# Current Academic Year

Upcoming Math Circle Meeting dates: 12/8, 1/26, 2/2, 2/9, 2/16, 2/23, 3/2, 3/23, 3/30, 4/13, 4/27, 5/4

### Upcoming Math Circle Activity: December 8th

**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

**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.

**Problem-Solving Beginner Group: BLOC 205**

**Instructor: **Dr. Shilin Yu, Texas A&M University

**Problem-Solving Intermediate Group: BLOC 203**

**Instructor: **Dr. Hao Guo, Texas A&M University

**Problem-Solving Advanced Group: BLOC 202**

**Instructors: **Dr. Zhizhang Xie and Dr. Guoliang Yu, Texas A&M University

### 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 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.

### October 13, 2018

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

**Speaker:**Erica Metheney, Grad Student at Texas A&M University

**Title: **The What, Why, and How of Random Samples

**Abstract:** We will discuss what makes a sample good or bad as well as what is special about random samples. After discussing what kind of questions we can answer using random samples, we will practice various methods for obtaining them.

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

**Speaker:** Frank Sottile, Texas A&M University

**Title: **Hyperbolic Soccer Ball

**Abstract:** We are all familiar with the basic Euclidean geometry of the plane, including the behavior of parallel lines and angles in triangles. This familiarity may lead us to that it is a law of nature that parallel lines are always the same distance apart and the sum of the angles of a triangle is 180 degrees. The purpose of this activity is to disabuse us of this misconception. We will do that by building and studying a beautiful and thought-provoking model of the hyperbolic plane.

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

**Speaker:** John Weeks, Grad Student at Texas A&M University

**Title: **Zermelo-Frankel Logic and the Banach-Tarski Paradox

**Abstract:** Mathematics desires to break down our reality into components where it can be understood by the use of logical deduction, but to do that we must make a few assumptions about how our universe works. We will discuss the most popular of these axiomatic systems and show how it still might not be good enough to accurately represent common-sense physical notions. To do this we will cut a candy bar into five pieces, do some fancy rotations, and end up with two candy bars so that we may begin a lucrative business enterprise.

### October 6, 2018

**Beginner Group: BLOC 220 **

**Speaker:**Patrick Orchard, Texas A&M University

**Title: **Towers of Hanoi

**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.

**Intermediate Group: BLOC 203 **

**Speaker: **David Kerr, Texas A&M University

**Title: **Search Engine

**Abstract: **We will explore and experiment with the idea of a random walk as a way for an internet search engine to generate a ranking of webpages, and see how this idea is implemented from a computation viewpoint through the use of matrices

**Advanced Group: BLOC 202 **

**Speaker:** Frank Sottile, Texas A&M University

**Title: **Hyperbolic Soccer Ball

**Abstract:** We are all familiar with the basic Euclidean geometry of the plane, including the behavior of parallel lines and angles in triangles. This familiarity may lead us to that it is a law of nature that parallel lines are always the same distance apart and the sum of the angles of a triangle is 180 degrees. The purpose of this activity is to disabuse us of this misconception. We will do that by building and studying a beautiful and thought-provoking model of the hyperbolic plane.

### September 29, 2018

**Beginner Group: BLOC 220 **

**Speaker: **Zhizhang Xie, Texas A&M University

**Title: **Mechanical Drawing

**Abstract:** We will draw various shapes only using a straightedge and a compass. For instance, we will learn how to draw an equilateral triangle, a square, a regular pentagon, and a regular hexagon. Basic techniques including bisecting an angle, finding a midpoint of a segment, and drawing a perpendicular line from a point to a line will be explained. Challenge: can you draw a regular heptagon?

**Intermediate Group: BLOC 203 **

**Speaker: **Volodia Nekrashavych, Texas A&M University

**Title: **Finding a Fake Coin and Other Algorithmic Puzzles

**Abstract: **We will solve and discuss a series of classical puzzles related to seeking information in the most efficient way. One of the classes of such puzzles is about finding an object of unusual weight. All of these puzzles are easy to formulate, but many of them are highly nontrivial and related to serious mathematical topics.

**Advanced Group: BLOC 202 **

**Speaker:** Roger Howe

**Title: **Products of Reflections

**Abstract:** We will study transformations of the plane, starting with reflections, and looking at what happens when several reflections are done in a row. This turns out to have some beautiful connections with triangle geometry, both classical and non-classical.

### September 22, 2018

**Beginner Group: BLOC 220**

**Speaker: **David Sykes, Texas A&M University

**Title: **Varignon Parallelograms

**Abstract:** This activity will guide students to discover a striking relationship between midpoints of sides of quadrilaterals. Afterwards we will explore why these patterns can be generalized.

**Intermediate Group: BLOC 203**

**Speaker: **Colleen Delaney, University of California-Santa Barbara

**Title: **Math of Quantum Materials

**Abstract: **In this workshop we'll use elementary and middle-school level math to explore the quantum world. We'll encounter the distributive property and sequences of numbers, but the only prerequisite is knowing our times tables! We will talk about what the word "quantum" means and the role that math plays in the physical sciences. We'll also learn how quantum materials might be used to build the next generation of computers.

**Advanced Group: BLOC 202**

**Speaker:** Philip Yasskin, Texas A&M University

**Title: **Search Engines

**Abstract:** If a search engine finds 5 websites which meet the criterion of a search, in what order should the results be listed (ignoring any financial incentive from the owner of the sites)? We will be learning about steady state vectors of probability matrices.

### September 15, 2018

**Beginner Group:**

**Speaker: **Guergana Petrova

**Title: **Area and Perimeter

**Abstract:** We will discuss strategies for solving problems related to area and perimeter of several geometric figures.

**Intermediate and Advanced Group: **

**Speaker: **Joonhyun La

**Title: **Usefulness of Studying Motions of Fluid

**Abstract:** In this talk I will briefly introduce the topic of fluid dynamics and its applications.

### September 8, 2018

**Beginner Group: BLOC 220**

**Speaker: **Philip Yasskin, Texas A&M University

**Title: **Pile Splitting and Handshakes

**Abstract:** **Pile Splitting: **Take a pile of poker chips, say 12. Split it into two piles of say 5 and 7 chips. Write down 5*7=35. Now split one of those, say split the 7 into 3 and 4 chips. Write down 3*4=12. Continue splitting piles and writing down products until you have all 1. Now sum the products. What are all possible products from all possible orders you split the piles? **Handshakes: **You walk into a room of people, say 12. Each person shakes hands with each other person. What is the total number of handshakes? **Remark: **It is a surprising fact that these two problems are really the same problem.

**Intermediate Group: BLOC 203**

**Speaker: **Gregory Berkolaiko

**Title: **Controlled Burn and Queen Dido’s Problem

**Abstract:** We will discuss a puzzle about starting a controlled fire on a 8×8 grid by lighting as few places as possible and relate its solution to a class of mathematical problems with rich history.

**Advanced Group: BLOC 202**

**Speaker: **Junehyuk Jung, Texas A&M University

**Title: **Fibonacci Numbers and Mathematical Induction

**Abstract:** We will learn various formulae regarding Fibonacci numbers and prove these using mathematical induction. Students will present their proofs at the end of the activity.