M University

Title:  Pile Splitting, Handshakes, & Diagonals

Abstract:   We will look at three problems:

Hand Shaking: If N people all shake hands, how many handshakes will happen?

Pile Splitting: Start with 10 poker chips. Split them into two piles, say 4 and 6. Multiply those numbers to get 24.

Now pick one of those piles, split it and multiply the numbers. Keep going until all the piles have 1 chip.

Finally add up all the products. What is this sum?

We will find these two problems are closely related.

If we have time, we will count the number of non-touching diagonals which can be drawn in an NxN grid of squares.

The answer is related to the other two problems.

Problem-Solving: Beginner Group

Instructor:  Dr. Kun Wang (Texas A&M), Dr.  Irina Bobkova  (Texas A&M), and Dr. Guangbo Xu (Texas A&M)

Problem-Solving: Intermediate Group

Instructor: Xiaoyu Su (Texas A&M), Dr. Jinmin Wang (Texas A&M),  and Dr. Bo Zhu(Texas A&M)

Problem-Solving: Advanced Group

Instructors:  Andrew Yu (Phillips Academy), Dr. Sherry Gong (Texas A&M), and  Dr. Zhizhang Xie (Texas A&M)

October 1, 2022

Discovery Learning: Beginner Group (Pre-Algebra and below)

Speaker:  Logan Knudsen, Texas A&M University

Title:  Towers of Hanoi

Abstract:  Based on a children's toy, the Tower of Hanoi problem asks how many moves it takes to move a stack of disks from one post to another while keeping the disks in decreasing order of size. We will find the algorithm for how to do this as fast as possible as well as the number of steps when there are N disks. Further, we will explore the number of steps when there are N disks for more pegs, and introduce the concept of induction.

Discovery Learning: Intermediate Group (in Algebra I or above)

Speaker:  Nick Treuer, Texas A&M University

Title:  Rook's Move

Abstract:  In Rook's Move, two players start with a single rook on a chess board.  Players take turns moving the rook down or to the left on a chess board.  The player to place the rook in the bottom left hand corner wins. We will investigate properties of symmetry and optimal game play in this activity.  Variations of this activity will also be explored.

Discovery Learning: Advanced Group (in Algebra II or above)

Speaker:  David Cates

Title:  Bulgarian Solitaire

Abstract:  N cubes are placed on the table, in some number of piles. From each pile, we take one cube off and place them in a new pile. If this process is repeated, will the cubes eventually reach a loop, or not? If it does reach a loop, how many states are in the loop? Is it possible to have a loop of period one? Further questions will be investigated along these lines.

Problem-Solving: Beginner Group

Instructor:  Dr. Kun Wang (Texas A&M), Dr.  Irina Bobkova  (Texas A&M), and Dr. Guangbo Xu (Texas A&M)

Problem-Solving: Intermediate Group

Instructor: Xiaoyu Su (Texas A&M), Dr. Jinmin Wang (Texas A&M),  and Dr. Bo Zhu(Texas A&M)

Problem-Solving: Advanced Group

Instructors:  Andrew Yu (Phillips Academy), Dr. Sherry Gong (Texas A&M), and  Dr. Zhizhang Xie (Texas A&M)

September 24, 2022

Discovery Learning: Beginner Group (Pre-Algebra and below)

Speaker:  Phil Yasskin, Texas A&M University

Title:  Hand Shaking and Pile Splitting

Abstract:  We will look at two problems:

Hand Shaking: If N people all shake hands, how many handshakes will happen?

Pile Splitting: Start with 10 poker chips. Split them into two piles, say 4 and 6.

Multiply those numbers to get 24. Now pick one of those piles, split it and multiply the numbers.

Keep going until all the piles have 1 chip. Finally add up all the products. What is this sum?

We will find these two problems are closely related.

Discovery Learning: Intermediate Group (in Algebra I or above)

Speaker:  Shuqin Zhou, Texas A&M University

Title:  Switching Light Bulbs

Abstract:  Say 100 people numbered 1 through 100 walk past 100 light bulbs with pull strings. Initially, the lights are all off. When the string is pulled the light changes from off to on or from on to off. Each person, when they walk down the hallway, will pull the string of every light bulb whose number is a multiple of theirs. (So, for example, person 1 will pull every string; person 2 will pull the strings of bulb number 2, 4, 6, 8, 10, …, and person 17 will pull the strings of bulb number 17, 34, 51, 68, ….)  Which light bulbs are on after all the 100 people are done walking? We will discuss this problem and generalizations.  

Discovery Learning: Advanced Group (in Algebra II or above)

Speaker:  Logan Knudsen, Texas A&M University

Title:  Towers of Hanoi

Abstract:  Based on a children's toy, the Tower of Hanoi problem asks how many moves it takes to move a stack of disks from one post to another while keeping the disks in decreasing order of size. We will find the algorithm for how to do this as fast as possible as well as the number of steps when there are N disks. Further, we will explore the number of steps when there are N disks for more pegs, and introduce the concept of induction.

Problem-Solving: Beginner Group

Instructor: Kun Wang, Texas A&M University

Problem-Solving: Intermediate Group

Instructor: Xiaoyu Su, Texas A&M University

Problem-Solving: Advanced Group

Instructor: Guoliang Yu, Texas A&M University

May 14, 2022

Discovery Learning: Beginner Group (12.00 - 1.30 PM) (Pre-Algebra and below)

Speaker: Logan Knudsen (TAMU)

Title: Double Latin Squares

Abstract: We will inspect a variation of the traditional Latin Square, known as the Double Latin Square, where the player will attempt to arrange n colors and n numbers such that each row and column has only one of each color and number.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM) (in Algebra I or above)

Speaker: Dr. Maurice Rojas (TAMU)

Title: Dividing, conquering, and detecting compositeness

Abstract: "Divide and conquer" is a useful trick in many important algorithms. We'll see two examples: One coming from computational geometry and the other from cryptography. The first example is the computation of convex hulls in the plane (a construction useful in robotics). The second example involves deciding whether a number is composite (i.e., not prime) *without* factoring the number. This turns out to be useful for securely sending credit card numbers over the internet.

Discovery Learning: Advanced Group (3.30 - 5.00 PM) (in Algebra II or above)

Speaker: Dr. Maurice Rojas (TAMU)

Title: Dividing, conquering, and detecting compositeness

Abstract: "Divide and conquer" is a useful trick in many important algorithms. We'll see two examples: One coming from computational geometry and the other from cryptography. The first example is the computation of convex hulls in the plane (a construction useful in robotics). The second example involves deciding whether a number is composite (i.e., not prime) *without* factoring the number. This turns out to be useful for securely sending credit card numbers over the internet.

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Dr. Irina Bobkova (Texas A&M), Dr. Guangbo Xu (Texas A&M) Dr. Peyam Tabrizian (Texas A&M)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Dr. Jinmin Wang (Texas A&M), Dr. Rodrigo Matos (Texas A&M), and Xiaoyu Su (Texas A&M)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Andrew Yu, Dr. Sherry Gong and Dr. Zhizhang Xie (Texas A&M)

April 30, 2022

Discovery Learning: Beginner Group (12.00 - 1.30 PM) (Pre-Algebra and below)

Speaker: David Manuel (TAMU)

Title: Proofs Without Words

Abstract: There are many patterns in mathematics.  Is it possible to represent these entirely in pictures?  What can a seven year-old math whiz teach us about these?  In this session, we will discover some of these patterns and how to represent them entirely in pictures, including a well-known theorem about a certain type of triangle. 

Discovery Learning: Intermediate Group (1.45 - 3.15 PM) (in Algebra I or above)

Speaker: David Manuel (TAMU)

Title: Proofs Without Words

Abstract: There are many patterns in mathematics.  Is it possible to represent these entirely in pictures?  What can a seven year-old math whiz teach us about these?  In this session, we will discover some of these patterns and how to represent them entirely in pictures, including a well-known theorem about a certain type of triangle. 

Discovery Learning: Advanced Group (3.30 - 5.00 PM) (in Algebra II or above)

Speaker: David Manuel (TAMU)

Title: Proofs Without Words

Abstract: There are many patterns in mathematics.  Is it possible to represent these entirely in pictures?  What can a seven year-old math whiz teach us about these?  In this session, we will discover some of these patterns and how to represent them entirely in pictures, including a well-known theorem about a certain type of triangle. 

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Dr. Irina Bobkova (Texas A&M), Dr. Guangbo Xu (Texas A&M) Dr. Peyam Tabrizian (Texas A&M)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Dr. Jinmin Wang (Texas A&M), Dr. Rodrigo Matos (Texas A&M), and Xiaoyu Su (Texas A&M)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Andrew Yu, Dr. Sherry Gong and Dr. Zhizhang Xie (Texas A&M)

April 23, 2022

Discovery Learning: Beginner Group (12.00 - 1.30 PM) (Pre-Algebra and below)

Speaker: Dr. Nick Treuer (TAMU)

Title: Blue Dot Solitaire

Abstract: In this activity, we will investigate what are the essential conditions for beating the game "Blue Dot Solitaire" developed by the Julia Robinson Mathematics Festival.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM) (in Algebra I or above)

Speaker: Logan Knudsen (TAMU)

Title: Double Latin Squares

Abstract: We will inspect a variation of the traditional Latin Square, known as the Double Latin Square, where the player will attempt to arrange n colors and n numbers such that each row and column has only one of each color and number.

Discovery Learning: Advanced Group (3.30 - 5.00 PM) (in Algebra II or above)

Speaker: Logan Knudsen (TAMU)

Title: Double Latin Squares

Abstract: We will inspect a variation of the traditional Latin Square, known as the Double Latin Square, where the player will attempt to arrange n colors and n numbers such that each row and column has only one of each color and number.

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Dr. Irina Bobkova (Texas A&M), Dr. Guangbo Xu (Texas A&M) Dr. Peyam Tabrizian (Texas A&M)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Dr. Jinmin Wang (Texas A&M), Dr. Rodrigo Matos (Texas A&M), and Xiaoyu Su (Texas A&M)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Andrew Yu, Dr. Sherry Gong and Dr. Zhizhang Xie (Texas A&M)

April 9, 2022

Discovery Learning: Beginner Group (12.00 - 1.30 PM) (Pre-Algebra and below)

Speaker: Sheagan John (TAMU)

Title: Modular Arithmetic and Special Magic Squares

Abstract: A whole number N is called summable of length n if it has a special kind of digit representation, which we will define in our activity. We will investigate how to construct summable numbers of varying length, prove some statements about them, and introduce a notion of Magic Squares using summable numbers.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM) (in Algebra I or above)

Speaker: Sheagan John (TAMU)

Title: Modular Arithmetic and Special Magic Squares

Abstract: A whole number N is called summable of length n if it has a special kind of digit representation, which we will define in our activity. We will investigate how to construct summable numbers of varying length, prove some statements about them, and introduce a notion of Magic Squares using summable numbers.

Discovery Learning: Advanced Group (3.30 - 5.00 PM) (in Algebra II or above)

Speaker: Soumendra Ganguly (TAMU)

Title: Graceful Graphs

Abstract: For graphs with m edges, we will label their vertices with some subset of integers from 0 to m ensuring that no two vertices have the same label. To an edge, the endpoints of which have already been labelled, a value equal to the absolute value of the difference between the labels of its endpoints will then be automatically assigned. To obtain a graceful graph, we have to label the vertices in such a way that the edges end up having all the values from 1 to m.

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Dr. Irina Bobkova (Texas A&M), Dr. Guangbo Xu (Texas A&M) Dr. Peyam Tabrizian (Texas A&M)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Dr. Jinmin Wang (Texas A&M), Dr. Rodrigo Matos (Texas A&M), and Xiaoyu Su (Texas A&M)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Andrew Yu, Dr. Sherry Gong and Dr. Zhizhang Xie (Texas A&M)

March 26, 2022

Discovery Learning: Beginner Group (12.00 - 1.30 PM) (Pre-Algebra and below)

Speaker: Matthew Atanas (TAMU)

Title: Search and Rank

Abstract: We will be modeling a basic search engine by analysing some simple webpages that link to each other to find out which webpages are the most 'popular'. We will expand this concept to explore the math of Markov Chains.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM) (in Algebra I or above)

Speaker: Matthew Atanas (TAMU)

Title: Search and Rank

Abstract: We will be modeling a basic search engine by analysing some simple webpages that link to each other to find out which webpages are the most 'popular'. We will expand this concept to explore the math of Markov Chains.

Discovery Learning: Advanced Group (3.30 - 5.00 PM) (in Algebra II or above)

Speaker: Matthew Atanas (TAMU)

Title: Search and Rank

Abstract: We will be modeling a basic search engine by analysing some simple webpages that link to each other to find out which webpages are the most 'popular'. We will expand this concept to explore the math of Markov Chains.

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Dr. Irina Bobkova (Texas A&M), Dr. Guangbo Xu (Texas A&M) Dr. Peyam Tabrizian (Texas A&M)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Dr. Jinmin Wang (Texas A&M), Dr. Rodrigo Matos (Texas A&M), and Xiaoyu Su (Texas A&M)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Andrew Yu, Dr. Sherry Gong and Dr. Zhizhang Xie (Texas A&M)

March 5, 2022

Discovery Learning: Beginner Group (12.00 - 1.30 PM) (Pre-Algebra and below)

Speaker: Nick Treuer (TAMU)

Title: Colored Loops

Abstract: We will explore modular arithmetic (and secretly cyclic groups) using the JRMF application Colored Loops.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM) (in Algebra I or above)

Speaker: Nick Treuer (TAMU)

Title: Colored Loops

Abstract: We will explore modular arithmetic (and secretly cyclic groups) using the JRMF application Colored Loops.

Discovery Learning: Advanced Group (3.30 - 5.00 PM) (in Algebra II or above)

Speaker: Nick Treuer (TAMU)

Title: Colored Loops

Abstract: We will explore modular arithmetic (and secretly cyclic groups) using the JRMF application Colored Loops.

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Dr. Irina Bobkova (Texas A&M), Dr. Guangbo Xu (Texas A&M) Dr. Peyam Tabrizian (Texas A&M)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Dr. Jinmin Wang (Texas A&M), Dr. Rodrigo Matos (Texas A&M), and Xiaoyu Su (Texas A&M)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Andrew Yu, Dr. Sherry Gong and Dr. Zhizhang Xie (Texas A&M)

Feb. 19, 2022

Discovery Learning: Beginner Group (12.00 - 1.30 PM) (Pre-Algebra and below)

Speaker: Dr. Phil Yasskin

Title: Pop Tac Toe

Abstract: We will play the game Pop Tac Toe in which two players alternately place checkers on a checker trying to get three in a row. The complication is that when a piece is placed on the board, any pieces on adjacent spaces fly away.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM) (in Algebra I or above)

Speaker: Alexander Riedel

Title: Fibonacci Sequences, Recursions, and the Chicken McNugget Theorem

Abstract: What is the Fibonacci sequence? What can we figure out about its terms? What other sequences can we make if we switch up the first terms? We will explore these sequences and how to construct numbers from them. Extensions of these topics will get into more complicated recursions and the Chicken McNugget Theorem.

Discovery Learning: Advanced Group (3.30 - 5.00 PM) (in Algebra II or above)

Speaker: Alexander Riedel

Title: Fibonacci Sequences, Recursions, and the Chicken McNugget Theorem

Abstract: What is the Fibonacci sequence? What can we figure out about its terms? What other sequences can we make if we switch up the first terms? We will explore these sequences and how to construct numbers from them. Extensions of these topics will get into more complicated recursions and the Chicken McNugget Theorem.

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Dr. Irina Bobkova (Texas A&M), Dr. Guangbo Xu (Texas A&M) Dr. Peyam Tabrizian (Texas A&M)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Dr. Jinmin Wang (Texas A&M), Dr. Rodrigo Matos (Texas A&M), and Xiaoyu Su (Texas A&M)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Andrew Yu, Dr. Sherry Gong and Dr. Zhizhang Xie (Texas A&M)

Feb. 12, 2022

Discovery Learning: Beginner Group (12.00 - 1.30 PM) (Pre-Algebra and below)

Speaker: Nick Treuer

Title: River Crossings

Abstract: We will begin with the classic game of bringing a goat, wolf, and cabbage all safely in a small boat to the opposite side of a river.  We will then consider variations of the game by adding Zombies and Monsters.  We will vary the size of our boat that transports our passengers and use this activity to discuss prime numbers.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM) (in Algebra I or above)

Speaker: Nick Treuer

Title: River Crossings

Abstract: We will begin with the classic game of bringing a goat, wolf, and cabbage all safely in a small boat to the opposite side of a river.  We will then consider variations of the game by adding Zombies and Monsters.  We will vary the size of our boat that transports our passengers and use this activity to discuss prime numbers.

Discovery Learning: Advanced Group (3.30 - 5.00 PM) (in Algebra II or above)

Speaker: Nick Treuer

Title: River Crossings

Abstract: We will begin with the classic game of bringing a goat, wolf, and cabbage all safely in a small boat to the opposite side of a river.  We will then consider variations of the game by adding Zombies and Monsters.  We will vary the size of our boat that transports our passengers and use this activity to discuss prime numbers.

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Dr. Irina Bobkova (Texas A&M), Dr. Guangbo Xu (Texas A&M) Dr. Peyam Tabrizian (Texas A&M)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Dr. Jinmin Wang (Texas A&M), Dr. Rodrigo Matos (Texas A&M), and Xiaoyu Su (Texas A&M)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Andrew Yu, Dr. Sherry Gong and Dr. Zhizhang Xie (Texas A&M)

Feb. 5, 2022

Discovery Learning: Beginner Group (12.00 - 1.30 PM) (Pre-Algebra and below)

Speaker: Dr. Phil Yasskin (TAMU)

Title: Painting Cubes

Abstract: We paint a 3x3x3 cube. Then we cut it into 1x1x1 cubes. How are the small cubes colored?

