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2016-2017 Academic Year Activities
2016-2017 Academic Year Activities
Sept. 17, 2016
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.
Sept. 24, 2016
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.
Oct. 1, 2016
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.
Oct. 8, 2016
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. 15, 2016
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.
Nov. 5th, 2016
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.
Nov. 19th, 2016
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.
Dec. 3rd, 2016
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.
Jan. 21, 2017
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.
Jan. 28, 2017
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.
Feb. 4, 2017
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.
Feb. 11, 2017
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. 18, 2017
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. 25, 2017
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!
March 4, 2017
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.
April 8, 2017
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.
April 22, 2017
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 29, 2017
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.
May 6, 2017
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/
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