Past Meetings

Feb. 18, 2017
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.

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!

  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
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.

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!

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.

  Jan. 28, 2017
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.

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)?

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?

  Jan. 21, 2017
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.

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?

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.

  Dec. 3rd, 2016
Advanced Group: Konrad Wrobel on Distinct Distances in the Plane

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.

Intermediate Group: Tamara Carter on CLUE in the Math Department

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.

Beginner Group: Philip Yasskin on Domino Circles

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?

  Nov. 19th, 2016
Advanced Group: Peter Kuchment on Unreasonable Effectiveness of Mathematics

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.

Intermediate Group: R. Saravanan on Hash functions, Cryptography

Presenter: R. Saravanan 
Department of Atmospheric Sciences, Texas A&M University 

Beginner Group: Alex Sprinston on Design of Combinational Circuits Using Boolean Algebra

 

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.

  Nov. 5th, 2016
Intermediate Group: Parth Sarin on How Fast Can You Gossip?

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.

Beginner Group: Eviatar Procaccia on Folding the Platonic Solids

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.

  Oct. 15, 2016
Advanced Group: Kim Currens & Dr. Sandra Nite on Modeling Sound Waves with Periodic Functions

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.

Intermediate Group: Jens Forsgård on The a+b+ab Problem

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?

Beginner Group: Tamara Carter on CLUE in the Math Department

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.

  Oct. 8, 2016
Advanced Group: Dr. Luciana Barroso & Dr. Sandra Nite on Exploring Lung Capacity

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.

Intermediate Group: Dr. Mary Margaret Capraro on Locker Problem, Arithmagons, Magic Squares

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.

Beginner Group: Dr. Robert Capraro on Counting Cows & 3 Bean Salad

Presenter: Dr. Robert Capraro
Department of TLAC, Texas A&M University

 
Abstract: For “Counting Cows” students will use cubes to organize thinking and solve algebraic problems in the context of cows in different pastures. In “3 Bean Salad” students use several types of beans to represent salad mixtures and solve equations to determine the total number of beans in the salad.
  Oct. 1, 2016
Advanced Group: Zoran Sunic on "Wait, was I supposed to turn left or right?"

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.

Intermediate Group: Riad Masri on Explorations with Prime Numbers

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.

Beginner Group: David Kerr on Random Walks and Search Engines

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.

  Sept. 24, 2016
Advanced Group: Maurice Rojas on Gift Boxes, Mongoose in the Middle, and Secret Codes

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.

Beginner & Intermediate Group: Philip Yasskin on Trapezoid Numbers

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.

  Sept. 17, 2016
Advanced 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.

Intermediate Group: Dr. Ali Bicer & Dr. Sandra Nite on Dilutions

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.

Beginner Group: Ola Sobieska on Even and Odd Numbers

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.

  May 14, 2016
Advanced Group: Riad Masri on the Arithmetic of Integer Partitions

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.

Beginner and Intermediate Groups: Kaitlyn Phillipson on Math Games

Presenter: Kaitlyn Phillipson
Department of Mathematics, Texas A&M University

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

  May 7, 2016
Advanced Group: Timo de Wolff on Public Key Cryptography

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.

Intermediate Group: Gregory Berkolaiko on Icosahedron Made from Scratch

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.

Beginner Group: Philip Yasskin on Balance Beams

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.

  April 30, 2016
Advanced Group: Eric Rowell on Mathematical Knots and Links

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?

Intermediate Group: Christopher O’Neill on When Can You Draw a Picture Without Picking Up Your Pencil?

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?

Beginner Group: Frank Sottile on Meet the Cube

Presenter: Frank Sottile
Department of Mathematics, Texas A&M University

Abstract: We will investigate the familiar cube, using it
to study three-dimensional geometry.

  April 23, 2016:
Advanced Group: David Dynerman on Normal Mapping and Video Games

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.

Beginner Group: Roger Howe on Around the Pythagorean Theorem

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?

  March 26, 2016:
Advanced Group: Matt Young on Which Numbers are Sums of Two Squares?

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.

Intermediate Group: David Sykes on Dinner Party Problems and Graph Coloring

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.

Beginner Group: Ola Sobieska on Weighings and Counterfeit Coins

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.

  March 5, 2016:
Advanced Group: Volodymyr Nekrashevych on Binomial Coefficients and Their Properties

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.

Intermediate Group: Eviatar Procaccia on The Gambler's Ruin and a Disoriented Bird

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.

Beginner Group: Phil Yasskin on Splitting Piles and Handshakes

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?

  February 27, 2016:
Advanced Group: Konrad Wrobel on Dealing with Infinite Sets

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.

Beginner and Intermediate Group: Michelle Pruett on Code-Breaking Through the Years

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.

  February 20, 2016:
Advanced Group: Ramalingam Saravanan on Predictability of Weather and Climate

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.

Intermediate Group: Igor Zelenko on Domino Puzzles, Invariants, and Walking Along the Grids and Bridges

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.

Beginner Group: Anneliese Slaton on The Bridge Problem: A Puzzle That Changed the Mathematical World

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!

  February 13, 2016:
Advanced Group: William Rundell on A 5,000 Year History into Mathematical Innovation

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.

Intermediate Group: Maurice Rojas on Hats, Codes, and Lattice Points

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.

Beginner Group: Frank Sottile on Word Problems and Common Sense

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.

  February 6, 2016:
Advanced Group: Maurice Rojas on Polygons, Lattice Points, and Equations

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.

Intermediate Group: Phil Yasskin on The a+b+ab Problem

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?

Beginner Group: Frank Sottile on Mathematical Auction

Presenter: Professor Frank Sottile
Department of Mathematics, Texas A&M University

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

  September 19, 2015:
Advanced Group: Kaitlyn Phillipson on Catalan Structures

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.

Intermediate Group: Phillip B. Yasskin on The Candy Conundrum

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.

Beginner Group: Frank Sotille on How to Solve a Problem

Presenter: Frank Sotille
Department of Mathematics, Texas A&M University
Abstract: We will work together to solve and discuss some
interesting puzzles and problems.

April 25, 2015:
Beginner - Matthew Barry - Turk's Head Knots

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.

Intermediate

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.

Advanced

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.

March 14, 2015: Pi Day of the Century March 7, 2015:
Beginner

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.

Intermediate

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.

Advanced

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?

February 28, 2015:
Beginner

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.

Intermediate

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.

Advanced

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.

February 21, 2015:
Beginner

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.

Intermediate

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.

Advanced

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.

February 14, 2015: Mitchell Physics Show February 7, 2015:
Beginner

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?

Intermediate

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?

Advanced

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.

January 24, 2015:
Beginner

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.

Intermediate

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.

Advanced

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).