Discovery Learning: Intermediate Group (1.45 - 3.15 PM) (in Algebra I or above)

Speaker: Dr. Phil Yasskin (TAMU)

Title: Painting Cubes

Abstract: We paint a 3x3x3 cube. Then we cut it into 1x1x1 cubes. How are the small cubes colored?

Discovery Learning: Advanced Group (3.30 - 5.00 PM) (in Algebra II or above)

Speaker: Dr. Phil Yasskin (TAMU)

Title: Painting Cubes

Abstract: We paint a 3x3x3 cube. Then we cut it into 1x1x1 cubes. How are the small cubes colored?

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Dr. Irina Bobkova (Texas A&M), Dr. Guangbo Xu (Texas A&M) Dr. Peyam Tabrizian (Texas A&M)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Dr. Jinmin Wang (Texas A&M), Dr. Rodrigo Matos (Texas A&M), and Xiaoyu Su (Texas A&M)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Andrew Yu, Dr. Sherry Gong and Dr. Zhizhang Xie (Texas A&M)

Nov. 20, 2021

Discovery Learning: Beginner Group (12.00 - 1.30 PM) (Pre-Algebra and below)

Speaker: Erika Gonzalez Brizuela (Texas A&M)

Title: Switching Lightbulbs

Abstract: We will be exploring factorization patterns through a game where all of the lightbulbs are turned off, and when a person walks down the hallway, they pull the string of certain lights to turn them on based on the number on their shirt. We will predict and prove solutions to scenarios with a small fixed number of lightbulbs and look into patterns to solve larger quantities.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM) (in Algebra I or above)

Speaker: Erika Gonzalez Brizuela (Texas A&M)

Title: Switching Lightbulbs

Abstract: We will be exploring factorization patterns through a game where all of the lightbulbs are turned off, and when a person walks down the hallway, they pull the string of certain lights to turn them on based on the number on their shirt. We will predict and prove solutions to scenarios with a small fixed number of lightbulbs and look into patterns to solve larger quantities.

Discovery Learning: Advanced Group (3.30 - 5.00 PM) (in Algebra II or above)

Speaker: Matthew Atanas (Texas A&M)

Title: Euclidean Motions in the Plane (Part III)

Abstract: We will continue to explore and do proofs regarding Euclidean Motions in R^2.

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Dr. Irina Bobkova (Texas A&M), Dr. Guangbo Xu (Texas A&M) Dr. Peyam Tabrizian (Texas A&M)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Dr. Jinmin Wang (Texas A&M), Dr. Rodrigo Matos (Texas A&M), and Xiaoyu Su (Texas A&M)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Andrew Yu, Dr. Sherry Gong and Dr. Zhizhang Xie (Texas A&M)

Nov. 6, 2021

Discovery Learning: Beginner Group (12.00 - 1.30 PM) (Pre-Algebra and below)

Speaker: Priyanga Ganesan (Texas A&M)

Title: Wolves and Sheep

Abstract: We will be playing a combinatorial game on an nxn square involving wolves and sheeps. The wolves can eat any sheep that they see horizontally, vertically or diagonally. Our goal is to arrange them on the square in a way that all sheep are safe from the wolves. We will explore winning strategies for the game and learn some cool counting techniques along the way.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM) (in Algebra I or above)

Speaker: Dr. JD Kim (Texas A&M)

Title: Human vs. Computer or Human with Computer

Abstract: In this talk we will discuss the limits of humans and the limits of computers, and the power we will see when humans use computers wisely and powerfully.

Discovery Learning: Advanced Group (3.30 - 5.00 PM) (in Algebra II or above)

Speaker: Dr. Sherry Gong (Texas A&M)

Title: TBA

Abstract: TBA

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Dr. Irina Bobkova (Texas A&M), Dr. Guangbo Xu (Texas A&M) Dr. Peyam Tabrizian (Texas A&M)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Dr. Jinmin Wang (Texas A&M), Dr. Rodrigo Matos (Texas A&M), and Xiaoyu Su (Texas A&M)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Andrew Yu, Dr. Sherry Gong and Dr. Zhizhang Xie (Texas A&M)

Oct. 23, 2021

Discovery Learning: Beginner Group (12.00 - 1.30 PM) (Pre-Algebra and below)

Speaker: Logan Knudsen (Texas A&M)

Title: Minesweeper Investigation

Abstract: Students will investigate the computer game Minesweeper in a competition to see who are the best players, as well as work to identify any patterns they see as they play. Students will learn if Minesweeper is a game of logic or just chance by the end of the activity.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM) (in Algebra I or above)

Speaker: Logan Knudsen (Texas A&M)

Title: Minesweeper Investigation

Abstract: Students will investigate the computer game Minesweeper in a competition to see who are the best players, as well as work to identify any patterns they see as they play. Students will learn if Minesweeper is a game of logic or just chance by the end of the activity.

Discovery Learning: Advanced Group (3.30 - 5.00 PM) (in Algebra II or above)

Speaker: Logan Knudsen (Texas A&M)

Title: Minesweeper Investigation

Abstract: Students will investigate the computer game Minesweeper in a competition to see who are the best players, as well as work to identify any patterns they see as they play. Students will learn if Minesweeper is a game of logic or just chance by the end of the activity.

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Dr. Irina Bobkova (Texas A&M), Dr. Guangbo Xu (Texas A&M) Dr. Peyam Tabrizian (Texas A&M)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Dr. Jinmin Wang (Texas A&M), Dr. Rodrigo Matos (Texas A&M), and Xiaoyu Su (Texas A&M)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Andrew Yu, Dr. Sherry Gong and Dr. Zhizhang Xie (Texas A&M)

Oct. 9, 2021

Discovery Learning: Beginner Group (12.00 - 1.30 PM) (Pre-Algebra and below)

Speaker: Dr. Shoo Seto (CSUF)

Title: The Möbius Strip

Abstract: We will be learning about the Möbius strip and what it means to have a surface with only one side. Some paper, scissors and tape will help but is not strictly necessary.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM) (in Algebra I or above)

Speaker: Sheagan John (Texas A&M)

Title: Tiling Grids

Abstract: We will investigate the possibility of coloring an n x n  grid with three distinct colors given that there exists no chain of same-colored adjacent blocks with length k. Whether such a task is possible will be shown to depend both on the grid size and the value of k.

Discovery Learning: Advanced Group (3.30 - 5.00 PM) (in Algebra II or above)

Speaker: Sheagan John (Texas A&M)

Title: Tiling Grids

Abstract: We will investigate the possibility of coloring an n x n  grid with three distinct colors given that there exists no chain of same-colored adjacent blocks with length k. Whether such a task is possible will be shown to depend both on the grid size and the value of k.

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Dr. Irina Bobkova (Texas A&M), Dr. Guangbo Xu (Texas A&M) Dr. Peyam Tabrizian (Texas A&M)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Dr. Jinmin Wang (Texas A&M), Dr. Rodrigo Matos (Texas A&M), and Xiaoyu Su (Texas A&M)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Andrew Yu, Dr. Sherry Gong and Dr. Zhizhang Xie (Texas A&M)

Oct. 2, 2021

Discovery Learning: Beginner Group (12.00 - 1.30 PM) (Pre-Algebra and below)

Speaker: Cristian Andrei (Texas A&M)

Title: Towers of Hanoi

Abstract: The Tower of Hanoi was invented in 1883. It consists of three rods and a number of disks of different sizes, which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod with the smallest disk at the top. The objective of the puzzle is to move the entire stack to another rod, obeying the following rules: (1) Only one disk can be moved at a time; (2) Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod; (3) No larger disk may be placed on top of a smaller disk. We will discuss the most efficient solution to the game and, time permitting, a more general version and its solution.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM) (in Algebra I or above)

Speaker: Cristian Andrei (Texas A&M)

Title: Towers of Hanoi

Abstract: The Tower of Hanoi was invented in 1883. It consists of three rods and a number of disks of different sizes, which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod with the smallest disk at the top. The objective of the puzzle is to move the entire stack to another rod, obeying the following rules: (1) Only one disk can be moved at a time; (2) Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod; (3) No larger disk may be placed on top of a smaller disk. We will discuss the most efficient solution to the game and, time permitting, a more general version and its solution.

Discovery Learning: Advanced Group (3.30 - 5.00 PM) (in Algebra II or above)

Speaker: Matthew Atanas (Texas A&M)

Title: Euclidean Motions in the Plane

Abstract: We will explore and do proofs regarding Euclidean Motions in R^2.

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Dr. Irina Bobkova (Texas A&M), Dr. Guangbo Xu (Texas A&M) Dr. Peyam Tabrizian (Texas A&M)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Dr. Jinmin Wang (Texas A&M), Dr. Rodrigo Matos (Texas A&M), and Xiaoyu Su (Texas A&M)

Sept. 25, 2021

Discovery Learning: Beginner Group (12.00 - 1.30 PM) (Pre-Algebra and below)

Speaker: Jonathan Aberle (Texas A&M)

Title: Juice Jumble

Abstract: We will be studying a game where you move around glasses of juice to sort them by color. We'll start by looking for a strategy to win, then move on to variations on the game and looking for formulas for the fastest solution.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM) (in Algebra I or above)

Speaker: Jonathan Aberle (Texas A&M)

Title: Juice Jumble

Abstract: We will be studying a game where you move around glasses of juice to sort them by color. We'll start by looking for a strategy to win, then move on to variations on the game and looking for formulas for the fastest solution.

Discovery Learning: Advanced Group (3.30 - 5.00 PM) (in Algebra II or above)

Speaker: Jonathan Aberle (Texas A&M)

Title: Juice Jumble

Abstract: We will be studying a game where you move around glasses of juice to sort them by color. We'll start by looking for a strategy to win, then move on to variations on the game and looking for formulas for the fastest solution.

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Dr. Irina Bobkova (Texas A&M), Dr. Guangbo Xu (Texas A&M) Dr. Peyam Tabrizian (Texas A&M)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Dr. Jinmin Wang (Texas A&M), Dr. Rodrigo Matos (Texas A&M), and Xiaoyu Su (Texas A&M)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Andrew Yu, Dr. Sherry Gong and Dr. Zhizhang Xie (Texas A&M)

Sept. 18, 2021

Discovery Learning: Beginner Group (12.00 - 1.30 PM) (Pre-Algebra and below)

Speaker: Dr. John Treuer (Texas A&M)

Title: Prime Cubes

Abstract: Can you place the numbers 1 through 8 on the vertices of a cube so that adjacent vertices sum to a prime number? We will be exploring this and other fun related questions this weekend!

Discovery Learning: Intermediate Group (1.45 - 3.15 PM) (in Algebra I or above)

Speaker: Dr. John Treuer (Texas A&M)

Title: Prime Cubes

Abstract: Can you place the numbers 1 through 8 on the vertices of a cube so that adjacent vertices sum to a prime number? We will be exploring this and other fun related questions this weekend!

Discovery Learning: Advanced Group (3.30 - 5.00 PM) (in Algebra II or above)

Speaker: Dr. John Treuer (Texas A&M)

Title: Prime Cubes

Abstract: Can you place the numbers 1 through 8 on the vertices of a cube so that adjacent vertices sum to a prime number? We will be exploring this and other fun related questions this weekend!

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Dr. Irina Bobkova (Texas A&M), Dr. Guangbo Xu (Texas A&M) Dr. Peyam Tabrizian (Texas A&M)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Dr. Jinmin Wang (Texas A&M), Dr. Rodrigo Matos (Texas A&M), and Xiaoyu Su (Texas A&M)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Andrew Yu, Dr. Sherry Gong and Dr. Zhizhang Xie (Texas A&M)

Sept. 11, 2021

Discovery Learning: Beginner Group (12.00 - 1.30 PM) (Pre-Algebra and below)

Speaker: Dr. Phil Yasskin (Texas A&M)

Title: Diagonals

Abstract: We will count the number of diagonals in a rectangular grid with certain restrictions on which diagonals to count.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM) (in Algebra I or above)

Speaker: Dr. Phil Yasskin (Texas A&M)

Title: Diagonals

Abstract: We will count the number of diagonals in a rectangular grid with certain restrictions on which diagonals to count.

Discovery Learning: Advanced Group (3.30 - 5.00 PM) (in Algebra II or above)

Speaker: Dr. Phil Yasskin (Texas A&M)

Title: Diagonals

Abstract: We will count the number of diagonals in a rectangular grid with certain restrictions on which diagonals to count.

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Dr. Irina Bobkova (Texas A&M), Dr. Guangbo Xu (Texas A&M) Dr. Peyam Tabrizian (Texas A&M)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Dr. Jinmin Wang (Texas A&M), Dr. Rodrigo Matos (Texas A&M), and Xiaoyu Su (Texas A&M)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Andrew Yu, Dr. Sherry Gong and Dr. Zhizhang Xie (Texas A&M)

May 15, 2021

Discovery Learning: Beginner Group (12.00 - 1.30 PM)

Speaker: Joshua Goldstein (TAMU)

Title: Penguin Island

Abstract: In this activity we will discuss Bayes’ Theorem and some more interesting questions from probability. No prior knowledge of probability or Bayes’ Theorem is assumed.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM)

Speaker: Joshua Goldstein (TAMU)

Title: Penguin Island

Abstract: In this activity we will discuss Bayes’ Theorem and some more interesting questions from probability. No prior knowledge of probability or Bayes’ Theorem is assumed.

Discovery Learning: Advanced Group (3.30 - 5.00 PM)

Speaker: Joshua Goldstein (TAMU)

Title: Penguin Island Returns (Bayesian Version)

Abstract: In this activity we will discuss Bayes’ Theorem and some more interesting questions from probability. No prior knowledge of probability or Bayes’ Theorem is assumed.

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Drs. Irina Bobkova and Guangbo Xu (Texas A&M University)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Xiaoyu Su & Drs. Li Gao, Hao Guo (Texas A&M University)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Drs. Zhizhang Xie, Rodrigo Matos, Andrew Yu (Texas A&M University)

May 8, 2021

Discovery Learning: Beginner Group (12.00 - 1.30 PM)

Speaker: Logan Knudsen (TAMU)

Title: Arranging Skyscrapers

Abstract: We will help the City Planner to arrange skyscrapers so that certain rules and condition set out by the City Council are met.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM)

Speaker: Dr. Phil Yasskin (TAMU)

Title: Counting Diagonals

Abstract: We will try to count how many diagonals can fit in a n x n square grid so that no two touch.

Discovery Learning: Advanced Group (3.30 - 5.00 PM)

Speaker: Dr. Phil Yasskin (TAMU)

Title: Counting Diagonals

Abstract: We will try to count how many diagonals can fit in a n x n square grid so that no two touch.

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Drs. Irina Bobkova and Guangbo Xu (Texas A&M University)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Xiaoyu Su & Drs. Li Gao, Hao Guo (Texas A&M University)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Drs. Zhizhang Xie, Rodrigo Matos, Andrew Yu (Texas A&M University)

April 24, 2021

Discovery Learning: Beginner Group (12.00 - 1.30 PM)

Speaker: Prof. Lauren Rose (Bard College)

Title: Quads, a SET-like game with a twist

Abstract: We will learn how to play Quads and then explore some of the math behind it.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM)

Speaker: Prof. Lauren Rose (Bard College)

Title: Quads, a SET-like game with a twist

Abstract: We will learn how to play Quads and then explore some of the math behind it.

Discovery Learning: Advanced Group (3.30 - 5.00 PM)

Speaker: Prof. Lauren Rose (Bard College)

Title: Quads, a SET-like game with a twist

Abstract: We will learn how to play Quads and then explore some of the math behind it.

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Drs. Irina Bobkova and Guangbo Xu (Texas A&M University)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Xiaoyu Su & Drs. Li Gao, Hao Guo (Texas A&M University)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Drs. Zhizhang Xie, Rodrigo Matos, Andrew Yu (Texas A&M University)

April 17, 2021

Discovery Learning: Beginner Group (12.00 - 1.30 PM)

Speaker: David Manuel (TAMU)

Title: Pigeonhole Problems

Abstract: In this activity, we will learn what the Pigeonhole Principle is and use it to solve problems of varying levels of difficulty.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM)

Speaker: David Manuel (TAMU)

Title: Pigeonhole Problems

Abstract: In this activity, we will learn what the Pigeonhole Principle is and use it to solve problems of varying levels of difficulty.

Discovery Learning: Advanced Group (3.30 - 5.00 PM)

Speaker: David Manuel (TAMU)

Title: Pigeonhole Problems

Abstract: In this activity, we will learn what the Pigeonhole Principle is and use it to solve problems of varying levels of difficulty.

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Drs. Irina Bobkova and Guangbo Xu (Texas A&M University)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Xiaoyu Su & Drs. Li Gao, Hao Guo (Texas A&M University)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Drs. Zhizhang Xie, Rodrigo Matos, Andrew Yu (Texas A&M University)

March 13, 2021

Discovery Learning: Beginner Group (12.00 - 1.30 PM)

Speaker: William Frendreiss (TAMU)

Title: Exploring Radians

Abstract: We will be learning how to use radians and explore the connection between the definition of pi and our usage of radians. Students will learn how to use radians and why they are so important. 

Discovery Learning: Intermediate Group (1.45 - 3.15 PM)

Speaker: Dr. Erika Ordog (TAMU)

Title: Pick's Theorem

Abstract: Draw a polygon whose vertices are on lattice points of a grid. Can you come up with a formula that gives the area of the polygon in terms of the number of lattice points in the interior of the polygon and the number of lattice points along the perimeter?

Discovery Learning: Advanced Group (3.30 - 5.00 PM)

Speaker: Jonathan Aberle (TAMU)

Title: Polyominoes on Chess Boards

Abstract: Can you cover a chessboard with dominos? What if two of the corners are snapped off? We will look at different grid shapes and try to cover them with different shaped tiles. Some tile shapes work, and others do not. We will try to find what makes a shape work as a grid tile.

