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2019-20 Academic Year Activities
2019-20 Academic Year Activities
September 28, 2019
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.
October 5, 2019
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.
October 26, 2019
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.
November 2, 2019
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.
November 16, 2019
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 23, 2019
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.
December 7, 2019
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).
December 14, 2019
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.
January 25, 2020
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.
February 1, 2020
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.
February 8, 2020
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 15, 2020
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 29, 2020
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.
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