**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/

**Presenter:** Ola Sobieska

Department of Mathematics, Texas A&M University

**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.

**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.

**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.

**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!

**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.

**Presenter:** Dr. Philip Yasskin

Department of Mathematics, Texas A&M University

**Abstract: **We will play a game that models scientific research.

**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.

**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.

**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!

**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.

**Presenter:** Janice Epstein

Texas A&M University, Department of Mathematics

**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.

**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!

**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.**

**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.

**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!

**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.

**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.

**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)?

**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?

**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.

**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?

**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.

**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.

**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.

**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?

**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.

**Presenter: **R. Saravanan

Department of Atmospheric Sciences, Texas A&M University

**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.

**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.

**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.

**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.

**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?

**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.

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.

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.

Presenter: Dr. Robert Capraro

Department of TLAC, Texas A&M University

**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.

**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.

**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.

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.

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.

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.

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.

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.

Presenter: Riad Masri

Department of Mathematics, Texas A&M University

Abstract: The goal of this project is to explore some arithmetic aspects of integer partitions. In particular, we will focus on Ramanujan's famous congruences for the partition function, and study how the Dyson rank and the Andrews/Garvan crank can be used to give a combinatorial explanation for these congruences.

Presenter: Kaitlyn Phillipson

Department of Mathematics, Texas A&M University

Abstract: We'll discuss some games and try to come up with winning strategies.

Presenter: Timo de Wolff

Department of Mathematics, Texas A&M University

Abstract: Cryptography handles with the secure transmission of secret

messages. More precisely, a third party is supposed to be unable to

understand the content of an intercepted message if it is encrypted.

Classically, both parties exchange secret keys for a secure en- and

decryption. Nowadays, however, a lot of communication happens via

insecure channels like the internet. Thus, secret keys often cannot be

exchanged securely. Thus, one needs a new type of crypto system, in

which parts of the keys do not need to be hidden anymore. This is called

public key cryptography.

In this talk we will first review a couple of classical symmetric crypto

systems like the Ceasar cipher. In the second part I will explain and

show the RSA crypto system, which is the current industry standard for

public key cryptography.

Presenter: Gregory Berkolaiko

Department of Mathematics, Texas A&M University

Abstract: The task is to make an icosahedron from scratch using only paper and glue (plus compass, ruler, scissors and pencil). Along the way we will need to solve the problem of dividing the circle into the equal parts lengthwise.

Presenter: Philip Yasskin

Department of Mathematics, Texas A&M University

Abstract: We use a meter stick as a balance beam with a pencil at the 50 cm mark. In each problem, we put weights at the locations indicated and experiment to figure out where to put the extra weights. We will progress to using equations to figure out where to put the weights.

Presenter: Eric Rowell

Department of Mathematics, Texas A&M University

Abstract: Knots and links have been used as decorations for centuries, but their mathematical study only began in the 19th century. For a brief period it was believed that atoms were just knotted bits of swirling ether, and physicists set to work to tabulate them. It turned out they were completely wrong, but this led to the development of topology. More than 100 years later, knots may again be useful in physics though Topological Quantum Computation. We will explore important questions surrounding knots and links, such as: how do we know when two knots are actually the same? How can we tell that they are genuinely different?

Presenter: Christopher O'Neill

Department of Mathematics, Texas A&M University

Abstract: Suppose someone hands you a picture and asks you to trace it in one continuous motion, that is, without picking up your pencil or backtracking. When is it possible to succeed? How should you decide where to start tracing?

Presenter: Frank Sottile

Department of Mathematics, Texas A&M University

Abstract: We will investigate the familiar cube, using it

to study three-dimensional geometry.

Presenter: David Dynerman

Department of Mathematics, University of California, Berkley

Abstract: Normal mapping is a way of increasing surface detail when rendering 3D graphics and has become a standard technique in the video game industry. Normal mapping sneaks in higher quality lighting detail over a lower-quality polygonal model. This talk will give an overview on how this interesting application of math, computer science and physics creates better looking video games.

Presenter: Roger Howe

Department of Mathematics, Yale University

Abstract: This session will discuss a few of the many applications of the Pythagorean Theorem in the real world. Among the questions to be considered will be, why do ladders work, taking shortcuts, and how far can we see?

Presenter: Matt Young

Department of Mathematics, Texas A&M University

Abstract: Some numbers are the sum of two squares, and some numbers aren’t. For example, 5 is (since 5 = 1 +4) but 7 isn’t. Numbers that can be expressed as the sum of two squares have many amazing properties, and we will discover many of these patterns in this math circle.

Presenter: David Sykes

Department of Mathematics, Texas A&M University

Abstract: We will be discussing the Dinner Party Problem along with some of its generalizations while exploring the concept of graph coloring. The problems are special cases of a theorem established by Frank Ramsey around 1930. The discussion will build towards the solution to a challenging Ramsey Theory problem along with the statement of problems that remain unsolved today.