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Drs. Irina Bobkova and Guangbo Xu (Texas A&M University)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Xiaoyu Su & Drs. Li Gao, Hao Guo (Texas A&M University)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Drs. Zhizhang Xie, Rodrigo Matos, Andrew Yu (Texas A&M University)

March 6, 2021

Discovery Learning: Beginner Group (12.00 - 1.30 PM)

Speaker: Dr. Erika Ordog (TAMU)

Title: Pick's Theorem

Abstract: Draw a polygon whose vertices are on lattice points of a grid. Can you come up with a formula that gives the area of the polygon in terms of the number of lattice points in the interior of the polygon and the number of lattice points along the perimeter?

Discovery Learning: Intermediate Group (1.45 - 3.15 PM)

Speaker: Jonathan Aberle (TAMU)

Title: Polyominoes on Chess Boards

Abstract: Can you cover a chessboard with dominos? What if two of the corners are snapped off? We will look at different grid shapes and try to cover them with different shaped tiles. Some tile shapes work, and others do not. We will try to find what makes a shape work as a grid tile.

Discovery Learning: Advanced Group (3.30 - 5.00 PM)

Speaker: Matthew Atanas (TAMU)

Title: Penguin Island

Abstract: Penguins and humans are engaged in a fierce competition on a remote island. In this activity we will seek the optimal strategy to maximize the population of penguins on our island. In the process we will discuss several concepts from probability and learn about games of chance.

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Drs. Irina Bobkova and Guangbo Xu (Texas A&M University)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Xiaoyu Su & Drs. Li Gao, Hao Guo (Texas A&M University)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Drs. Zhizhang Xie, Rodrigo Matos, Andrew Yu (Texas A&M University)

February 13, 2021

Discovery Learning: Beginner Group (12.00 - 1.30 PM)

Speaker: Matthew Atanas (TAMU)

Title: Hex (the Board Game)

Abstract: Hex is a game where two competing players try to connect their two sides together while preventing their opponent from doing the same.  In this session, we will examine this game in more depth.  Does one side always necessarily win, or is it possible to draw?  If one side does always win, does it depend on the board size?  What is the winning strategy?

Discovery Learning: Intermediate Group (1.45 - 3.15 PM)

Speaker: Dr. Phil Yasskin (TAMU)

Title: King Arthur's Round Table

Abstract: King Arthur is selecting a Knight from around his round table to marry his daughter.

There is a process of elimination and the winner is the one who can find a formula for the process.

Discovery Learning: Advanced Group (3.30 - 5.00 PM)

Speaker: Logan Knudsen (TAMU)

Title: Pool Testing Technique

Abstract: The Lab you work at testing for a virus employs the Pool Testing Technique, and they have placed you in charge of organizing their tests to be more efficient and better fit time constraints while still finding the infected individuals. We will develop some mathematical techniques to help solve this problem.

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Drs. Irina Bobkova and Guangbo Xu (Texas A&M University)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Xiaoyu Su & Drs. Li Gao, Hao Guo (Texas A&M University)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Drs. Zhizhang Xie, Rodrigo Matos, Andrew Yu (Texas A&M University)

February 6, 2021

Discovery Learning: Beginner Group (12.00 - 1.30 PM)

Speaker: Dr. Phil Yasskin (TAMU)

Title: King Arthur's Round Table

Abstract: King Arthur is selecting a Knight from around his round table to marry his daughter.

There is a process of elimination and the winner is the one who can find a formula for the process.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM)

Speaker: Logan Knudsen (TAMU)

Title: Pool Testing Technique

Abstract: The Lab you work at testing for a virus employs the Pool Testing Technique, and they have placed you in charge of organizing their tests to be more efficient and better fit time constraints while still finding the infected individuals. We will develop some mathematical techniques to help solve this problem.

Discovery Learning: Advanced Group (3.30 - 5.00 PM)

Speaker: Matthew Atanas (TAMU)

Title: Hex (the Board Game)

Abstract: Hex is a game where two competing players try to connect their two sides together while preventing their opponent from doing the same.  In this session, we will examine this game in more depth.  Does one side always necessarily win, or is it possible to draw?  If one side does always win, does it depend on the board size?  What is the winning strategy?

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Drs. Irina Bobkova and Guangbo Xu (Texas A&M University)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Xiaoyu Su & Drs. Li Gao, Hao Guo (Texas A&M University)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Drs. Zhizhang Xie, Rodrigo Matos, Andrew Yu (Texas A&M University)

January 30, 2021

Discovery Learning: Beginner Group (12.00 - 1.30 PM)

Speaker: Logan Knudsen (TAMU)

Title: Pool Testing Technique

Abstract: The Lab you work at testing for a virus employs the Pool Testing Technique, and they have placed you in charge of organizing their tests to be more efficient and better fit time constraints while still finding the infected individuals. We will develop some mathematical techniques to help solve this problem.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM)

Speaker: William Frendreiss (TAMU)

Title: Gerrymandering: How to Win Elections the Sneaky Way

Abstract: Every ten years, local and state officials are allowed to change the boundaries of voting districts to account for changes in population. But a widespread technique called "gerrymandering" involves strategically drawing these boundaries so that members of the ruling party can be re-elected, even if most of the voters in their region vote against them. We'll explore how gerrymandering works, draw our own voting district maps, and investigate mathematical techniques for choosing drawing districts that are fair for everyone.

Discovery Learning: Advanced Group (3.30 - 5.00 PM)

Speaker: Dr. Phil Yasskin (TAMU)

Title: King Arthur's Round Table

Abstract: King Arthur is selecting a Knight from around his round table to marry his daughter.

There is a process of elimination and the winner is the one who can find a formula for the process.

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Drs. Irina Bobkova and Guangbo Xu (Texas A&M University)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Xiaoyu Su & Drs. Li Gao, Hao Guo (Texas A&M University)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Drs. Zhizhang Xie, Rodrigo Matos, Andrew Yu (Texas A&M University)

December 12, 2020

Discovery Learning: Beginner Group (12.00 - 1.30 PM)

Speaker: Dr. Maya Johnson (TAMU)

Title: Lady Bugs

Abstract: How many lady bugs can you save? This activity involves helping lady buys safely land on leaves. There are two leaves and lady bugs with an integer number of dots on their backs. You must place the lady bugs on each leaf in consecutive order starting from number one. If you place a lady bug on a leaf where the sum of the dots on the backs of any two existing lady bugs equals the number of dots on that lady bug’s back, then all the lady bugs will fly off the leaf. If you reach a point where any move you make would cause the lady bugs on both leaves to fly off, then the game is over and you have to start again. The question is: how many lady bugs can you get onto the leaves without them all flying away? We will explore what’s the best strategy for placing the lady bugs to get the most lady bugs to safety as possible with consecutive numbers first and then see what happens if we switch to even numbers, odd numbers, primes, and other different cases. Come join us for some buggy fun with numbers!

Discovery Learning: Intermediate Group (1.45 - 3.15 PM)

Speaker: Matthew Atanas (TAMU)

Title: "What's for Dinner?" - An Examination of Different Voting Systems

Abstract: In this activity we will explore several different voting systems and evaluate the benefits and detriments of each. We will conclude with a surprising result on the possibility of "fair" voting systems.

Discovery Learning: Advanced Group (3.30 - 5.00 PM)

Speaker: Alexander Riedel (TAMU)

Title: Power of a Point and Radical Axis: Proving a theorem relating the chords in circles with high school geometry

Abstract: We will first examine the intersection of chords in circles and prove a theorem using high school geometry techniques. Then we will define the Power of a point and the Radical Axis of two circles. We will proceed to find what the radical axis is for two circles and prove some useful facts about it.

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Drs. Irina Bobkova and Guangbo Xu (Texas A&M University)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Xiaoyu Su & Drs. Li Gao, Hao Guo (Texas A&M University)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Drs. Zhizhang Xie, Rodrigo Matos, Andrew Yu (Texas A&M University)

December 5, 2020

Discovery Learning: Beginner Group (12.00 - 1.30 PM)

Speaker: Dr. Ed Keppelmann (University of Nevada-Reno)

Title: Dice Games of Elimination

Abstract: The classic game of Shut The Box involves rolling two die repeatedly in an attempt to obtain and thereby eliminate (thus never to be used again) each number from 1 to 12. Usually this is a one person solitare type game and so after playing and discovering some basic strategy we will introduce a multiplayer competitive version and see how things change. We will then repeat this exercise for a geometric version of shut the box which can be played on a grid in the plane. What happens here and what variations do you suggest for even more suspense, strategic planning and fun?

Playing grids and random dice will all be available on line but ordinary dice and graph paper are great for playing some more offline after the circle.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM)

Speaker: Dr. Ed Keppelmann (University of Nevada-Reno)

Title: Dice Games of Elimination

Abstract: The classic game of Shut The Box involves rolling two die repeatedly in an attempt to obtain and thereby eliminate (thus never to be used again) each number from 1 to 12. Usually this is a one person solitare type game and so after playing and discovering some basic strategy we will introduce a multiplayer competitive version and see how things change. We will then repeat this exercise for a geometric version of shut the box which can be played on a grid in the plane. What happens here and what variations do you suggest for even more suspense, strategic planning and fun?

Playing grids and random dice will all be available on line but ordinary dice and graph paper are great for playing some more offline after the circle.

Discovery Learning: Advanced Group (3.30 - 5.00 PM)

Speaker: Dr. Ed Keppelmann (University of Nevada-Reno)

Title: Dice Games of Elimination

Abstract: The classic game of Shut The Box involves rolling two die repeatedly in an attempt to obtain and thereby eliminate (thus never to be used again) each number from 1 to 12. Usually this is a one person solitare type game and so after playing and discovering some basic strategy we will introduce a multiplayer competitive version and see how things change. We will then repeat this exercise for a geometric version of shut the box which can be played on a grid in the plane. What happens here and what variations do you suggest for even more suspense, strategic planning and fun?

Playing grids and random dice will all be available on line but ordinary dice and graph paper are great for playing some more offline after the circle.

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Drs. Irina Bobkova and Guangbo Xu (Texas A&M University)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Xiaoyu Su & Drs. Li Gao, Hao Guo (Texas A&M University)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Drs. Zhizhang Xie, Rodrigo Matos, Andrew Yu (Texas A&M University)

November 21, 2020

Discovery Learning: Beginner Group (12.00 - 1.30 PM)

Speaker: Logan Knudsen (TAMU)

Title: Wolves and Sheep: Solving and Generalizing

Abstract: We will explore puzzle problems relating to the Wolves and Sheep Puzzle, consisting of arranging wolves and sheep in patterns that protect the sheep. We will also explore ways to maximize or minimize the area covered by the wolves.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM)

Speaker: Dr. Phil Yasskin (TAMU)

Title: Counting Diagonals

Abstract: We will count the number of diagonals in an n x n grid that do not touch each other. 

Discovery Learning: Advanced Group (3.30 - 5.00 PM)

Speaker: William Frendreiss (TAMU)

Title: Deriving Pi using Limits and Geometry

Abstract: We will be using two methods to approximate pi from both above and below, by increasing the number of sides on arbitrary inscribed and circumscribed polygons. We will be using Excel to visually see how the area of these polygons approaches pi, the circle constant, from above and below. Advanced topics such as limits will be touched on, but not rigorously discussed.

November 14, 2020

Discovery Learning: Beginner Group (12.00 - 1.30 PM)

Speaker: William Frendreiss (TAMU)

Title: Counting Chameleons

Abstract: We will be going over several problems related to the color-changing properties of virtual chameleons. We begin with a set of chameleons that can change colors with another chameleon. Our goal in each problem is to make it so that all the chameleons end up being the same color. In our simulation, we will explore how odd and even numbers in the initial conditions affect our answer, and cases where there may not be an answer.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM)

Speaker: Dr. Erika Ordog (TAMU)

Title: Generalizations of Bridges of Koenigsberg

Abstract: The city of Koenigsberg is made up of islands connected to each other by bridges. Is it possible to walk across all of the bridges once and only once, ending up where you started? We will see if this is possible in Koenigsberg and solve other related and more general problems.

Discovery Learning: Advanced Group (3.30 - 5.00 PM)

Speaker: Dr. Phil Yasskin (TAMU)

Title: The a+b+ab Problem

Abstract: Write down the numbers from 1 to 100. Randomly select 2 numbers from the list, say a and b, and cross them off, but add to the list the number a+b+ab. You now have 99 numbers. Repeat this process until you have only 1 number left. What are all possible final numbers?

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Drs. Irina Bobkova and Guangbo Xu (Texas A&M University)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Xiaoyu Su & Drs. Li Gao, Hao Guo (Texas A&M University)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Drs. Zhizhang Xie, Rodrigo Matos, Andrew Yu (Texas A&M University)

November 7, 2020

Discovery Learning: Beginner Group (12.00 - 1.30 PM)

Speaker: Erika Ordog (TAMU)

Title: Bridges of Koenigsberg

Abstract: The city of Koenigsberg is made up of islands connected to each other by bridges. Is it possible to walk across all of the bridges once and only once, ending up where you started? We will see if this is possible in Koenigsberg and in other cities and will solve other related problems.

Discovery Learning: Intermediate Group (1.45 - 3.15 PM)

Speaker: William Frendreiss (TAMU)

Title: Counting Chameleons

Abstract: We will be going over several problems related to the color-changing properties of virtual chameleons. We begin with a set of chameleons that can change colors with another chameleon. Our goal in each problem is to make it so that all the chameleons end up being the same color. In our simulation, we will explore how odd and even numbers in the initial conditions affect our answer, and cases where there may not be an answer.

Discovery Learning: Advanced Group (3.30 - 5.00 PM)

Speaker: Dr. Joung Dong "JD" Kim (TAMU)

Title: From Algebra to Computational Fluid Dynamics

Abstract: In this talk we will discuss the slope of a line (in algebra) and how we can use it for numerical PDE problems (Computational Fluid Dynamics). As an application, I will demonstrate coding for simple PDE problems and introduce the Front Tracking method for Parachute model.

October 31, 2020

Discovery Learning: ALL SECTIONS

Speaker: -

Title: -

Abstract: Discovery Learning is cancelled this week due to Buzz Contest, which will be hosted on Discord by Prof. Josh Dever (UT Austin). Problem Solving will run as normal. If you are interested in participating, please register here. The contest will start at 1.45 (Central Time).

Problem-Solving: Beginner Group (1.45 - 3.15 PM)

Instructor: Drs. Irina Bobkova and Guangbo Xu (Texas A&M University)

Problem-Solving: Intermediate Group (3.30 - 5.00 PM)

Instructor: Xiaoyu Su & Drs. Li Gao, Hao Guo (Texas A&M University)

Problem-Solving: Advanced Group (12.00 - 1.30 PM)

Instructors: Drs. Zhizhang Xie, Rodrigo Matos, Andrew Yu (Texas A&M University)

October 24, 2020

Beginner Group (in Pre-Algebra and below)

Speaker: Dr. Doug Hensley (TAMU)

Title: Buzz Contest Training

Abstract: Dr. Doug Hensley will explain what is a Buzz Contest and train our students for next week's (Oct. 31) Buzz Contest that will be held in association with the Math Circle at UT Austin.

Intermediate Group (in Algebra 1 or above)

Speaker: Dr. Doug Hensley (TAMU)

Title: Buzz Contest Training

Abstract: Dr. Doug Hensley will explain what is a Buzz Contest and train our students for next week's (Oct. 31) Buzz Contest that will be held in association with the Math Circle at UT Austin.

Advanced Group (in Algebra 2 or above)

Speaker: Dr. Doug Hensley (TAMU)

Title: Buzz Contest Training

Abstract: Dr. Doug Hensley will explain what is a Buzz Contest and train our students for next week's (Oct. 31) Buzz Contest that will be held in association with the Math Circle at UT Austin.

Problem-Solving: Beginner Group

Instructor: Drs. Irina Bobkova and Guangbo Xu (Texas A&M University)

Problem-Solving: Intermediate Group

Instructor: Xiaoyu Su & Drs. Li Gao, Hao Guo (Texas A&M University)

Problem-Solving: Advanced Group

Instructors: Drs. Zhizhang Xie, Rodrigo Matos, Andrew Yu (Texas A&M University)

October 17, 2020

Beginner Group (in Pre-Algebra and below)

Speaker: Pablo S. Ocal (Texas A&M)

Title: Hat Problems

Abstract: You and your friends are put into a room with hats in your heads. You cannot see your own hat, but you can see your friend's. Can you find a way of guessing our own hat? Can you find a way of everybody guessing their own hat? How about if you're not allowed to communicate? We will be discussing these and other hat problems.

Intermediate Group (in Algebra 1 or above)

Speaker: Pablo S. Ocal (Texas A&M)

Title: Hat Problems

Abstract: You and your friends are put into a room with hats in your heads. You cannot see your own hat, but you can see your friend's. Can you find a way of guessing our own hat? Can you find a way of everybody guessing their own hat? How about if you're not allowed to communicate? We will be discussing these and other hat problems.

Advanced Group (in Algebra 2 or above)

Speaker: Pablo S. Ocal (Texas A&M)

Title: Hat Problems

Abstract: You and your friends are put into a room with hats in your heads. You cannot see your own hat, but you can see your friend's. Can you find a way of guessing our own hat? Can you find a way of everybody guessing their own hat? How about if you're not allowed to communicate? We will be discussing these and other hat problems.

Problem-Solving: Beginner Group

Instructor: Drs. Irina Bobkova and Guangbo Xu (Texas A&M University)

Problem-Solving: Intermediate Group

Instructor: Xiaoyu Su & Drs. Li Gao, Hao Guo (Texas A&M University)

Problem-Solving: Advanced Group

Instructors: Drs. Guoliang Yu, Zhizhang Xie, Rodrigo Matos, Andrew Yu (Texas A&M University)

October 10, 2020

Beginner Group (in Pre-Algebra and below)

Speaker: Dr. Rodrigo Matos (Texas A&M)

Title: The Odd Subtraction Game

Abstract: We continue playing the Subtraction Game but change the goal to be the person who takes an odd number of chips.

