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2018-19 Academic Year Activities
2018-19 Academic Year Activities
November 3, 2018
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.
November 10, 2018
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 17, 2018
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 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.
December 1, 2018
December 1, 2018
Beginner Group: BLOC 220 (in Pre-Algebra and below)
Speaker: Maurice Rojas, Texas A&M University
Title: Protecting Your Data I
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.
December 8, 2018
December 8, 2018
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).
January 26, 2019
January 26, 2019
Beginner Group: BLOC 220 (in Pre-Algebra and below)
Speaker: Chun-hung Liu, Texas A&M University
Title: Rooks and Dating
Abstract: Given an 8x8 chessboard where some positions are removed, can you place 8 rooks so than none of them can attack another? A couple of boys want to date a couple of girls, where every pair of boy and girl either like each other or do not like each other. Can you pair them so that everybody is happy? These problems are special cases of graph matching theory. We will see how we can put as many rooks as possible and how can we pair as many boys and girls as possible.
Intermediate Group: BLOC 203 (in Algebra 1 or above)
Speaker: John Weeks, Texas A&M University
Title: Generating Functions
Abstract: How many integer solutions (a, b, c, d) are there to the equation a+b+c+d=25? We will answer this question using a simple answer from a generating function. We will also cover the stars-and-bars method in the partitions of integers problem.
Advanced Group: BLOC 202 (in Algebra 2 or above)
Speaker: Kris Watkins, Texas A&M University
Title: Topology Series: Introduction to Logic, Set Theory, and Point-Set Topology
Abstract: Topology is often looked at as rubber sheet Geometry. We are able to treat everything like playdoh and still recover extremely strong results about the properties of these things. We can even say that a doughnut and a coffee cup are "topologically equivalent". For our first session we will quickly explore things such as the Konigsberg bridge problem and the Euler Characteristic of a polyhedron. We won't necessarily give these things a formal proof, but they will give us the motivation to learn other things that will make us capable of developing a formal proof. Afterwards we'll start with some basic Set Theory and Logic rules that will aide us in further studying Point-Set Topology.
February 2, 2019
February 2, 2019
Beginner Group: BLOC 220 (in Pre-Algebra and below)
Speaker: Matthew Young, Texas A&M University
Title: Conway's Game of Life
Abstract: Conway's game of life gives a way for creating amazingly complicated and beautiful patterns out of simple designs. To play the game, one places live cells on a grid. Each round, cells either live, die, or are newly born, according to some definite rules. We will learn the rules of Conway's game of life, see how some initial shapes evolve, and also do some computer experimentation.
Intermediate Group: BLOC 203 (in Algebra 1 or above)
Speaker: Chun-hung Liu, Texas A&M University
Title: Rooks and Dating
Abstract: Given an 8x8 chessboard where some positions are removed, can you place 8 rooks so than none of them can attack another? A couple of boys want to date a couple of girls, where every pair of boy and girl either like each other or do not like each other. Can you pair them so that everybody is happy? These problems are special cases of graph matching theory. We will see how we can put as many rooks as possible and how can we pair as many boys and girls as possible.
Advanced Group: BLOC 202 (in Algebra 2 or above)
Speaker: Kris Watkins, Texas A&M University
Title: Topology Series 2: What Are Topologies and How Do We Verify Them?
Abstract: At the end of our last section we introduced what it means for "T" to be a topology on a space "X". We will begin to look at various topologies and verify topologies that we have been using our entire lives.
February 9, 2019
February 9, 2019
Beginner Group: BLOC 220 (in Pre-Algebra and below)
Speaker: Phil Yasskin, Texas A&M University
Title: Bulgarian Solitaire
Abstract: Begin with a small number of poker chips in a small number of piles. Remove one chip from each pile and put them in a new pile. If a pile becomes empty, it disappears. We will study what happens when this process is repeated.
Intermediate/Advanced Groups: BLOC 203 (in Algebra 1 or above)
Speaker: Matthias Maier, Texas A&M University
Title: Fractals
Abstract: We will explore the wonderful world of fractals. These are complex patterns that are self-similar across different scales. This means that no matter how far you zoom into these structures you will always see the same basic shape. We will also explore how simple recursive procedures can create a fractal structure, where to find such structures in nature, and how seemingly simple mathematical conditions can lead to very surprising fractal sets.
February 16, 2019
February 16, 2019
Beginner Group: BLOC 220 (in Pre-Algebra and below)
Speaker: Junehyuk Jung, Texas A&M University
Title: How to Eat More Pizza
Abstract: We look for the best strategy of slicing the pizza to ensure you eat more than the other person, under certain rules. (Disclaimer: real pizzas are not included in the activity). This activity is based on a mathematical conjecture which was resolved only 10 years ago.
Intermediate Group: BLOC 203 (in Algebra 1 or above)
Speaker: Matthew Young, Texas A&M University
Title: Conway’s Game of Life
Abstract: Conway's game of life gives a way for creating amazingly complicated and beautiful patterns out of simple designs. To play the game, one places live cells on a grid. Each round, cells either live, die, or are newly born, according to some definite rules. We will learn the rules of Conway's game of life, see how some initial shapes evolve, and also do some computer experimentation.
Advanced Group: BLOC 202 (in Algebra 2 or above)
Speaker: Kris Watkins, Texas A&M University
Title: Topology Series: Generating and Verifying a Basis For a Topology
Abstract: Last time we looked at various different topologies and even verified that the Finite-Complement topology really is a topology. Through doing that we were able to see how it would be impossible for us to list every single open set within some topologies. Our way of fixing this is to define a basis and to learn how to use a basis to define an entire topology.