Presenter: Ola Sobieska

Department of Mathematics, Texas A&M University

Abstract: This session will focus on problems about balance scales and weights. The students will learn to identify counterfeit coins, discover tricky ways to weigh objects, and solve other puzzles.

Presenter: Volodymyr Nekrashevych

Department of Mathematics, Texas A&M University

Abstract: We will discuss Pascal's triangle, binomial coefficients,

combinations, triangular numbers, and different interesting facts

about them.

Presenter: Eviatar Procaccia

Department of Mathematics, Texas A&M University

Abstract: Probability theory is the mathematical framework to study

randomness in the universe. We will learn how to use one source of

randomness to create another and why a disoriented bird will never find its

nest.

Presenter: Phil Yasskin

Department of Mathematics, Texas A&M University

Abstract: We will consider 2 problems and ultimately see how they are related.

1) Take a pile of coins, say 10 coins. Split it into two piles, with say 4 and 6 coins. Write down the product 4*6=24. Split each of those piles into two piles, with say 1 and 3, and say 2 and 4. Write down those products 1*3=3 and 2*4=8. Continue in this way until you have ten plies each with 1 coin. Then add all the products, say 24+3+8+... What are all possible sums?

2) If 10 people are in a room, how many ways can they shake hands?

Presenter: Konrad Wrobel

Department of Mathematics, Texas A&M University

Abstract: The roots of modern day set theory stem from Georg Cantor’s work in 1874, when he introduced several concepts that many mathematicians of the time found disconcerting. We’ll delve into his notion of size, or cardinality, and what it means when applied to infinite sets.

Presenter: Michelle Pruett

Texas State University at San Marcos

Abstract: A variety of codes have been used throughout history. We will discover how

to code and decode messages using several techniques.

Presenter: Ramalingam Saravanan

Department of Mathematics, Texas A&M University

Abstract: The discovery of the limits to weather predictability by Edward Lorenz was a seminal event both in theoretical meteorology and in nonlinear dynamics. The mathematical and physical basis for the predictability of weather and climate will be discussed in the context of this discovery. Topics to be covered will include trigonometric functions, limit cycles, and chaotic attractors.

Presenter: Igor Zelenko

Department of Mathematics, Texas A&M University

Abstract: During the activity we will try to solve various problems regarding covering grids by dominos, trominos, transforming the tables of numbers according to certain rules, moving along grids without raising a pencil, or walking along the bridges of cities with many bridges. In all these problems we will ask whether we can complete certain tasks, the answer will often follow from certain nontrivial observations or properties of certain quantities, called invariants, that are preserved by natural transformations allowed in the problem.

Presenter: Anneliese Slaton

Undergraduate Student at George Mason University

Abstract: We will be discussing The Koningsberg Bridge Problem, a seemingly simple problem that was solved by Euler and opened the door to the development of graph theory as we know it. We will not only look at Euler’s original proof, but will explore variations of the problems in physically get up and try to walk to the path!

Presenter: William Rundell

Department of Mathematics, Texas A&M University

Abstract: Here are a series of questions. How does your calculator come up with it’s approximation to the square root of, say, 2? How were the square roots calculated in antiquity? Is there anything new to say about the problem? This talk will explore some of the answers.

Presenter: Maurice Rojas

Department of Mathematics, Texas A&M University

Abstract: We will see how a puzzle involving hats relates to codes that help protect data from noise. We’ll then see how lattice points come up in many different mathematical puzzles, as well as the modern study of secret codes.

Presenter: Frank Sottile

Department of Mathematics, Texas A&M University

Abstract: While we are taught to use algebra to solve word problems, many can be solved just using common sense. In this circle, we will use our common sense to solve word problems.

Presenter: Professor Maurice Rojas

Department of Mathematics, Texas A&M University

Abstract: We'll see how geometric series and the Triangle Inequality allow us to understand hard equations with simple pictures. We'll then see how counting lattice points in polygons leads us to some beautiful and unexpected applications of mathematics.

Presenter: Professor Phil Yasskin

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?

Presenter: Professor Frank Sottile

Department of Mathematics, Texas A&M University

Abstract: We will be doing a team contest called ‘mathematical auction.’

Presenter: Kaitlyn Phillipson

Department of Mathematics, Texas A&M University

Abstract: The Catalan numbers are one of the most common sequences in mathematics. There are many structures counted by the Catalan numbers, and in this activity we take a look at several of them.

Presenter: Philip B. Yasskin

Department of Mathematics, Texas A&M University

Abstract: A candy company wants to a advertise the large number of flavors that can be made by mixing candies in your mouth. Let's figure it out.