Intermediate Group (in Algebra 1 or above)

Speaker: Dr. Phil Yasskin (Texas A&M)

Title: Polygon Differencing

Abstract: Put 4 non-negative integers on the corners of a square. Put their differences at the midpoint of each side. Connect the midpoints producing a new square. Repeat the process until you discover something. What do you conjecture? Prove it. Repeat for a triangle, a pentagon, an N-gon. What do you conjecture? Prove it.

Advanced Group (in Algebra 2 or above)

Speaker: Dr. Phil Yasskin (Texas A&M)

Title: Polygon Differencing

Abstract: Put 4 non-negative integers on the corners of a square. Put their differences at the midpoint of each side. Connect the midpoints producing a new square. Repeat the process until you discover something. What do you conjecture? Prove it. Repeat for a triangle, a pentagon, an N-gon. What do you conjecture? Prove it.

Problem-Solving: Beginner Group

Instructor: Drs. Irina Bobkova and Guangbo Xu (Texas A&M University)

Problem-Solving: Intermediate Group

Instructor: Xiaoyu Su & Drs. Li Gao, Hao Guo (Texas A&M University)

Problem-Solving: Advanced Group

Instructors: Drs. Guoliang Yu, Zhizhang Xie, Rodrigo Matos, Andrew Yu (Texas A&M University)

October 3, 2020

Beginner Group (in Pre-Algebra and below)

Speaker: Dr. Phil Yasskin (TAMU)

Title: The Substraction Game & NIM

Abstract: Participants will play one another (virtually) in a subtraction game and explore the mathematical underpinnings of this game. If time permits we will also discuss the games NIM and Tip the Die.

Intermediate Group (in Algebra 1 or above)

Speaker: Dr. Phil Yasskin (TAMU)

Title: The Substraction Game & NIM

Abstract: Participants will play one another (virtually) in a subtraction game and explore the mathematical underpinnings of this game. If time permits we will also discuss the games NIM and Tip the Die.

Advanced Group (in Algebra 2 or above)

Speaker: Dr. Phil Yasskin (TAMU)

Title: The Substraction Game & NIM

Abstract: Participants will play one another (virtually) in a subtraction game and explore the mathematical underpinnings of this game. If time permits we will also discuss the games NIM and Tip the Die.

Problem-Solving: Beginner Group

Instructor: Drs. Irina Bobkova and Guangbo Xu (Texas A&M University)

Problem-Solving: Intermediate Group

Instructor: Xiaoyu Su & Drs. Li Gao, Hao Guo (Texas A&M University)

Problem-Solving: Advanced Group

Instructors: Drs. Guoliang Yu, Zhizhang Xie, Rodrigo Matos, Andrew Yu (Texas A&M University)

February 29, 2020

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Priyanga Ganesan, Texas A&M University

Title: Island of Knights and Knaves

Abstract: We will solve logic puzzles in the setting of a fictional island where every inhabitant is either a knight (who always tells the truth) or a knave (who always lies). The goal is to deduce an inhabitant's type based on their statement and some additional information given. Along the way, we will learn several elements of mathematical logic like negation, conjunction and disjunction.

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: Dr. Matthew Young, Texas A&M University

Title: Gerrymandering: How to Win Elections the Sneaky Way

Abstract: Every ten years, local and state officials are allowed to change the boundaries of voting districts to account for changes in population. But a widespread technique called "gerrymandering" involves strategically drawing these boundaries so that members of the ruling party can be re-elected, even if most of the voters in their region vote against them. We'll explore how gerrymandering works, draw our own voting district maps, and investigate mathematical techniques for choosing drawing districts that are fair for everyone.

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: Dr Phillip Yasskin, Texas A&M University

Title: Special Relativity

Abstract: We will learn what happens near the speed of light.

February 15, 2020

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Andrew Winn, Texas A&M University

Title: Gerrymandering: How to Win Elections the Sneaky Way

Abstract: Every ten years, local and state officials are allowed to change the boundaries of voting districts to account for changes in population. But a widespread technique called "gerrymandering" involves strategically drawing these boundaries so that members of the ruling party can be re-elected, even if most of the voters in their region vote against them. We'll explore how gerrymandering works, draw our own voting district maps, and investigate mathematical techniques for choosing drawing districts that are fair for everyone.

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: Priyanga Ganesan, Texas A&M University

Title: Island of Knights and Knaves

Abstract: We will solve logic puzzles in the setting of a fictional island where every inhabitant is either a knight (who always tells the truth) or a knave (who always lies). The goal is to deduce an inhabitant's type based on their statement and some additional information given. Along the way, we will learn several elements of mathematical logic like negation, conjunction and disjunction.

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: Dr. Phillip Yasskin, Texas A&M University

Title: Special Relativity

Abstract: We will learn what happens near the speed of light.

February 8, 2020

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Ola Sobieska, Texas A&M University

Title: Trapezoidal Numbers

Abstract: Sums of consecutive integers, like 3+4+5 or 4+5+6+7+8 or 5+6+...+80+81, are called trapezoidal numbers. In this activity, we will investigate which numbers are trapezoidal, how to tell, and find out how many different trapezoidal representations it has.

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: Marshall King, Texas A&M University

Title: The Factor-Collecting Tax Man

Abstract: The tax man game begins with 12 available paychecks worth $1-$12. Each time you choose a paycheck, the tax collector collects all the paychecks that are factors of what you have chosen as a tax. You cannot choose a paycheck if the tax collector cannot collect tax on it. Once you have no more paychecks to legally choose, the tax man collects the rest of the paychecks. Is it possible to get more money than the tax collector? How much money is it possible to make playing this game? What changes if we start with more than 12 paychecks? We will play this game and work together to see if we can answer these questions.

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: Dr. Matt Papanikolas, Texas A&M University

Title: Complex Numbers II

Abstract: We will explore more properties of complex numbers and investigate their rich connections with algebra and geometry. As an application we will look into the construction and complexity of the Mandelbrot set from fractal geometry.

February 1, 2020

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Jordan Hoffart, Texas A&M University

Title: Change for a Dollar

Abstract: We will count "how many ways there are to make change for a dollar?"

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: Joshua Goldstein, Texas A&M University

Title: Skyscrapers

Abstract: We will engage in a hands-on activity helping a city planner figure out the optimal locations of different skyscrapers under various rules.

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: Dr. Phillip Yasskin, Texas A&M University

Title: Special Relativity

Abstract: We will learn what happens near the speed of light.

January 25, 2020

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Dr. Irina Holmes, Texas A&M University

Title: Skyscrapers

Abstract: We will engage in a hands-on activity helping a city planner figure out the optimal locations of different skyscrapers under various rules.

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: Dr. Jonas Luhrmann, Texas A&M University

Title: How Big is Infinity?

Abstract: We will step into the shoes of a night manager working at Hilbert’s hotel (a totally booked up hotel with infinitely many rooms) who has to deal with logistical nightmares such as making room for a countably infinite number of new guests. Along the way we will compare the "sizes" of the natural numbers, the rational numbers, and the real numbers. Eventually, we will come to realize that infinity comes in different sizes.

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: Dr. Wencai Liu, Texas A&M University

Title: Complex Numbers

Abstract: I will first introduce the imaginary number from Cardano’s formula of the cubic equation. Then the complex number and geometric description will be discussed. Finally, I will introduce Euler’s formula and prove the trigonometric identities.

December 14, 2019

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Andrew Winn, Texas A&M University

Title: Billiards Geometry

Abstract: In this lesson we will explore the geometry of billiards. What kinds of paths can we make? Can we classify all possible paths? Can we predict where they will end? We will conclude with a discussion of some open problems related to ergodic theory and dynamical systems.

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: Dr. Li Gao, Texas A&M University

Title: Switching Light Bulbs

Abstract: A long hallway has 100 light bulbs with pull strings, numbered 1 through 100. Pulling the string will switch the light from off to on, or, from on to off. At one end of the hallway, 100 people numbered 1 through 100 wait. Each person, when they walk down the hallway will pull the string of every light bulb whose number is a multiple of theirs. Which light bulbs are left on after all people with prime numbers are done walking? In this activity, we will explore different variations of this question and discuss a general strategy to approaching such problems.

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: Kris Watkins, Texas A&M University

Title: Cryptography

Abstract: We will continue exploring the Diffie-Hellman Key Exchange and ElGamal as well as RSA. While doing this, we will investigate what makes the Binary Square-Multiply algorithm work and why it's so special to us. If time permits we will quickly explore how RSA and DHK/ElGamal can be broken.

December 7, 2019

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Priyanga Ganesan, Texas A&M University

Title: Traveling the Checkerboard

Abstract: Given two points on a 5x5 checkerboard, can you travel through the board starting at one point and reache the other point in a way that you visit each square on the checkerboard exactly once? In this activity, we will explore different variations of this problem and learn when there does or does not exist a solution to the problem.

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: Joshua Goldstein, Texas A&M University

Title: Billiards Geometry

Abstract: In this lesson we will explore the geometry of billiards. What kinds of paths can we make? Can we classify all possible paths? Can we predict where they will end? We will conclude with a discussion of some open problems related to ergodic theory and dynamical systems.

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: Kris Watkins, Texas A&M University

Title: Cryptography

Abstract: We will utilize various different things that have been presented this semester while exploring cryptosystems such as the Diffie-Hellman Key Exchange, ElGamal, McEliece, RSA, and others if time permits. While doing this we will also discuss what makes these systems good/bad and what mathematical problems they are based off of (such as the Discrete Logarithm Problem and the Integer Factoring Problem).

November 23, 2019

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Parker Duncan, Texas A&M University

Title: Trapezoidal Numbers

Abstract: We will study which numbers can be written as the sum of consecutive positive integers.

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: Dr.Frank Sottile, Texas A&M University

Title: Archimedean Solids

Abstract: Most of us know the five Platonic (or regular) solids; next to the sphere, they are the most regular and beautiful objects in our three-dimensional world. Less well-known are the Archimedean or semi-regular solids. In this math circle activity, we will recall the Platonic solids, and then explore the Archimedean solids, and some relations between them. We will be building them and then studying our constructions.

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: Jurij Volcic, Texas A&M University

Title: Inequalities and Squares

Abstract: We will dive deeper into inequalities. Many of them are a consequence of the simple fact that a square is always positive. We will see to what extent this is a general principle, and what we can do with it. This activity will be accessible for anyone who missed the last week.

November 16, 2019

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Andrew Winn, Texas A&M University

Title: How to Take a Walk in Koenigsberg

Abstract: Sometimes when I go for a walk, I have a certain route in mind that I'd like to take, such as through the park or past the fire station. But what if I wanted to cross a river a few times by walking exactly once on each of the river's bridges? Can I choose a route that does that? We'll explore a classic problem of Euler which, in answering that question, laid the groundwork for the fields of graph theory and topology.

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: Pablo Ocal, Texas A&M University

Title: Chess Knights and Bipartite Graphs

Abstract: There is a patent affinity between Mathematics and chess: in both of them, a very limited set of rules yields enormous depth, challenging problems, obnoxious frustrations, and endless beauty. We will see how the knight and its characteristic leap aids in understanding the concept of bipartite graph, and how some mathematical problems can be solved using a chess board.

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: Jurij Volcic, Texas A&M University

Title: Mean Inequalities

Abstract: The usual average of two numbers a and b is (a+b)/2, their arithmetic mean. But there are also other means between numbers. We will take a look at some of them, explore relations between them, and see how we can use them when handling inequalities.

November 2, 2019

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Dr. Maya Johnson, Texas A&M University

Title: Let's Play a Game

Abstract: A game is a situation of conflict between two players. If you were playing a game with your friend, the conflict would be that you both want to win. If you we playing a game with your friend in which each of you could win or lose some specified amount of money, you would be playing a "zero sum" game if whenever you WON an amount of money your friend LOST that same amount of money. In this activity we will see that, for certain games, there is in fact an optimal strategy for you to win or suffer the least amount of loss. With these games, it's even possible to determine that even with your best strategy that you will always lose to your friend. Knowing that fact could help you avoid heading into a losing game. Not all games are this nice, where you can find an optimal strategy. Some games you can't tell for sure what will happen, and you will just have to take your chances!

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: Parker Duncan, Texas A&M University

Title: Trapezoidal Numbers

Abstract: We will study which numbers can be written as the sum of consecutive positive integers.

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: Pablo Ocal, Texas A&M University

Title: Chess Knights and Bipartite Graphs

Abstract: There is a patent affinity between Mathematics and chess: in both of them, a very limited set of rules yields enormous depth, challenging problems, obnoxious frustrations, and endless beauty. We will see how the knight and its characteristic leap aids in understanding the concept of bipartite graph, and how some mathematical problems can be solved using a chess board.

October 26, 2019

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Dr. Wencai Liu, Texas A&M University

Title: Tower of Hanoi

Abstract: The Tower of Hanoi was invented in 1883. It consists of three rods and a number of disks of different sizes, which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod with the smallest disk at the top. The objective of the puzzle is to move the entire stack to another rod, obeying the following rules: (1) Only one disk can be moved at a time; (2) Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod; (3) No larger disk may be placed on top of a smaller disk. We will discuss the minimal number of moves required to solve a Tower of Hanoi puzzles with 3 disks and 4 disks. If time permits, we will explore the formula for n disks.

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: Joshua Goldstein, Texas A&M University

Title: Random Walks

Abstract: What is a random walk? In this game we will discuss what are random walks and explore their connection to probability.

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: David Sykes, Texas A&M University

Title: Euclidean Motions

Abstract: We will explore properties of orthogonal matrices along with a method for describing distance using a special Hermitian matrix. This activity will complement the Euclidean motions activities from previous weeks, and it will be accessible for anyone who has missed those activities as well.

October 5, 2019

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Joshua Goldstein, Texas A&M University

Title: Random Walks

Abstract: What is a random walk? In this game we will discuss what are random walks and explore their connection to probability.

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: Dr. Tom Gannon, University of Texas at Austin

Title: But What Are Imaginary Numbers, Anyway?

Abstract: Sometimes people talk about "complex" numbers, but the hard part is there normally isn't a picture of the complex numbers like the number line. We'll talk about a way to draw the "complex number line." We'll also talk about whether imaginary numbers really "exists," and how they can apply to things in the real world. Time permitting, we'll also talk about how we know the real numbers aren't the same thing as the rational numbers (and we'll talk about what this means).

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: David Sykes, Texas A&M University

Title: Euclidean Motions

Abstract: Complementing last week's topic, we will study Euclidean motions using matrices.

September 28, 2019

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Dr. Philip Yasskin, Texas A&M University

Title: Squareable Numbers

Abstract: We will study collections of squares which can be assembled to form other squares or rectangles.

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: Ola Sobieska, Texas A&M University

Title: Mathematical Auction

Abstract: We will be doing a team contest called ‘mathematical auction.’

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: David Sykes, Texas A&M University

Title: Euclidean Motions

Abstract: We will explore ways that transformations of the Euclidean plane preserving distances can be described as compositions of reflections, rotations, and translations.

May 4, 2019

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Philip Yasskin, Texas A&M University

Title: Problems with Toilet Paper

Abstract: There are 3 kinds of people in the world:

Those who crumble toilet paper - the chaotic people.

Those who fold in half repeatedly - the exponential people.

Those who fold from the end repeatedly - the linear people.

We will investigate several problems involving linear and exponential folding of toilet paper.

Intermediate and Advanced Groups: BLOC 203 (in Algebra 1 or above)

Speaker: Pablo Ocal

Title: The Best Way How Not to Hang Pictures in Walls

Abstract: We will discuss how to hang a picture on the wall using two nails in such a way that removing either of the nails will make the picture fall down to the foor. We will see how one can come up with a solution without experimentation. In fact, the same statement holds for any number of nails, and we will find a way to compute the solutions.

April 27, 2019

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Priyanga Ganesan, Texas A&M University

Title: The a + b + ab Problem

Abstract: Write down the numbers from 1 to 100. Randomly select 2 numbers from the list, say a and b, and cross them off, but add to the list the number a + b + ab. You now have 99 numbers. Repeat this process until you have only 1 number left. What are all possible final numbers?

Intermediate and Advanced Groups: BLOC 203 (in Algebra 1 or above)

Speaker: Lan Li, University of Texas at Austin

Title: Can You Decipher This?

Abstract: We communicate everyday; with individuals, groups, and now, a global audience if we wish. While some messages we don’t mind letting everybody hear, others may be more personal in nature. As we rely more and more on technology to communicate everyday, how can we be sure that our messages are secured? We’ll explore this question in this session.

April 13, 2019

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Sinjini Sengupta, Texas A&M University

Title: Dots on a Grid

Abstract: We will discuss the different ways we can place dots on a grid so that no two dots are the same distance apart from each other. We will have fun identifying how many unique distances can exist between points on an (n x m) grid.

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: Phil Yasskin, Texas A&M University

Title: The a + b + ab Problem

Abstract: Write down the numbers from 1 to 100. Randomly select 2 numbers from the list, say a and b, and cross them off, but add to the list the number a + b + ab. You now have 99 numbers. Repeat this process until you have only 1 number left. What are all possible final numbers?

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: Kris Watkins, Texas A&M University

Title: Topology Series 6: Topological Properties and Equivalence

Abstract: Given that we have now seen the main Topologies used and how to verify them, we will now look at which things are topologically equivalent, what does such an equivalence give us, and what topological invariants are. Before we can do that though, we must develop the fundamentals and definitions that are need to discuss those things.

March 30, 2019

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Phil Yaskin

Title: The King Arthur Problem

Abstract: King Arthur's daughter is supposed to marry one of the Knights of the Round Table. She devises an interesting method to select which knight to marry. We will study the problem.

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: David Sykes

Title: Mondrian Art Puzzles

Abstract: We will work on puzzles inspired by Piet Mondrian's art. The activity leads to fun and challenging geometric dissection problems.

