### 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.