Presenter: Frank Sotille

Department of Mathematics, Texas A&M University

Abstract: We will work together to solve and discuss some

interesting puzzles and problems.

Title:

Turk's Head Knots

Speaker:

Matthew Barry (with help from Philip Yasskin and Michael Sprintson)

Texas Engineering Extension Station

TAMU Class of 2014

Abstract:

The Turk's head knot, flat mat, and pineapple knot all belong to a family of interwoven decorative knots favored by many people for many centuries, notably the Celtics. In its final form, the turks head knot is a symmetric prime knot that can be classified by the number of intersections the rope makes with itself. In the knot-tying community, Turk's head knots are classified by counting leads and bights: the lead count is the number of times the rope goes around the knot, and the bight count is the number of loops at each end. For example a 3x5 Turk's head knot has three leads and five bights. Here we explore the math theory behind these knots and use it to plan and tie Turk's head knots of any size.

Title:

Turk's Head Knots

Speaker:

Matthew Barry (with help from Philip Yasskin and Michael Sprintson)

Texas Engineering Extension Station

TAMU Class of 2014

Abstract:

The Turk's head knot, flat mat, and pineapple knot all belong to a family of interwoven decorative knots favored by many people for many centuries, notably the Celtics. In its final form, the turks head knot is a symmetric prime knot that can be classified by the number of intersections the rope makes with itself. In the knot-tying community, Turk's head knots are classified by counting leads and bights: the lead count is the number of times the rope goes around the knot, and the bight count is the number of loops at each end. For example a 3x5 Turk's head knot has three leads and five bights. Here we explore the math theory behind these knots and use it to plan and tie Turk's head knots of any size.

Title:

Turk's Head Knots

Speaker:

Matthew Barry (with help from Philip Yasskin and Michael Sprintson)

Texas Engineering Extension Station

TAMU Class of 2014

Abstract:

The Turk's head knot, flat mat, and pineapple knot all belong to a family of interwoven decorative knots favored by many people for many centuries, notably the Celtics. In its final form, the turks head knot is a symmetric prime knot that can be classified by the number of intersections the rope makes with itself. In the knot-tying community, Turk's head knots are classified by counting leads and bights: the lead count is the number of times the rope goes around the knot, and the bight count is the number of loops at each end. For example a 3x5 Turk's head knot has three leads and five bights. Here we explore the math theory behind these knots and use it to plan and tie Turk's head knots of any size.

*Pi Day of the Century*

Speaker Ms. Kaitlyn Phillipson

Department of Mathematics

Texas A&M University,

Title: Guarding an Art Gallery

Abstract: We will discuss the "Art Gallery Problem," a well-studied problem in mathematics.

Speaker Ms. Kaitlyn Phillipson

Department of Mathematics

Texas A&M University,

Title: Guarding an Art Gallery

Abstract: We will discuss the "Art Gallery Problem," a well-studied problem in mathematics.

Speaker: Dr. Nicholas Long

Department of Mathematics

Stephen F. Austin State University

Title: “Pressing Buttons on a Calculator.”

Abstract: One of the first things kids do when they start playing with a calculator is explore what happens to the screen when you keep hitting the same button over and over. We can figure out pretty quickly what happens when we keep pressing the addition or multiplication buttons. What happens if we had some buttons on a calculator that used multiplication and addition together? What would the result be if we keep pressing a button like that?

Speaker: Dr. Altha Rodin

Department of Mathematics

University of Texas

Title: The Next Move: Some Theory and Practice with Impartial Games

We will discuss combinatorial impartial games defined as follow.

Combinatorial games are two-player games with the following characteristics:

* Two players alternate moves.

* Play continues until there are no legal moves remaining.

* No element of chance is involved (i.e. dice, spinners, etc.).

* Each player has full knowledge of the game position at all times.

In normal play, the last player to make a legal move wins. In misère play, the last player to make a legal move loses. A combinatorial game is called impartial if both players have the same set of allowable moves at each position of the game. A game in which the allowable moves depends on the player is called a partisan game.

Speaker: Dr. Altha Rodin

Department of Mathematics

University of Texas

Title: The Next Move: Some Theory and Practice with Impartial Games

We will discuss combinatorial impartial games defined as follow.

Combinatorial games are two-player games with the following characteristics:

* Two players alternate moves.

* Play continues until there are no legal moves remaining.

* No element of chance is involved (i.e. dice, spinners, etc.).

* Each player has full knowledge of the game position at all times.

In normal play, the last player to make a legal move wins. In misère play, the last player to make a legal move loses. A combinatorial game is called impartial if both players have the same set of allowable moves at each position of the game. A game in which the allowable moves depends on the player is called a partisan game.