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: Kris Watkins

Title: Topology Series 6: Topological Properties and Equivalence

Abstract: Given that we have now seen the main topologies used by topologists and that we have also seen how to verify them, we will now look at which things are topologically equivalent, what does such an equivalence give us, and what topological invariant are. Before we can do that though, we must develop the fundamentals and definitions that are necessary to discuss those things.

March 23, 2019

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: David Sykes, Texas A&M University

Title: Mondrian Art Puzzles

Abstract: We will work on puzzles inspired by Piet Mondrian's art. The activity leads to fun and challenging geometric dissection problems.

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: Igor Zelenko, Texas A&M University

Title: Solving Extremum Problem in Planar Geometry Using Reflections and Rotations: the Law of Reflections, the Fermat-Torichelli point, and the Euclidean Steiner tree problem

Abstract: We will try to solve together a list of geometric extremum problems (from more simple to more complicated), concerning finding paths of minimal length among all paths with prescribed properties using elementary transformations such as reflections and rotations. In this way we will justify the law of reflection in Physics and describe the algorithm to find networks of minimal length with given vertices (terminals), called Steiner minimal trees.

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: John Weeks, Texas A&M University

Title: Topology Series 5: Quotient Topology

Abstract: We will now begin to look at one of the most crazy/wacky parts of topology that leads to some very interesting results. The Quotient Topology allows us to look at things in a completely different way and it allows us to take objects that appear completely distinct and identify them with each other.

March 2, 2019

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Dean Baskin, Texas A&M University

Title: “Magic Squares” in Set

Abstract: We will introduce the card game Set. Set is played with 81 unique cards, each of which has four attributes: number, color, shading, and shape. The aim of the game is to collect sets of three cards in which each attribute is the same or different. We will use the cards from this game to construct “magic squares” in which every line is a set. Time permitting, we will attempt to find “magic cubes” or “magic hypercubes” with the cards.

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: Phil Yasskin, Texas A&M University

Title: Bulgarian Solitaire

Abstract: Begin with a small number of poker chips in a small number of piles. Remove one chip from each pile and put them in a new pile. If a pile becomes empty, it disappears. We will study what happens when this process is repeated.

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: Kris Watkins, Texas A&M University

Title: Topology Series 4: Product and Subspace Topology, Along With Metrics

Abstract: We’ve now not only established what a topology is but we also know how to verify that something is a topology and how to define it with a basis. We’ve seen various topologies, but now we’ll introduce the product topology and subspace topology. Afterwards we’ll look at one of the most important parts of Topology, namely metric spaces.

February 16, 2019

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Junehyuk Jung, Texas A&M University

Title: How to Eat More Pizza

Abstract: We look for the best strategy of slicing the pizza to ensure you eat more than the other person, under certain rules. (Disclaimer: real pizzas are not included in the activity). This activity is based on a mathematical conjecture which was resolved only 10 years ago.

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: Matthew Young, Texas A&M University

Title: Conway’s Game of Life

Abstract: Conway's game of life gives a way for creating amazingly complicated and beautiful patterns out of simple designs. To play the game, one places live cells on a grid. Each round, cells either live, die, or are newly born, according to some definite rules. We will learn the rules of Conway's game of life, see how some initial shapes evolve, and also do some computer experimentation.

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: Kris Watkins, Texas A&M University

Title: Topology Series: Generating and Verifying a Basis For a Topology

Abstract: Last time we looked at various different topologies and even verified that the Finite-Complement topology really is a topology. Through doing that we were able to see how it would be impossible for us to list every single open set within some topologies. Our way of fixing this is to define a basis and to learn how to use a basis to define an entire topology.

February 9, 2019

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Phil Yasskin, Texas A&M University

Title: Bulgarian Solitaire

Abstract: Begin with a small number of poker chips in a small number of piles. Remove one chip from each pile and put them in a new pile. If a pile becomes empty, it disappears. We will study what happens when this process is repeated.

Intermediate/Advanced Groups: BLOC 203 (in Algebra 1 or above)

Speaker: Matthias Maier, Texas A&M University

Title: Fractals

Abstract: We will explore the wonderful world of fractals. These are complex patterns that are self-similar across different scales. This means that no matter how far you zoom into these structures you will always see the same basic shape. We will also explore how simple recursive procedures can create a fractal structure, where to find such structures in nature, and how seemingly simple mathematical conditions can lead to very surprising fractal sets.

February 2, 2019

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Matthew Young, Texas A&M University

Title: Conway's Game of Life

Abstract: Conway's game of life gives a way for creating amazingly complicated and beautiful patterns out of simple designs. To play the game, one places live cells on a grid. Each round, cells either live, die, or are newly born, according to some definite rules. We will learn the rules of Conway's game of life, see how some initial shapes evolve, and also do some computer experimentation.

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: Chun-hung Liu, Texas A&M University

Title: Rooks and Dating

Abstract: Given an 8x8 chessboard where some positions are removed, can you place 8 rooks so than none of them can attack another? A couple of boys want to date a couple of girls, where every pair of boy and girl either like each other or do not like each other. Can you pair them so that everybody is happy? These problems are special cases of graph matching theory. We will see how we can put as many rooks as possible and how can we pair as many boys and girls as possible.

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: Kris Watkins, Texas A&M University

Title: Topology Series 2: What Are Topologies and How Do We Verify Them?

Abstract: At the end of our last section we introduced what it means for "T" to be a topology on a space "X". We will begin to look at various topologies and verify topologies that we have been using our entire lives.

January 26, 2019

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Chun-hung Liu, Texas A&M University

Title: Rooks and Dating

Abstract: Given an 8x8 chessboard where some positions are removed, can you place 8 rooks so than none of them can attack another? A couple of boys want to date a couple of girls, where every pair of boy and girl either like each other or do not like each other. Can you pair them so that everybody is happy? These problems are special cases of graph matching theory. We will see how we can put as many rooks as possible and how can we pair as many boys and girls as possible.

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: John Weeks, Texas A&M University

Title: Generating Functions

Abstract: How many integer solutions (a, b, c, d) are there to the equation a+b+c+d=25? We will answer this question using a simple answer from a generating function. We will also cover the stars-and-bars method in the partitions of integers problem.

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: Kris Watkins, Texas A&M University

Title: Topology Series: Introduction to Logic, Set Theory, and Point-Set Topology

Abstract: Topology is often looked at as rubber sheet Geometry. We are able to treat everything like playdoh and still recover extremely strong results about the properties of these things. We can even say that a doughnut and a coffee cup are "topologically equivalent". For our first session we will quickly explore things such as the Konigsberg bridge problem and the Euler Characteristic of a polyhedron. We won't necessarily give these things a formal proof, but they will give us the motivation to learn other things that will make us capable of developing a formal proof. Afterwards we'll start with some basic Set Theory and Logic rules that will aide us in further studying Point-Set Topology.

December 8, 2018

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Maurice Rojas, Texas A&M University

Title: Protecting Your Data II

Abstract: Last weekend, we saw the basics of modular arithmetic, and a connection to music. This weekend, we'll continue learning more about modular arithmetic: specifically, division and exponentiation. We'll then see how this is related to secret codes used now on the internet. Time permitting, we'll also see a cute puzzle related to error correcting codes. The latter kind of code is important for transmitting data in a noisy environment.

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: JD Kim, Texas A&M University

Title: Slope of a Line and Its Applications

Abstract: In this talk we will discuss the slope of a line and how we can use it for numerical PDE problems. As an application, I will demonstrate coding for simple PDE problems and introduce the Front Tracking method for the Parachute model.

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: John Weeks, Texas A&M University

Title: Construction of the Real Numbers

Abstract: A set is, roughly speaking, a collection of objects. You may have heard that the abstract notion of a set currently resides as a basis for all we do in mathematics. But how do we understand numbers in terms of sets? We will discuss John von Neumann's (1903-1957) set-theoretic definition of a number and relate it to the axiomatic structure of the counting numbers given by Giuseppe Peano (1858-1932). We then continue onward (but backward in history!) to construct the real number system from the rational numbers using the methods of Augustin-Louis Cauchy (1789-1857).

December 1, 2018

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Maurice Rojas, Texas A&M University

Title: Protecting Your Data I

Abstract: Cryptology is the study of making (and breaking) codes to protect important information. This could mean protecting private information (like medical or financial records) or recovering information that is hard to retrieve (like distant signals from a spacecraft). We’ll do some activities related to codes that help recover data and codes that hide information. We’ll learn how randomness and computations with very large integers are centrally important in modern cryptology.

Intermediate and Advanced Group: BLOC 203 (in Algebra 1 or above)

Speaker: Eric Rowell, Texas A&M University

Title: Counting Holes in Twisted Surfaces

Abstract: We will explore properties of surfaces such as different kinds of holes, two-versus one-sidedness, coloring maps, and the Euler characteristic.

November 17, 2018

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Jennifer Whitfield, Texas A&M University

Title: Patterns Within Pascal's Triangle

Abstract: Pascal's Triangle is a triangular array that has many interesting patterns as well as many important mathematical concepts. In this session we will explore Pascal's Triangle and discover some of the patterns in the triangle. We will also discuss how these patterns are tied to different areas in mathematics.

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: Catherine Yan, Texas A&M University

Title: Parking Functions and Chip Firing Game

Abstract: We will look at two combinatorial models: a parking process on a one-way street and a one-player chip firing game that re-distributes chips over a graph. From these models we get two different objects: parking functions and critical configurations. We show that they are actually the same object if we look at them from the right point of view.

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: Igor Zelenko, Texas A&M University

Title: Extremum problem, Law of Reflection, Fermat-Torichelli point, and Euclidean Steiner Tree problem

Abstract: We will try to solve together a list of geometric extremum problems (from more simple to more complicated), concerning finding paths of minimal length among all paths with prescribed properties using elementary transformations such as reflection and rotations. In this way we will justify the Law of Reflection in Physics and describe the algorithm to find networks of minimal length with given vertices (terminals), called Steiner minimal trees.

November 10, 2018

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Edriss Titi, Texas A&M University

Title: Evolution of Numbers and Their Use: From Ancient Egypt to Barcodes

Abstract: In this lecture I will talk about the mathematics behind the evolution of numbers, their writings, and their use. I will start with the number system of the ancient Egyptians and end up with the binary system and their use in barcodes.

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: Junehyuk Jung, Texas A&M University

Title: Tiling and Numbering

Abstract:

Can you fill and 8 by 8 checker board with two corners removed with 31 dominoes that are in the form of 1 by 2? The answer depends on which corners are removed. Students will find out the answer to this question by trial and error. Related problems are going to be introduced and we will learn basic concepts of the proof by contradiction.

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: JD Kim, Texas A&M University

Title: Slope of a Line and Its Applications

Abstract: In this talk we will discuss the slope of a line and how we can use it for numerical PDE problems. As an application, I will demonstrate coding for simple PDE problems and introduce the Front Tracking method for the Parachute model.

November 3, 2018

Beginner Group: BLOC 220 (in Pre-Algebra and below)

Speaker: Junehyuk Jung, Texas A&M University

Title: Tiling and Numbering

Abstract: Can you fill and 8 by 8 checker board with two corners removed with 31 dominoes that are in the form of 1 by 2.?The answer depends on which corners are removed. Students will find out the answer to this question by trial and error. Related problems are going to be introduced, including: a rectangular floor is covered by 2 by 2 and 1 by 4 tiles. One tile got smashed. There is a tile of the other kind available. Can cover the floor by rearranging tiles?

Intermediate Group: BLOC 203 (in Algebra 1 or above)

Speaker: Patrick Orchard, Texas A&M University

Title: Towers of Hanoi Puzzles

Abstract: The towers of Hanoi (also known as the Tower of Brahma or Lucas Tower) is a puzzle dating from 1883 consisting of three rods and a certain number of disks. The goal is to move the tower of disks from the left rod to the right rod following certain rules. Since then, it has appeared in TV shows, movies, and most notably in videogames. We will learn how to solve it in small cases and look for the smallest number of moves needed to do so, coming up with a formula for it.

Advanced Group: BLOC 202 (in Algebra 2 or above)

Speaker: Bill Rundell, Texas A&M University

Title: 5,000 Years of Square Roots

Abstract: By 3000BC the Sumarian civilization had both discovered "Pythagoras' Theorem" and the need, followed by the ability, to calculate square roots. Greek civilization did it quite differently. By 1700 the process was quite refined and used extensively for scientific computations; essentially what we know today about computation of, say, the square root of 2018, dates from this time. But it isn't all history. There are new needs with slightly different "numbers" and this turns out to be a cornerstone of modern cryptography.

May 12, 2018

Beginner Group:

Speaker: Max Warshauer, Texas State University

Title: Modular arithmetic and divisibility

Abstract: In this Math Circle, participants will learn about modular arithmetic and use this to discover divisibility properties. This will be a hands-on exploration where participants investigate problems, make conjectures, and then give careful arguments to prove or disprove their conjectures.

Intermediate Group:

Speaker: Alex Sprintson, Texas A&M University

Title: Introduction to Finite State Machine Design

Abstract: We will discuss mathematical aspects of logic design. We will start with a review of the fundamentals of boolean algebra and design of K-maps. Next, we will discuss the fundamentals of design and implementation of the Finite State Machines (FSM) that solve engineering problems.

Advanced Group:

Speaker: Amudhan Krishnaswamy-Usha, Texas A&M University

Title: Rigid motions and symmetries in 2 and 3 dimensions

Abstract: Rigid motions are transformations which preserve angles and distances (for example, rotations). We will explore what these look like in two and three dimensions and attempt to classify them. If time permits, we will also look at rigid motions which preserve a given figure (the symmetries of the figure), and see what happens in the case of regular polygons.

May 5, 2018

Beginner Group:

Speaker: Erica Metheney, Texas A&M University

Title: Intro to Data: What’s the Story?

Abstract: We will begin with discussing what statistics is and why it is useful. During the session, students will learn about different data types, summary statistics, and data visualization techniques then apply their new skills on data they will collect themselves. After the session, students should be able to identify data types, summarize different types of data, and create appropriate data visualization graphics.

Intermediate Group:

Speaker: Theodora Chaspari, Texas A&M University

Title: How is mathematics used in artificial intelligence and machine learning applications?

Abstract: Artificial intelligence (AI) is the field of study that focuses on machines or computer programs that are capable of thinking, acting, and learning like humans. Machine learning is the sub-field of AI that develops computer programs able to access and automatically learn from data without human assistance or intervention. AI and machine learning applications are found in every aspect of everyday life from health and well-being to entertainment and military applications. Examples of these include online games, self-driving cars, chatbots, fitness monitors, and others. Mathematics is one of the most important tools for developing AI and machine learning applications since they allow representation of real-world objects into numbers and derive meaningful interpretations from these numbers. For example, an image taken by our camera can be represented as a matrix of integers, whose structure can convey meaningful information regarding the content of the image (e.g., whether an image contains a cat or a dog). This lecture will cover basic AI and machine learning concepts and will discuss how mathematics is tightly connected to these, inspired by two applications from the computer vision and biomedical health informatics domains.

Advanced Group:

Speaker: John Weeks, Texas A&M University

Title: Groups, Cosets, and Lagrange’s Theorem

Abstract: We will explore the concepts of an algebraic group and subgroup and discuss some natural partitions of a group called cosets. If time allows, we will use modulo arithmetic to investigate how the number of elements in these groups compares with that of any subgroup contained within them. This will be an elementary talk with a goal of introducing students to the nature of upper-level mathematics.

April 28, 2018

Speaker: David W. Gent, P.E. (Founder and Chairman of SofTest Designs)

Title: Amateur Radio Satellite Orbital Mechanics

Abstract: There are countless objects currently orbiting Earth. Some of these are Communication Satellites built by Amateur Radio operators like me.

To talk through these Satellites, we must chart their current locations in space and predict their future passes above our horizon. This tracking depends upon various concepts developed by several brilliant mathematicians over the years. This is the story of that development. Example calculations using the International Space Station (ISS) are given.

April 21, 2018

Beginner Group:

Speaker: David Sykes, Texas A&M University

Title: The Icosian Game

Abstract: We will play variants of William Rowan Hamilton’s icosian game and explore its relation to other mathematical puzzles.

Intermediate Group:

Speaker: Pedro Morales, The University of Texas at Austin

Title: Internet privacy: How secure communication workss

Abstract: We will explore one of the most used encryption methods, known as the RSA. This is one of the most important applications of number theory and prime numbers. By applying basic concepts of modular arithmetic, we can develop a public key system which enables the secure exchange of information between two strangers.

Advanced Group:

Speaker: Eviatar Procaccia, Texas A&M University

Title: Simulations of random walks

Abstract: We will learn basic MATLAB programming and then simulate a process called “simple random walk”, which models fundamental natural phenomena. We will use these simulations to compute some probabilities and verify the numerical results with theoretical calculations.

April 14, 2018

Beginner/Intermediate Group:

Speaker: Josiah Coad, Texas A&M University

Title: Everyone Can Code!

Abstract: We are excited to announce a new opportunity for the students in TAMU Math Circle to learn how to code. We will be using a website code.org, which has developed many fun and educational programs for kids of all ages and skill levels to learn how to code, no previous experience necessary. In an hour, the students will learn through a drag/drop interface the basics of coding logic, all while programming their own game! With many opportunities to rank up fast, we hope to inspire students to a self-discovery of this exciting field.

Advanced Group:

Speaker: Roger Howe, Texas A&M University

Title: The medial triangle, the Euler line, and the nine-point circle.

Abstract: Studying the relationship between a triangle and the triangle formed by the midpoints of its sides (known as the medial triangle) gives deeper insights into the triangle geometry than were found by the Greeks. A key part of this development is the Euler line, which exhibits a beautiful relationship between circumcenters, orthocenters, and centroids. This in turn sheds light on the nine-point circle and beautiful related configurations.

March 24, 2018

Beginner Group:

Speaker: Josiah Coad , Texas A&M University

Title: Everyone Can Code!