March 2, 2019
March 2, 2019
Beginner Group: BLOC 220 (in Pre-Algebra and below)
Speaker: Dean Baskin, Texas A&M University
Title: “Magic Squares” in Set
Abstract: We will introduce the card game Set. Set is played with 81 unique cards, each of which has four attributes: number, color, shading, and shape. The aim of the game is to collect sets of three cards in which each attribute is the same or different. We will use the cards from this game to construct “magic squares” in which every line is a set. Time permitting, we will attempt to find “magic cubes” or “magic hypercubes” with the cards.
Intermediate Group: BLOC 203 (in Algebra 1 or above)
Speaker: Phil Yasskin, Texas A&M University
Title: Bulgarian Solitaire
Abstract: Begin with a small number of poker chips in a small number of piles. Remove one chip from each pile and put them in a new pile. If a pile becomes empty, it disappears. We will study what happens when this process is repeated.
Advanced Group: BLOC 202 (in Algebra 2 or above)
Speaker: Kris Watkins, Texas A&M University
Title: Topology Series 4: Product and Subspace Topology, Along With Metrics
Abstract: We’ve now not only established what a topology is but we also know how to verify that something is a topology and how to define it with a basis. We’ve seen various topologies, but now we’ll introduce the product topology and subspace topology. Afterwards we’ll look at one of the most important parts of Topology, namely metric spaces.
March 23, 2019
March 23, 2019
Beginner Group: BLOC 220 (in Pre-Algebra and below)
Speaker: David Sykes, Texas A&M University
Title: Mondrian Art Puzzles
Abstract: We will work on puzzles inspired by Piet Mondrian's art. The activity leads to fun and challenging geometric dissection problems.
Intermediate Group: BLOC 203 (in Algebra 1 or above)
Speaker: Igor Zelenko, Texas A&M University
Title: Solving Extremum Problem in Planar Geometry Using Reflections and Rotations: the Law of Reflections, the Fermat-Torichelli point, and the 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 reflections 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.
Advanced Group: BLOC 202 (in Algebra 2 or above)
Speaker: John Weeks, Texas A&M University
Title: Topology Series 5: Quotient Topology
Abstract: We will now begin to look at one of the most crazy/wacky parts of topology that leads to some very interesting results. The Quotient Topology allows us to look at things in a completely different way and it allows us to take objects that appear completely distinct and identify them with each other.
March 30, 2019
March 30, 2019
Beginner Group: BLOC 220 (in Pre-Algebra and below)
Speaker: Phil Yaskin
Title: The King Arthur Problem
Abstract: King Arthur's daughter is supposed to marry one of the Knights of the Round Table. She devises an interesting method to select which knight to marry. We will study the problem.
Intermediate Group: BLOC 203 (in Algebra 1 or above)
Speaker: David Sykes
Title: Mondrian Art Puzzles
Abstract: We will work on puzzles inspired by Piet Mondrian's art. The activity leads to fun and challenging geometric dissection problems.
Advanced Group: BLOC 202 (in Algebra 2 or above)
Speaker: Kris Watkins
Title: Topology Series 6: Topological Properties and Equivalence
Abstract: Given that we have now seen the main topologies used by topologists and that we have also seen how to verify them, we will now look at which things are topologically equivalent, what does such an equivalence give us, and what topological invariant are. Before we can do that though, we must develop the fundamentals and definitions that are necessary to discuss those things.
April 13, 2019
April 13, 2019
Beginner Group: BLOC 220 (in Pre-Algebra and below)
Speaker: Sinjini Sengupta, Texas A&M University
Title: Dots on a Grid
Abstract: We will discuss the different ways we can place dots on a grid so that no two dots are the same distance apart from each other. We will have fun identifying how many unique distances can exist between points on an (n x m) grid.
Intermediate Group: BLOC 203 (in Algebra 1 or above)
Speaker: Phil Yasskin, Texas A&M University
Title: The a + b + ab Problem
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?
Advanced Group: BLOC 202 (in Algebra 2 or above)
Speaker: Kris Watkins, Texas A&M University
Title: Topology Series 6: Topological Properties and Equivalence
Abstract: Given that we have now seen the main Topologies used and how to verify them, we will now look at which things are topologically equivalent, what does such an equivalence give us, and what topological invariants are. Before we can do that though, we must develop the fundamentals and definitions that are need to discuss those things.
April 27, 2019
April 27, 2019
Beginner Group: BLOC 220 (in Pre-Algebra and below)
Speaker: Priyanga Ganesan, Texas A&M University
Title: The a + b + ab Problem
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?
Intermediate and Advanced Groups: BLOC 203 (in Algebra 1 or above)
Speaker: Lan Li, University of Texas at Austin
Title: Can You Decipher This?
Abstract: We communicate everyday; with individuals, groups, and now, a global audience if we wish. While some messages we don’t mind letting everybody hear, others may be more personal in nature. As we rely more and more on technology to communicate everyday, how can we be sure that our messages are secured? We’ll explore this question in this session.
May 4, 2019
May 4, 2019
Beginner Group: BLOC 220 (in Pre-Algebra and below)
Speaker: Philip Yasskin, Texas A&M University
Title: Problems with Toilet Paper
Abstract: There are 3 kinds of people in the world:
Those who crumble toilet paper - the chaotic people.
Those who fold in half repeatedly - the exponential people.
Those who fold from the end repeatedly - the linear people.
We will investigate several problems involving linear and exponential folding of toilet paper.
Intermediate and Advanced Groups: BLOC 203 (in Algebra 1 or above)
Speaker: Pablo Ocal
Title: The Best Way How Not to Hang Pictures in Walls
Abstract: We will discuss how to hang a picture on the wall using two nails in such a way that removing either of the nails will make the picture fall down to the foor. We will see how one can come up with a solution without experimentation. In fact, the same statement holds for any number of nails, and we will find a way to compute the solutions.
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