Speaker: Dr. Lucas Macri

Department of Physics & Astronomy

Texas A&M University

Title: The Mathematics of Astronomy (part I)

In this class, we will talk about the math used by ancient astronomers to learn about the Universe even before the telescope was invented. How did they determine the size of Earth, the distance to the Moon and the Sun? We will also talk about how we can measure the distances to other stars and figure out how much light they produce.

Speaker: Dr. Lucas Macri

Department of Physics & Astronomy

Texas A&M University

Title: The Mathematics of Astronomy (part I)

In this class, we will talk about the math used by ancient astronomers to learn about the Universe even before the telescope was invented. How did they determine the size of Earth, the distance to the Moon and the Sun? We will also talk about how we can measure the distances to other stars and figure out how much light they produce.

Speaker Mr. Trevor Olsen

Department of Mathematics

Texas A&M University

Title: Kinetic Origami (Curlicue)

Abstract: Are you ready to make amazing shape changing origami? Well I sure am! We will be making Curlicues that go from being flat paper to different 3D shapes. We will understand how these structures work and learn what other types of Curlicues we can make.

Speaker Dr. Igor Zelenko

Department of Mathematics

Texas A&M University

Title Sums of k’th powers and other interesting sums

Abstract: The formula for the sum of first n positive integers is taught in school. What is the sum of their squares, cubes etc? We will learn how to derive formulas for these sums and other interesting sums and give applications for calculating areas.

*Mitchell Physics Show*February 7, 2015:

Speaker: Dr. Phil Yasskin

Department of Mathematics

Texas A&M University

Title: GCD, LCM, Prime Factorization, and the Division and Euclidean Algorithms

Abstract:

I will present a series of problems whose solutions involve the Greatest Common Divisor, the Least Common Multiple, the Unique Prime Factorization Theorem, the Division Algorithm and/or the Euclidean Algorithm. For example:

Problem 1: You have an unmarked 5 liter bucket and an unmarked 9 liter bucket and an unlimited amount of water. Can you measure out exactly 2 liters of water? How?

Problem 2: How many 12 cent and 27 cent postage stamps should you buy to put exactly 83 cents worth of postage on an envelope?

Problem 3: You have a 3 foot by 5 foot pool table. The cue ball is located at a point which is 1 foot from the 5 foot side and 2 feet from the 3 foot side. You hit the ball at 45 degrees. Every time the ball hits a side it bounces back at 45 degrees with no loss of velocity. Will the ball eventually hit the corner of the pool table?

Speaker: Dr. Phil Yasskin

Department of Mathematics

Texas A&M University

Title: GCD, LCM, Prime Factorization, and the Division and Euclidean Algorithms

Abstract:

I will present a series of problems whose solutions involve the Greatest Common Divisor, the Least Common Multiple, the Unique Prime Factorization Theorem, the Division Algorithm and/or the Euclidean Algorithm. For example:

Problem 1: You have an unmarked 5 liter bucket and an unmarked 9 liter bucket and an unlimited amount of water. Can you measure out exactly 2 liters of water? How?

Problem 2: How many 12 cent and 27 cent postage stamps should you buy to put exactly 83 cents worth of postage on an envelope?

Problem 3: You have a 3 foot by 5 foot pool table. The cue ball is located at a point which is 1 foot from the 5 foot side and 2 feet from the 3 foot side. You hit the ball at 45 degrees. Every time the ball hits a side it bounces back at 45 degrees with no loss of velocity. Will the ball eventually hit the corner of the pool table?

Speaker Ms. Kaitlyn Phillipson

Department of Mathematics

Texas A&M University,

Title: Guarding an Art Gallery

Abstract: We will discuss the "Art Gallery Problem," a well-studied problem in mathematics.

Speaker: Dr. Jane Long

Department of Mathematics

Stephen F. Austin State University

Title: The Mathematics of Sona, Sand Drawings from Africa

Abstract: Many cultures around the world tell stories with the help of drawings made in sand. This activity will investigate interesting mathematics involved in some traditional sand drawings from Angola.

Speaker: Dr. Jane Long

Department of Mathematics

Stephen F. Austin State University

Title: The Mathematics of Sona, Sand Drawings from Africa

Abstract: Many cultures around the world tell stories with the help of drawings made in sand. This activity will investigate interesting mathematics involved in some traditional sand drawings from Angola.

Speaker: Dr. David Manuel

Department of Mathematics

Texas A&M University,

Title: The Algebra of Rubik's Cubes, part 3

Abstract: Many of us have learned how to solve the (3x3) Rubik's Cube from solutions presented in a book or online. But how does one come up with their own solution? In this final session, we will apply what we have learned about groups, permutations, and partial commutativity to the movements of the Rubik's Cube to develop our own strategies to solve the Cube. Bring your cubes, and, if possible, movements which exchange 2 cubes or rotate 1 cube in one row (regardless of what the other rows look like).