Abstract: We are excited to announce a new opportunity for the students in TAMU Math Circle to learn how to code. We will be using a website code.org, which has developed many fun and educational programs for kids of all ages and skill levels to learn how to code, no previous experience necessary. In an hour, the students will learn through a drag/drop interface the basics of coding logic, all while programming their own game! With many opportunities to rank up fast, we hope to inspire students to a self-discovery of this exciting field.

Intermediate Group:

Speaker: Dimitar Grantcharov, The University of Texas at Arlington

Title: Invariants

Abstract: Invariants are special “mysterious” tools that play an important role in various mathematical fields. We will solve several problems from number theory, game theory, combinatorics, and geometry that use invariants.

Advanced Group:

Speaker: David Sykes, Texas A&M University

Title: Counting Polyominoes

Abstract: We will be counting the number of polyominoes sharing certain properties. The activity will present several fun combinatorial problems, some of which remain unsolved; for example, to date, there is no explicit formula for the number of polyominoes having a given size.

March 3, 2018

Beginner Group:

Speaker: David Sykes , Texas A&M University

Title: Planar Graphs

Abstract: Given three cottages and three wells, can we find non-intersecting paths so that every cottage is connect to each well by a different path? We will consider this problem along with others that introduce the topic of planar graphs.

Intermediate Group:

Speaker: Nathan Green, Texas A&M University

Title: Polya Counting

Abstract: Polya counting theory allows us to count how many ways there are to arrange objects taking symmetry into account. For example, how many different bracelets can we make using only 3 colors of beads? How many ways can we color a cube using n colors? This counting technique has been used to count the number of different molecules which can be formed from certain sets of atoms and many other important applications.

Advanced Group:

Speaker: John Weeks, Texas A&M University

Title: Relations, Equivalence Classes, and Langrange’s Theorem

Abstract: We will give a few definitions related to the study of relations and introductory group theory, inquire into some examples of equivalence classes, and utilize this information to analyze the nature of subgroups in finite groups.

February 17, 2018

Beginner Group:

Speaker: Amudhan Krishnaswamy-Usha , Texas A&M University

Title: Fractions and bases

Abstract: We will look at decimal expansions of fractions and try to determine when they terminate. We will then try to expand fractions in other bases (such as binary).

Intermediate Group:

Speaker: Frank Sottile, Texas A&M University

Title: Shape of Space

Abstract: In mathematics and science, we often need to think about high (3 or more) dimensional objects, called spaces, which are hard or impossible to visualize. Besides the question of what such objects are or could be, is the problem of how we can make sense of such spaces.

The goal of this discussion is to give you an idea of how mathematicians manage to make sense of higher-dimensional spaces. We will do this by exploring the simplest spaces, and through our explorations, we will begin to see how we may tell different spaces apart. Along the way, we will dissect donuts, and I ask that at least half of the participants bring a belt.

Advanced Group:

Speaker: Parth Sarin, Texas A&M University

Title: Pancakes, Ham Sandwiches, and Topology

Abstract: Topology is a field of mathematics that tries to understand the shape of things without regards to distance or angles. In this Circle, we’ll explore some famous and surprising concepts from Topology. For example, we’ll consider whether there are two opposite points of the Earth that have the exact same temperature and pressure. And, we’ll explore how these questions are related to things you wouldn’t expect, like whether or not you can cut two pancakes in half with a very large knife using a single cut.

February 10, 2018

Beginner Group:

Speaker: David Sykes , Texas A&M University

Title: Patio Planning Problems

Abstract: How many ways can we configure non-overlapping square tiles to build a patio with a given shape and a given perimeter? We will explore variations of this problem by drawing patio designs with small perimeters and using what we will find to make informed guesses about the answer for larger perimeters and that we then prove or disprove.

Intermediate Group:

Speaker: Valentin Zakharevich, The University of Texas at Austin

Title: Symmetry and Affine Transformations

Abstract: One of the most important ideas in geometry is that of symmetry. Understanding the symmetry of a problem can often significantly simplify finding a solution. In this presentation, we will be considering the affine symmetries of the plane, i.e. the symmetries which preserve straight lines. We will apply these ideas to understand theorems of Ceva and Menelaus.

Advanced Group:

Speaker: Tom Gannon, The University of Texas at Austin

Title: How to Make Friends with Graph Theory

Abstract: We’re going to learn about a subject called graph theory, which will be sure to impress all your friends. Graph theory is a subject about dots and lines and the various ways you can draw them. We’ll talk about complete graphs and about how friendship can be modeled by graph theory. We’ll also discuss a problem that no one on earth knows the answer to!

February 3, 2018

Beginner Group:

Speaker: Philip Yasskin , Texas A&M University

Title: Cell Phone Dropping

Abstract: You work for a cell phone company. For advertising purposes, you are assigned the task of testing a new model of phone protector by dropping a phone from various floors of a 100 story building to determine the highest floor from which it can be dropped and not break. What is the most efficient way to perform this task if you are given 1, 2, or 3 phones?

Intermediate Group:

Speaker: Frank Sottile, Texas A&M University

Title: Balls and Boxes: Common shapes in uncommon dimensions

Abstract: Today, we will explore how common shapes- balls, cubes, triangles, and others –behave strangely in high-dimensional space. This is also an explorations of regular solids in dimensions greater than four. This is independent of last week’s circle activity.

Advanced Group:

Speaker: Alex Sprintson, Texas A&M University

Title: Fun with Finite State Machines

Abstract: We will continue our discussion about design and analysis of Finite State Machines (FSM). We will talk about minimization and equivalence problems. Towards the end, we will attend to write a program that plays a short five note song. Please bring your computer if at all possible.

January 27, 2018

Beginner Group:

Speaker: Alex Sprintson, Texas A&M University

Title: Pi Math Contest (PiMC)

Abstract: We will work on the Pi Math Contest (PiMC) written by an expert committee, many of whose members are from MIT/Harvard/Stanford (see pimathcontest.com). All students in 4th and 5th grade students will officially participate in the contest. However, all students in the beginner group will work on the problems. We will discuss the problem and their solutions later in the circle. Top scoring students in this round will be invited to a Final Round in Bay Area, California on April 28th 2018.

Rulers and compasses are allowed. Calculators are not allowed (no problem on the test will require the use of a calculator). The students are strongly encouraged to visit https://alphastar.academy/event/pimc/#PiMC_2017 to see prior year tests and solutions. Top students in the first round are invited to the final round.

Intermediate Group:

Speaker: Frank Sottile, Texas A&M University

Title: Regular solids in all dimensions

Abstract: While we are all familiar with regular polygons (equilateral triangles, squares, …), and many of us know about the Platonic, or regular solids (tetrahedron, cube, octahedron,….), few are familiar with their analogs in dimensions four and higher. Of course, this is because we are not equipped to perceive four-dimensional space directly.

Nevertheless, the description of the regular solids in all dimensions has been known for a long time. The purpose of my talk will be to introduce you to these objects, with an emphasis on how to think about them. This presentation will be spiced up with some models of four-dimensional regular solids, some of which you can build yourself. This is independent of last week’s circle activity.

There is a link to an animation:

http://www.math.tamu.edu/~sottile/talks/17/4D/index.html

Advanced Group:

Speaker: Philip Yasskin, Texas A&M University

Title: Point Set Topology

Abstract: We will discuss the basic definitions of point set topology.

January 20, 2018

Beginner Group:

Speaker: Amudhan Krishnaswamy-Usha, Texas A&M University

Title: Counting with Aliens

Abstract: We will discuss different number system and discover how to convert numbers from one base to another.

Intermediate Group:

Speaker: Frank Sottile, Texas A&M University

Title: Archimedean Solids

Abstract: Most of us know the five Platonic (or regular) solids; next to the sphere, they are the most regular and beautiful objects in our three-dimensional world. Less well-known are the Archimedean or semi-regular solids. In this math circle activity, we will recall the Platonic solids, and then explore the Archimedean solids and some relations between them. We will be building them and then studying our constructions. If time, I will explain their relation to fair dice.

Advanced Group:

Speaker: Alex Sprintson, Texas A&M University

Title: Introduction to Finite State Machine Design

Abstract: We will discuss mathematical aspects of logic design. We will start with a review the fundamentals of boolean algebra and design of K-maps. Next, we will discuss the fundamentals of design and implementation of Finite State Machines (FSM) that solve engineering problems. If time permits, we will discuss the capabilities and limitations of FSM.

December 9, 2017

Elementary Group – Dean Baskin on Towers of Hanoi

Presenter: Dean Baskin

Department of Mathematics, Texas A&M University

Abstract: This activity is aimed at students in second grade. We will introduce the Towers of Hanoi game, work out how to solve it in small cases and try to find a pattern in the number of moves required. If there is time left at the end, we will play some mathematically oriented games.

Beginner/Intermediate Group- Jane Long on Factors and Primes

Presenter: Jane Long

Department of Mathematics, Stephen F. Austin University

Abstract: Prime numbers, those counting numbers with exactly two distinct factors (themselves and one), are very special in mathematics. We’ll discuss ways to find prime numbers and other factors of counting numbers, and investigate perfect numbers, amicable numbers, and some really big numbers.

Intermediate/Advanced Group – Nicholas Long on Counting Rectangles with Integer Sequences

Presenter: Nicholas Long

Department of Mathematics, Stephen F. Austin University

Abstract: When you look at a chess board, you can see lots of squares. How many do you see? How many rectangles can you make with the blocks on a chess board? What if the chess board was a different size? Slightly different figures can lead to wildly different patterns when you think flexibly about where squares and rectangles come from. We will also look at how the sequence of integers generated by these other questions can lead to a lot of related problems on the OEIS (Online Encyclopedia of Integer Sequences).

November 25, 2017

Beginner Group – Amudhan Krishnaswamy-Usha on Fibonacci and Other Numbers

Presenter: Amudhan Krishnaswamy-Usha

Department of Mathematics, Texas A&M University

Abstract: Continuing the discussion led by David Sykes’ last math circle, we will look at Fibonacci numbers and a few of their properties. If time permits, we will look at a few other sequences coming from ‘recurrence relations’.

Intermediate Group- Phil Yasskin on When do 4 or more Points Lie on a Circle?

Presenter: Phil Yasskin

Department of Mathematics, Texas A&M University

Abstract: We will first answer the question: “When do 4 points lie on a circle?”. Then we will prove the Nine Point Theorem and maybe some others.

Advanced Group – Frank Sottile on The Five Color Theorem

Presenter: Frank Sottile

Department of Mathematics, Texas A&M University

Abstract: Doodling on a map of England in 1852, Francis Guthrie noticed that only four colors were needed to color the counties. He conjectured that any map could be colored with only four colors. Several mathematicians tried and failed to prove this; notably in 1879 Kempe published a proof and only in 1890 was the flaw found by Heawood. This four color conjecture evaded a proof until 1972, when Appel and Haken gave a proof that required a computer. While there is as yet no Human readable proof, Kempe’s argument suffices to prove that five color suffice, and this gives a flavor of known proofs of the four color theorem. I will sketch this history and prove the five color theorem, and then discuss the coloring theorem for other surfaces (torus, projective plane, Klein bottle…).

November 18, 2017

Beginner Group – David Sykes on The Fibonacci Sequence

Presenter: David Sykes

Department of Mathematics, Texas A&M University

Abstract: We will learn about the golden ratio while solving problems associated with Fibonacci Numbers.

Intermediate Group- Jennifer Whitfield on Using Euler and Hamiltonian Paths to Get Around

Presenter: Jennifer Whitfield

Department of Mathematics, Texas A&M University

Abstract: In this session, we will investigate the different paths that exist on a given graph. We will also discover some properties of Euler and Hamiltonian paths and then apply the properties to solve problems.

Advanced Group – Doug Hensley on Putnam Problems

Presenter: Doug Hensley

Department of Mathematics, Texas A&M University

Abstract: The “Putnam” is the William Lowell Putnam mathematical competition. It’s famous for being both challenging and fun. The hard part is that the problems always have a twist to where you never “know how to work that type”going in. The fun part is that there is always a sweet solution.

November 11, 2017

Beginner Group – Amudhan Krishnaswamy-Usha on The Euclidean Algorithm

Presenter: Amudhan Krishnaswamy-Usha

Department of Mathematics, Texas A&M University

Abstract: We will explore the GCD, LCM, and the Euclidean algorithm.

Intermediate Group- Abraham Martin del Campo on Probability and Algebra

Presenter: Abraham Martin del Campo

Department of Mathematics, CIMAT

Abstract: We will explore some basic probability concepts through a coin tossing game and use a little bit of algebra to find if we can play a fair game.

Advanced Group – Nathan Green on Polya Counting

Presenter: Nathan Green

Department of Mathematics, Texas A&M University

Abstract: Polya counting theory allows us to count how many ways there are to arrange objects taking symmetry into account. For example, how many different bracelets can we make using only 3 colors of beads? How many ways can we color a cube using n colors? This counting technique has been used to count the number of different molecules which can be formed from certain sets of atoms and many other important applications.

October 28, 2017

Beginner Group – Philip Yasskin on Playing with Toilet Paper

Presenter: Philip Yasskin

Department of Mathematics, Texas A&M University

Abstract: We will solve a series of problems associated with folding toilet paper.

Intermediate Group- Maurice Rojas on Guessing, Sorting, and Optimizing

Presenter: Maurice Rojas

Department of Mathematics, Texas A&M University

Abstract: The log function is something we should all know. In this activity, we’ll see how log pops up in the game of “high-low”, and in algorithms for sorting. We’ll then see log again appears in an interesting geometric problem: How do you find the rectangle with axis-parallel sides of largest area inside a polygon? We’ll see how this geometric problem is practically important in architectural design.

Advanced Group – Edriss S. Titi on What is mathematics? A journey through examples.

Presenter: Edriss S. Titi

Department of Mathematics, Texas A&M University

Abstract: Why the honeycomb has hexagonal cell shapes? Is it because bees are lazy, unlike what is commonly believed!! Remarkably, a new mathematical framework has to be invented, every now and then, in order to answer intriguing, yet simple, questions of the kind mentioned above. In this lecture, I will provide few other simple examples, that have played fundamental role in advancing mathematics, as an additional support of this observation.

October 14, 2017

Beginner Group – Amudhan Krishnaswamy-Usha on Primes

Presenter: Amudhan Krishnaswamy-Usha

Department of Mathematics, Texas A&M University

Intermediate Group- Philip Yasskin on Axiomatic Finite Geometries

Presenter: Philip Yasskin

Department of Mathematics, Texas A&M University

Abstract: We will study geometries with a finite number of points and lines satisfying a set of axioms.

Advanced Group – Igor Zelenko on Sums of kth Powers

Presenter: Igor Zelenko

Department of Mathematics, Texas A&M University

Title: Sums of kth powers: from telescopic sums and Lagrange interpolations to Bernoulli numbers and Euler-Maclaurin formula

Abstract: The formula for the sum of first n positive integers is taught in school. What is the sum of their squares, cubes etc? During this class, we will learn various methods to derive the formulas for these sums from more elementary to more advance.

September 30, 2017

Beginner Group – Kagan Samurkas on Mathematical Games of Strategy

Presenter: Kagan Samurkas

Department of Mathematics, Texas A&M University

Abstract: Some mathematical games that one part has a winning strategy.

Intermediate & Advanced Groups – Sherry Gong on Algebra Tricks for Math Contests

Presenter: Sherry Gong

Massachusetts Institute of Technology

September 23, 2017

Beginner Group – David Sykes on Euclid’s Algorithm

Presenter: David Sykes

Department of Mathematics, Texas A&M University

Abstract: We will explore properties of common divisors. In particular we will discuss how to find greatest common divisors using the Euclidean algorithm, and we will investigate why the Euclidean algorithm works.

Intermediate & Advanced Groups – Dr. Zuming Feng on An Example on Math Learning via Classroom, Extra Extracurricular, and Contest Activities

Presenter: Dr. Zuming Feng

Phillips Exeter Academy

Proof School Board member

Cogito, part of Johns Hopkins University’s CTY SET program Board member

Former coach of the USA International Mathematics Olympiad (IMO) team

September 16, 2017

Beginner Group – Amudhan Krishnaswamy-Usha on A Few Easy Tests for Divisibility

Presenter: Amudhan Krishnaswamy-Usha

Department of Mathematics, Texas A&M University

Abstract: I will present some tests for divisibility by small numbers, and introduce modular arithmetic and congruence to explain why they work.

Intermediate Group – Frank Sottile on The Five Color Theorem

Presenter: Frank Sottile

Department of Mathematics, Texas A&M University

Abstract: Doodling on a map of England in 1852, Francis Guthrie noticed that only four colors were needed to color the counties. He conjectured that any map could be colored with only four colors. Several mathematicians tried and failed to prove this; notably in 1879 Kempe published a proof and only in 1890 was the flaw found by Heawood. This four color conjecture evaded a proof until 1972, when Appel and Haken gave a proof that required a computer. While there is as yet no Human readable proof, Kempe’s argument suffice to prove that five color suffice, and this gives a flavor of known proofs of the four color theorem. I will sketch this history and prove the five color theorem.

Advanced Group – Alex Sprinston on Cracking the Code

Presenter: Alex Sprintson

Department of Engineering, Texas A&M University

Abstract: We will provide a brief overview of the fundamentals and applications of the coding theory. First, we will focus on efficient error and erasure correcting codes. Then, we will discuss network codes and codes for distributed storage.

May 6, 2017

Beginner group – Ola Sobieska

Presenter: Ola Sobieska

Department of Mathematics, Texas A&M University

Intermediate & Advanced Groups – Preston Wood on Variant – Limits Game

Presenter: Preston Wood

Triseum – Game Designer

Abstract: Limits is an Educational Game developed by Triseum to help students learn about the Calculus topic of Limits. For more information see https://triseum.com/calculus/variant/

April 29, 2017

Beginner group – Alex Sprintson & Michael Sprintson on the Mathematics of Sorting Algorithms

Presenter: Alex Sprinston & Michael Sprinston

Department of Electrical and Computer Engineering, Texas A&M University

AMCMS

Abstract: Sorting is a fundamental operation in the theory of algorithms and a building block for many computer programs. The activity will lead the students to think about efficient algorithms for sorting information. We will start with a simple exercise in strategic thinking that focuses on determining the ranking of football teams based an a partial information. Next, we will discuss systematic ways to design efficient sorting algorithms. Finally, we present tools for analyzing the complexity of sorting algorithms.

