### 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

### 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.