Intermediate & Advanced Groups – Isaac Harris on Introduction to Fractals-The Concept of Measure and Dimension

Presenter: Isaac Harris

Department of Mathematics, Texas A&M University

Abstract: We will look at how geometric quantities are measured. We normally think of length as 1 dimension, area as 2 dimensions and volume as 3 dimensions. Using a simple limiting process we will see that there are dimensions that are not whole numbers! This will lead us to consider the mathematical concept of Fractals and how one get these other dimensions for measurements.

April 22, 2017

Beginner Group: Maya Johnson on Humans vs. Aliens

Presenter: Maya Johnson

Department of Mathematics, Texas A&M University

Abstract: A group of 6 humans are abducted by aliens in the night. Each of these 6 humans represent one sixth of the human population on the planet. The aliens tell the humans that in the morning they will order them in a single file line and place either a green or a purple hat on top of each person’s head. Each of the humans will then be able to see all of the hats a top the heads of all the persons in front of them, but will not be able to see their own hat or the hats of the people behind them. For example, the very last person in line will be able to see the hats of all five people in front of them, the second to last person can see the hats of all four people in front of them and so on. The aliens say they will then start at the back of the line and ask each person for the color of the hat on their own head. The person is only allowed to answer either green or purple, they are not allowed to say any other words. If the person answers correctly, then that person, along with the one sixth of the population that they represent, will live. However, if they answer incorrectly, the opposite will happen. The aliens are not entirely evil, however, and so they give the humans the night to come up with a strategy.

The problem facing the humans is this: what is the optimal strategy? That is, how can they save as many of themselves as possible, thereby saving as much of the human race as possible? There is a strategy that will guarantee the lives of all but one of them, but it requires a brave sacrifice from one of the 6 humans. Of course this human would jump at the chance to save five sixth of the human population, but what is the strategy? Also, what would be the minimum number of humans that would need to make the ultimate sacrifice if there were more than two color options for the hats? Help the humans out smart the aliens and save the human race with Math and logic!

Intermediate & Advanced Groups: Roger Howe on Rules of Arithmetic

Presenter: Roger Howe

Department of Mathematics, Texas A&M University

Abstract: We will take a more in-depth look at the Rules of Arithmetic than is usual in school. They have some very important implications for arithmetic, and they can lead to some fun mathematics.

April 8, 2017

Beginner Group: Philip Yasskin on Eleusis

Presenter: Dr. Philip Yasskin

Department of Mathematics, Texas A&M University

Abstract: We will play a game that models scientific research.

Intermediate & Advanced Groups: Doug Hensley on Why is Long Division Serious Mathematics?

Presenter: Dr. Doug Hensley

Department of Mathematics, Texas A&M University

Abstract: The short answer is that it’s at the heart of the Euclidean algorithm, and that this algorithm is, in turn, the key to such computational mathematical challenges as, given integers a, b, and p (p prime or failing that, a and b relatively prime to p), finding c so that bc is congruent to a mod p. From a certain point of view, this is again division, as we can say c=a/b mod p.

March 4, 2017

Beginner & Intermediate Group: Philip Yasskin on Unexpected Probabilities

Presenter: Philip Yasskin

Texas A&M University, Department of Mathematics

Abstract: We will look at 2 probability problems. First we will guess the answer. Second we will find the probability experimentally. And third we will compute the probability theoretically.

Advanced Group: Nathan Green on Primes

Presenter: Nathan Green

Texas A&M University, Department of Mathematics

Abstract: Prime numbers have been studied since ancient history, and in modern times they are doubly important, having crucial applications to cryptography and computer security. We will discuss some of the basic theory of prime numbers, with particular emphasis on large prime numbers which come up in computer applications.

Feb. 25, 2017

Beginner Group: Janice Epstein on Magic Squares

Presenter: Janice Epstein

Texas A&M University, Department of Mathematics

Intermediate Group: Yeong Chung on The Math of Origami

Presenter: Yeong Chung

Texas A&M University, Department of Mathematics

Abstract: It is easy to divide a square sheet of paper into two equal parts, but how can we divide a square sheet of paper into three (or five or six) equal parts without using any tools? By investigating some ways of folding the paper, we will come up with a way to divide the paper into various numbers of equal parts. We may then also try to divide a rectangular sheet of paper into equal parts both horizontally and vertically.

Advanced Group: Maurice Rojas on Counting Lattice Points in Polygons

Presenter: Maurice Rojas

Texas A&M University, Department of Mathematics

Abstract: If you draw a polygon on a grid, you can try counting

the grid points (also called lattice points) insie the polygon.

This simple problem is at the heart of many deep ideas in combinatorics

and optimization. We’ll work out some basic examples, and see surprising

connections to geometric series, the computation of area, clever ways

to chop up regions into weighted regions. Be prepared to count!

Feb. 18, 2017

Beginner Group: Jane Long on A Math Without Words Puzzle

Presenter: Jane Long

Stephen F. Austin State University, Department of Mathematics

Abstract: Many people who enjoy mathematics also enjoy games and puzzles. Generally, when people meet a new puzzle or game, they begin by reading or talking about rules or instructions. In this session, we will take a different approach: we will examine an intriguing puzzle in the form of a picture with no description or instructions. It will be up to us to discover the rules and solve the puzzle!

Advanced and Intermediate Group: Nick Long on Which One Doesn’t Belong

Presenter: Nick Long

Stephen F. Austin State University, Department of Mathematics

Abstract: When you look at the set of letters {A, B,C, D}, which one doesn’t belong? Your answer might be that A is a vowel or that C does not contain a closed loop. Can you come up with a way that B doesn’t belong? What about D? We will look more at how to distinguish the elements of a set by which one does not belong and how to build interesting sets for this kind of discussion.

Feb. 11, 2017

Physics Show

Presenter: Tatiana Erukhimova

Texas A&M University, Department of Physics & Astronomy

The Math Circle will be visiting the Physics Department this week for their famous Physics Show.

Feb. 4, 2017

Beginner Group: Kun Wang on Penny Problems

Presenter: Kun Wang

Texas A&M University, Department of Mathematics

Abstract: We will play some games with pennies. Those games are about geometry, combinatorics, probability, etc.

Intermediate Group: Alan Demlow on An Introduction to Floating Point Arithmetic

Presenter: Alan Demlow

Texas A&M University, Department of Mathematics

Abstract: Computers are used in almost every facet of life. They enable us to predict the weather, how planes will behave in flight, and whether a bridge design will be sturdy. They also are used to control many systems, such as cars and guided missiles. Modern computers use a number system called the floating point system in order to do these calculations. We will describe floating point numbers. Students will investigate some examples where floating point arithmetic has different properties than the arithmetic we are used to. We’ll also give some examples of computer simulations that failed, leading to disastrous results!

Advanced Group: Philip Yasskin on Domino Circle & Diagonals

Presenter: Philip Yasskin

Texas A&M University, Department of Mathematics

Abstract: Problem (1) Each Domino has two halves and each half has a number usually from 0 to 6. A full set has one of each pair of numbers from double 0 to double 6. Can a full set of 0-6 dominoes be placed end to end in a circle so that every two adjacent dominoes have the same number on the adjacent halves?

Problem (2) We will count the number of diagonals in a rectangular grid with certain restrictions on which diagonals to count.

Jan. 28, 2017

Beginner Group: David Manuel on Tangram Origami

Presenter: David Manuel

Texas A&M University, Department of Mathematics

Abstract: Given seven identical square sheets of paper, is it possible using simple origami folding techniques to create each of the seven tangram pieces used to build the square?

Intermediate Group: Dean Baskin on Euler Numbers

Presenter: Dean Baskin

Texas A&M University, Department of Mathematics

Abstract: The Euler number of a shape is the sum V + F – E, where V is the number of vertices in the shape, E is the number of edges, and F is the number of faces. How does this number depend on the shape we draw (or build)?

Advanced Group: Volodymyr Nekrasheyvich on A Diophantine Equation and Uniform Tilings

Presenter: Volodymyr Nekrasheyvich

Texas A&M University, Department of Mathematics

Abstract: I will to talk about the equations in natural numbers of the form

1/a+1/b+1/c+1/d=1 and its relation to geometry.

Jan. 21, 2017

Beginner Group: Kun Wang on Card Games and Combinatorial Problems

Presenter: Kun Wang

Texas A&M University, Department of Mathematics

Abstract: We will find a way to order poker cards so that the numbers

appear in a magical way. After that we will solve some combinatorial

problems.

Intermediate Group: Philip Yasskin on Domino Circles

Presenter: Philip Yasskin

Texas A&M University, Department of Mathematics

Abstract: Each Domino has two halves and each half has a number usually from 0 to 6. A full set has one of each pair of numbers from double 0 to double 6. Can a full set of 0-6 dominoes be placed end to end in a circle so that every two adjacent dominoes have the same number on the adjacent halves?

Advanced Group: Alexander Engel on Zero-Knowledge Proofs

Presenter: Alexander Engel

Texas A&M University, Department of Mathematics

Abstract: In a zero-knowledge proof one proves to someone else that one has a certain secret information or that a certain statement is true without conveying any other information, i.e., the other party does not get any knowledge about the secret information or the statement. We will discuss examples of such zero-knowledge proofs in a variety of contexts.

Dec. 3rd, 2016

Beginner Group: Philip Yasskin on Domino Circles

Presenter: Philip Yasskin

Department of Mathematics , Texas A&M University

Abstract: Each Domino has two halves and each half has a number usually from 0 to 6. A full set has one of each pair of numbers from double 0 to double 6. Can a full set of 0-6 dominoes be placed end to end in a circle so that every two adjacent dominoes have the same number on the adjacent halves?

Intermediate Group: Tamara Carter on CLUE in the Math Department

Presenter: Tamara Carter

Department of Mathematics, Texas A&M University

Abstract: Students will explore ciphers, decipher clues, and use those clues to find the prize.

Advanced Group: Konrad Wrobel on Distinct Distances in the Plane

Presenter: Konrad Wrobel

Department of Mathematics, Texas A&M University

Abstract: We will look at collections of points with exactly 2 distinct distances between them and try to investigate all such collections. We’ll also work on some other problems in Euclidean geometry.

Nov. 19th, 2016

Beginner Group: Alex Sprinston on Design of Combinational Circuits Using Boolean Algebra

Presenter: Alex Sprinston

Department of Electrical and Computer Engineering , Texas A&M University

Abstract: We will start with a quick introduction to Boolean Algebra. Then, we will show how to use the rules of Boolean Algebra to construct simple logic circuits. Finally, we will introduce Karnaugh maps and show how to use them to design more efficient circuits.

Intermediate Group: R. Saravanan on Hash functions, Cryptography

Presenter: R. Saravanan

Department of Atmospheric Sciences, Texas A&M University

Advanced Group: Peter Kuchment on Unreasonable Effectiveness of Mathematics

Presenter: Peter Kuchment

Department of Mathematics, Texas A&M University

Abstract: Since antiquity, and especially nowadays mathematicians have been developing extremely abstract concepts, having no clear relation to reality, and “play” with them according to seemingly rather arbitrarily invented rules. In many (maybe most of) cases, the trigger for such developments is the aesthetic feeling of mathematical beauty. In this regard, mathematics is similar to other games, such as chess, go, and others. However, for some inexplicable reason, unlike other games, the mental math constructions eventually are applicable for producing practically useful results in natural sciences and engineering. The talk will be addressing this intriguing issue.

Nov. 5th, 2016

Beginner Group: Eviatar Procaccia on Folding the Platonic Solids

Presenter: Eviatar Procaccia

Department of Mathematics , Texas A&M University

Abstract: The Greek philosopher Plato believed true beauty exists only in a few geometric shapes we now call the Platonic solids. We will learn why there are only five of them, and fold some of them in paper.

Intermediate Group: Parth Sarin on How Fast Can You Gossip?

Presenter: Parth Sarin

TAMU Math Circle Organizer

Undergraduate in Department of Mathematics, Texas A&M University

Abstract: From visiting a website to making a call, modern society depends on our ability to exchange information online. But, modern computers can’t multi-task well – they can only exchange one piece of information at a time. We’ll explore how even with this limitation, networks of computers exchange information quickly and intelligently in order to keep our lives up to date.

Oct. 15, 2016

Beginner Group: Tamara Carter on CLUE in the Math Department

Presenter: Tamara Carter

Department of Mathematics, Texas A&M University

Abstract: Students will explore ciphers, decipher clues, and use those clues to find the prize.

Intermediate Group: Jens Forsgård on The a+b+ab Problem

Presenter: Jens Forsgaard

Department of Mathematics, Texas A&M University

Abstract: Write down the numbers from 1 to 100. Randomly select 2 numbers from the list, say a and b, and cross them off, but add to the list the number a+b+ab. You now have 99 numbers. Repeat this process until you have only 1 number left. What are all possible final numbers?

Advanced Group: Kim Currens & Dr. Sandra Nite on Modeling Sound Waves with Periodic Functions

Presenters: Kim Currens & Dr. Sandra Nite

Department of Mathematics, Texas A&M University

Abstract: We will use graphing calculators, calculator based laboratory (CBL), and probes to collect sound wave data. Then we will use at least two methods to model the data with a periodic function.

Oct. 8, 2016

Beginner Group: Dr. Robert Capraro on Counting Cows & 3 Bean Salad

Presenter: Dr. Robert Capraro

Department of TLAC, Texas A&M University

Abstract: For “Counting Cows” students will use cubes to organize thinking and solve algebraic problems in the context of cows in different pastures. In “3 Bean Salad” students use several types of beans to represent salad mixtures and solve equations to determine the total number of beans in the salad.

Intermediate Group: Dr. Mary Margaret Capraro on Locker Problem, Arithmagons, Magic Squares

Presenter: Dr. Mary Margaret Capraro

Department of TLAC, Texas A&M University

Abstract: These 3 problems use algebraic thinking by building habits of mind. The locker problem will focus on building rules to represent functions and doing-undoing. Arithmagons use a simple system of equations, and students will utilize intuitive and informal operation sense. The magic square problems will help develop symbol sense by requiring decisions as to when it is appropriate to invoke the use of symbols and also understand the meaning of symbolic solutions.

Advanced Group: Dr. Luciana Barroso & Dr. Sandra Nite on Exploring Lung Capacity

Presenter: Dr Luciana Barroso & Dr. Sandra Nite

Department of TLAC and Mathematics, Texas A&M University

Abstract: Students will use graphing calculators and calculator based laboratory (CBL) to gather and examine data for lung capacity.

Oct. 1, 2016

Beginner Group: David Kerr on Random Walks and Search Engines

Speaker: David Kerr

Department of Mathematics, Texas A&M University

Topic: Random Walks and Search Engines

Abstract: Abstract:

We will investigate the notion of chance by performing experiments with random walks, and see how this can be applied to the problem of internet search.

Intermediate Group: Riad Masri on Explorations with Prime Numbers

Speaker: Riad Masri

Department of Mathematics, Texas A&M University

Title: Explorations with Prime Numbers

Abstract: In this activity we will explore some of the many interesting properties of prime numbers. First, we will learn how to find prime numbers using a “sieve”. We will then study questions related to differences between consecutive primes, and the distribution of primes in residue classes.

Advanced Group: Zoran Sunic on “Wait, was I supposed to turn left or right?”

Speaker: Zoran Sunic

Department of Mathematics, Texas A&M University

Topic: Wait, was I supposed to turn left or right?

Abstract: We will consider journeys through a kingdom in which there are three roads out of every town, and the roads only intersect at the towns. Our knight will travel around, do a good deed here and there, and will have strange ideas how to get home. We will try to find out if he ever does get home, how many times he visits the same town along the way, and how long his journeys could be.

Sept. 24, 2016

Beginner & Intermediate Group: Philip Yasskin on Trapezoid Numbers

Presenter: Philip Yasskin

Department of Mathematics, Texas A&M University

Abstract: Modern cryptography gives us intricate ways to safely share secrets and protect private information. But some of the underlying ideas are very simple. We’ll see how these ideas come together in a method to share a private key when communicating over a public channel.

Advanced Group: Maurice Rojas on Gift Boxes, Mongoose in the Middle, and Secret Codes

Presenter: Maurice Rojas

Department of Mathematics, Texas A&M University

Abstract: Modern cryptography gives us intricate ways to safely share secrets and protect private information. But some of the underlying ideas are very simple. We’ll see how these ideas come together in a method to share a private key when communicating over a public channel.

Sept. 17, 2016

Beginner Group: Ola Sobieska on Even and Odd Numbers

Presenter: Ola Sobieska

Department of Mathematics, Texas A&M University

Abstract: In this activity, we will explore the topic of odds and evens, including various ways to define these numbers, learn several useful properties, and investigate how to apply them to problem solving.

Intermediate Group: Dr. Ali Bicer & Dr. Sandra Nite on Dilutions

Presenters: Dr. Ali Bicer & Dr. Sandra Nite

Department of Mathematics and Department of Teaching, Learning and Culture, Texas A&M University

Abstract: This activity will use food coloring and water to perform dilutions at several levels and then decide what level water with poisons will be safe to drink.

Advanced Group: Philip Yasskin on Axiomatic Finite Geometries

Presenter: Philip Yasskin

Department of Mathematics, Texas A&M University

Abstract: We will study geometries with a finite number of points and lines satisfying a set of axioms.

May 14, 2016

Beginner and Intermediate Groups: Kaitlyn Phillipson on Math Games

Presenter: Kaitlyn Phillipson

Department of Mathematics, Texas A&M University

Abstract: We’ll discuss some games and try to come up with winning strategies.

Advanced Group: Riad Masri on the Arithmetic of Integer Partitions

Presenter: Riad Masri

Department of Mathematics, Texas A&M University

Abstract: The goal of this project is to explore some arithmetic aspects of integer partitions. In particular, we will focus on Ramanujan’s famous congruences for the partition function, and study how the Dyson rank and the Andrews/Garvan crank can be used to give a combinatorial explanation for these congruences.

May 7, 2016

Beginner Group: Philip Yasskin on Balance Beams

Presenter: Philip Yasskin

Department of Mathematics, Texas A&M University

Abstract: We use a meter stick as a balance beam with a pencil at the 50 cm mark. In each problem, we put weights at the locations indicated and experiment to figure out where to put the extra weights. We will progress to using equations to figure out where to put the weights.

Intermediate Group: Gregory Berkolaiko on Icosahedron Made from Scratch

Presenter: Gregory Berkolaiko

Department of Mathematics, Texas A&M University

Abstract: The task is to make an icosahedron from scratch using only paper and glue (plus compass, ruler, scissors and pencil). Along the way we will need to solve the problem of dividing the circle into the equal parts lengthwise.

Advanced Group: Timo de Wolff on Public Key Cryptography

Presenter: Timo de Wolff

Department of Mathematics, Texas A&M University

Abstract: Cryptography handles with the secure transmission of secret messages. More precisely, a third party is supposed to be unable to understand the content of an intercepted message if it is encrypted. Classically, both parties exchange secret keys for a secure en- and decryption. Nowadays, however, a lot of communication happens via insecure channels like the internet. Thus, secret keys often cannot be exchanged securely. Thus, one needs a new type of crypto system, in which parts of the keys do not need to be hidden anymore. This is called public key cryptography. In this talk we will first review a couple of classical symmetric crypto systems like the Ceasar cipher. In the second part I will explain and show the RSA crypto system, which is the current industry standard for public key cryptography.

April 30, 2016

Beginner Group: Frank Sottile on Meet the Cube

Presenter: Frank Sottile

Department of Mathematics, Texas A&M University

Abstract: We will investigate the familiar cube, using it

to study three-dimensional geometry.

Intermediate Group: Christopher O’Neill on When Can You Draw a Picture Without Picking Up Your Pencil?

Presenter: Christopher O’Neill

Department of Mathematics, Texas A&M University

Abstract: Suppose someone hands you a picture and asks you to trace it in one continuous motion, that is, without picking up your pencil or backtracking. When is it possible to succeed? How should you decide where to start tracing?

Advanced Group: Eric Rowell on Mathematical Knots and Links

Presenter: Eric Rowell

Department of Mathematics, Texas A&M University

Abstract: Knots and links have been used as decorations for centuries, but their mathematical study only began in the 19th century. For a brief period it was believed that atoms were just knotted bits of swirling ether, and physicists set to work to tabulate them. It turned out they were completely wrong, but this led to the development of topology. More than 100 years later, knots may again be useful in physics though Topological Quantum Computation. We will explore important questions surrounding knots and links, such as: how do we know when two knots are actually the same? How can we tell that they are genuinely different?

April 23, 2016

Beginner Group: Roger Howe on Around the Pythagorean Theorem

Presenter: Roger Howe

Department of Mathematics, Yale University

Abstract: This session will discuss a few of the many applications of the Pythagorean Theorem in the real world. Among the questions to be considered will be, why do ladders work, taking shortcuts, and how far can we see?

Advanced Group: David Dynerman on Normal Mapping and Video Games

Presenter: David Dynerman

Department of Mathematics, University of California, Berkley

Abstract: Normal mapping is a way of increasing surface detail when rendering 3D graphics and has become a standard technique in the video game industry. Normal mapping sneaks in higher quality lighting detail over a lower-quality polygonal model. This talk will give an overview on how this interesting application of math, computer science and physics creates better looking video games.

March 26, 2016

Beginner Group: Ola Sobieska on Weighings and Counterfeit Coins

Presenter: Ola Sobieska

Department of Mathematics, Texas A&M University

Abstract: This session will focus on problems about balance scales and weights. The students will learn to identify counterfeit coins, discover tricky ways to weigh objects, and solve other puzzles.

Intermediate Group: David Sykes on Dinner Party Problems and Graph Coloring

Presenter: David Sykes

Department of Mathematics, Texas A&M University

Abstract: We will be discussing the Dinner Party Problem along with some of its generalizations while exploring the concept of graph coloring. The problems are special cases of a theorem established by Frank Ramsey around 1930. The discussion will build towards the solution to a challenging Ramsey Theory problem along with the statement of problems that remain unsolved today.

Advanced Group: Matt Young on Which Numbers are Sums of Two Squares?

Presenter: Matt Young

Department of Mathematics, Texas A&M University

Abstract: Some numbers are the sum of two squares, and some numbers aren’t. For example, 5 is (since 5 = 1 +4) but 7 isn’t. Numbers that can be expressed as the sum of two squares have many amazing properties, and we will discover many of these patterns in this math circle.

March 5, 2016

Beginner Group: Phil Yasskin on Splitting Piles and Handshakes

Presenter: Phil Yasskin

Department of Mathematics, Texas A&M University

Abstract: We will consider 2 problems and ultimately see how they are related.

1) Take a pile of coins, say 10 coins. Split it into two piles, with say 4 and 6 coins. Write down the product 4*6=24. Split each of those piles into two piles, with say 1 and 3, and say 2 and 4. Write down those products 1*3=3 and 2*4=8. Continue in this way until you have ten plies each with 1 coin. Then add all the products, say 24+3+8+… What are all possible sums?

2) If 10 people are in a room, how many ways can they shake hands?

Intermediate Group: Eviatar Procaccia on The Gambler’s Ruin and a Disoriented Bird

Presenter: Eviatar Procaccia

Department of Mathematics, Texas A&M University

Abstract: Probability theory is the mathematical framework to study randomness in the universe. We will learn how to use one source of randomness to create another and why a disoriented bird will never find its nest.

Advanced Group: Volodymyr Nekrashevych on Binomial Coefficients and Their Properties

Presenter: Volodymyr Nekrashevych

Department of Mathematics, Texas A&M University

Abstract: We will discuss Pascal’s triangle, binomial coefficients, combinations, triangular numbers, and different interesting facts about them.

February 27, 2016

Beginner and Intermediate Group: Michelle Pruett on Code-Breaking Through the Years

Presenter: Michelle Pruett

Texas State University at San Marcos

Abstract: A variety of codes have been used throughout history. We will discover how

to code and decode messages using several techniques.

Advanced Group: Konrad Wrobel on Dealing with Infinite Sets

Presenter: Konrad Wrobel

Department of Mathematics, Texas A&M University

Abstract: The roots of modern day set theory stem from Georg Cantor’s work in 1874, when he introduced several concepts that many mathematicians of the time found disconcerting. We’ll delve into his notion of size, or cardinality, and what it means when applied to infinite sets.

February 20, 2016

Beginner Group: Anneliese Slaton on The Bridge Problem: A Puzzle That Changed the Mathematical World

Presenter: Anneliese Slaton

Undergraduate Student at George Mason University

Abstract: We will be discussing The Koningsberg Bridge Problem, a seemingly simple problem that was solved by Euler and opened the door to the development of graph theory as we know it. We will not only look at Euler’s original proof, but will explore variations of the problems in physically get up and try to walk to the path!

Intermediate Group: Igor Zelenko on Domino Puzzles, Invariants, and Walking Along the Grids and Bridges

Presenter: Igor Zelenko

Department of Mathematics, Texas A&M University

Abstract: During the activity we will try to solve various problems regarding covering grids by dominos, trominos, transforming the tables of numbers according to certain rules, moving along grids without raising a pencil, or walking along the bridges of cities with many bridges. In all these problems we will ask whether we can complete certain tasks, the answer will often follow from certain nontrivial observations or properties of certain quantities, called invariants, that are preserved by natural transformations allowed in the problem.

Advanced Group: Ramalingam Saravanan on Predictability of Weather and Climate

Presenter: Ramalingam Saravanan

Department of Mathematics, Texas A&M University

Abstract: The discovery of the limits to weather predictability by Edward Lorenz was a seminal event both in theoretical meteorology and in nonlinear dynamics. The mathematical and physical basis for the predictability of weather and climate will be discussed in the context of this discovery. Topics to be covered will include trigonometric functions, limit cycles, and chaotic attractors.

February 13, 2016

Beginner Group: Frank Sottile on Word Problems and Common Sense

Presenter: Frank Sottile

Department of Mathematics, Texas A&M University

Abstract: While we are taught to use algebra to solve word problems, many can be solved just using common sense. In this circle, we will use our common sense to solve word problems.

Intermediate Group: Maurice Rojas on Hats, Codes, and Lattice Points

Presenter: Maurice Rojas

Department of Mathematics, Texas A&M University

Abstract: We will see how a puzzle involving hats relates to codes that help protect data from noise. We’ll then see how lattice points come up in many different mathematical puzzles, as well as the modern study of secret codes.

Advanced Group: William Rundell on A 5,000 Year History into Mathematical Innovation

Presenter: William Rundell

Department of Mathematics, Texas A&M University

Abstract: Here are a series of questions. How does your calculator come up with it’s approximation to the square root of, say, 2? How were the square roots calculated in antiquity? Is there anything new to say about the problem? This talk will explore some of the answers.

February 6, 2016

Beginner Group: Frank Sottile on Mathematical Auction

Presenter: Professor Frank Sottile

Department of Mathematics, Texas A&M University

Abstract: We will be doing a team contest called ‘mathematical auction.’

Intermediate Group: Phil Yasskin on The a+b+ab Problem

Presenter: Professor Phil Yasskin

Department of Mathematics, Texas A&M University

Abstract: Write down the numbers from 1 to 100. Randomly select 2 numbers from the list, say a and b, and cross them off, but add to the list the number a+b+ab. You now have 99 numbers. Repeat this process until you have only 1 number left. What are all possible final numbers?

Advanced Group: Maurice Rojas on Polygons, Lattice Points, and Equations

Presenter: Professor Maurice Rojas

Department of Mathematics, Texas A&M University

Abstract: We’ll see how geometric series and the Triangle Inequality allow us to understand hard equations with simple pictures. We’ll then see how counting lattice points in polygons leads us to some beautiful and unexpected applications of mathematics.

September 19, 2015

Beginner Group: Frank Sotille on How to Solve a Problem

Presenter: Frank Sotille

Department of Mathematics, Texas A&M University

Abstract: We will work together to solve and discuss some

interesting puzzles and problems.

Intermediate Group: Phillip B. Yasskin on The Candy Conundrum

Presenter: Philip B. Yasskin

Department of Mathematics, Texas A&M University

Abstract: A candy company wants to a advertise the large number of flavors that can be made by mixing candies in your mouth. Let’s figure it out.

Advanced Group: Kaitlyn Phillipson on Catalan Structures

Presenter: Kaitlyn Phillipson

Department of Mathematics, Texas A&M University

Abstract: The Catalan numbers are one of the most common sequences in mathematics. There are many structures counted by the Catalan numbers, and in this activity we take a look at several of them.

April 25, 2015

Matthew Barry – Turk’s Head Knots

Title: Turk’s Head Knots

Speaker: Matthew Barry (with help from Philip Yasskin and Michael Sprintson) (Texas Engineering Extension Station, TAMU Class of 2014)

Abstract: The Turk’s head knot, flat mat, and pineapple knot all belong to a family of interwoven decorative knots favored by many people for many centuries, notably the Celtics. In its final form, the turks head knot is a symmetric prime knot that can be classified by the number of intersections the rope makes with itself. In the knot-tying community, Turk’s head knots are classified by counting leads and bights: the lead count is the number of times the rope goes around the knot, and the bight count is the number of loops at each end. For example a 3×5 Turk’s head knot has three leads and five bights. Here we explore the math theory behind these knots and use it to plan and tie Turk’s head knots of any size.

March 7, 2015

Beginner / Intermediate

Speaker Ms. Kaitlyn Phillipson

Department of Mathematics

Texas A&M University,

Title: Guarding an Art Gallery

Abstract: We will discuss the “Art Gallery Problem,” a well-studied problem in mathematics.

Advanced

Speaker: Dr. Nicholas Long

Department of Mathematics

Stephen F. Austin State University

Title: “Pressing Buttons on a Calculator.”

Abstract: One of the first things kids do when they start playing with a calculator is explore what happens to the screen when you keep hitting the same button over and over. We can figure out pretty quickly what happens when we keep pressing the addition or multiplication buttons. What happens if we had some buttons on a calculator that used multiplication and addition together? What would the result be if we keep pressing a button like that?

February 28, 2015

Beginner / Intermediate

Speaker: Dr. Altha Rodin

Department of Mathematics

University of Texas

Title: The Next Move: Some Theory and Practice with Impartial Games

We will discuss combinatorial impartial games defined as follow.

Combinatorial games are two-player games with the following characteristics:

* Two players alternate moves.

* Play continues until there are no legal moves remaining.

* No element of chance is involved (i.e. dice, spinners, etc.).

* Each player has full knowledge of the game position at all times.

In normal play, the last player to make a legal move wins. In misère play, the last player to make a legal move loses. A combinatorial game is called impartial if both players have the same set of allowable moves at each position of the game. A game in which the allowable moves depends on the player is called a partisan game.

Advanced

Speaker: Dr. Lucas Macri

Department of Physics & Astronomy

Texas A&M University

Title: The Mathematics of Astronomy (part I)

In this class, we will talk about the math used by ancient astronomers to learn about the Universe even before the telescope was invented. How did they determine the size of Earth, the distance to the Moon and the Sun? We will also talk about how we can measure the distances to other stars and figure out how much light they produce.

February 21, 2015

Beginner

Speaker: Dr. Lucas Macri

Department of Physics & Astronomy

Texas A&M University

Title: The Mathematics of Astronomy (part I)

In this class, we will talk about the math used by ancient astronomers to learn about the Universe even before the telescope was invented. How did they determine the size of Earth, the distance to the Moon and the Sun? We will also talk about how we can measure the distances to other stars and figure out how much light they produce.

Intermediate

Speaker Mr. Trevor Olsen

Department of Mathematics

Texas A&M University

Title: Kinetic Origami (Curlicue)

Abstract: Are you ready to make amazing shape changing origami? Well I sure am! We will be making Curlicues that go from being flat paper to different 3D shapes. We will understand how these structures work and learn what other types of Curlicues we can make.

Advanced

Speaker Dr. Igor Zelenko

Department of Mathematics

Texas A&M University

Title Sums of k’th powers and other interesting sums

Abstract: The formula for the sum of first n positive integers is taught in school. What is the sum of their squares, cubes etc? We will learn how to derive formulas for these sums and other interesting sums and give applications for calculating areas.

February 14, 2015

Beginner

Speaker: Dr. Phil Yasskin

Department of Mathematics

Texas A&M University

Title: GCD, LCM, Prime Factorization, and the Division and Euclidean Algorithms

Abstract:

I will present a series of problems whose solutions involve the Greatest Common Divisor, the Least Common Multiple, the Unique Prime Factorization Theorem, the Division Algorithm and/or the Euclidean Algorithm. For example:

Problem 1: You have an unmarked 5 liter bucket and an unmarked 9 liter bucket and an unlimited amount of water. Can you measure out exactly 2 liters of water? How?

Problem 2: How many 12 cent and 27 cent postage stamps should you buy to put exactly 83 cents worth of postage on an envelope?

Problem 3: You have a 3 foot by 5 foot pool table. The cue ball is located at a point which is 1 foot from the 5 foot side and 2 feet from the 3 foot side. You hit the ball at 45 degrees. Every time the ball hits a side it bounces back at 45 degrees with no loss of velocity. Will the ball eventually hit the corner of the pool table?

Intermediate

Speaker: Dr. Phil Yasskin

Department of Mathematics

Texas A&M University

Title: GCD, LCM, Prime Factorization, and the Division and Euclidean Algorithms

Abstract:

I will present a series of problems whose solutions involve the Greatest Common Divisor, the Least Common Multiple, the Unique Prime Factorization Theorem, the Division Algorithm and/or the Euclidean Algorithm. For example:

Problem 1: You have an unmarked 5 liter bucket and an unmarked 9 liter bucket and an unlimited amount of water. Can you measure out exactly 2 liters of water? How?

Problem 2: How many 12 cent and 27 cent postage stamps should you buy to put exactly 83 cents worth of postage on an envelope?

Problem 3: You have a 3 foot by 5 foot pool table. The cue ball is located at a point which is 1 foot from the 5 foot side and 2 feet from the 3 foot side. You hit the ball at 45 degrees. Every time the ball hits a side it bounces back at 45 degrees with no loss of velocity. Will the ball eventually hit the corner of the pool table?

Advanced

Speaker Ms. Kaitlyn Phillipson

Department of Mathematics

Texas A&M University,

Title: Guarding an Art Gallery

Abstract: We will discuss the “Art Gallery Problem,” a well-studied problem in mathematics.

January 24, 2015

Beginner / Intermediate

Speaker: Dr. Jane Long

Department of Mathematics

Stephen F. Austin State University

Title: The Mathematics of Sona, Sand Drawings from Africa

Abstract: Many cultures around the world tell stories with the help of drawings made in sand. This activity will investigate interesting mathematics involved in some traditional sand drawings from Angola.

Advanced

Speaker: Dr. David Manuel

Department of Mathematics

Texas A&M University,

Title: The Algebra of Rubik’s Cubes, part 3

Abstract: Many of us have learned how to solve the (3×3) Rubik’s Cube from solutions presented in a book or online. But how does one come up with their own solution? In this final session, we will apply what we have learned about groups, permutations, and partial commutativity to the movements of the Rubik’s Cube to develop our own strategies to solve the Cube. Bring your cubes, and, if possible, movements which exchange 2 cubes or rotate 1 cube in one row (regardless of what the other rows look like).