# Undergraduate Colloquium Fall 2007

301A Jack Baskin Engineering Building.

There will be refreshments at 4:45pm

For further information regarding the talks, please contact

Prof. Frank Bauerle (bauerle@ucsc.edu) or Undergraduate Advisor, Andrea Gilovich (gilovich@ucsc.edu)

**October 10, 2007**

**Games Night**

**Frank Bauerle, Lecturer, Mathematics Department **

An informal get-together of people interested in playing and learning about games with depth. Games Nights will happen occasionally during the year, and each night will feature a new game. Games can be 100% strategic (such as "Hex"), involve chance and probability (such as "The game of Pigs") or require a certain amount of games psychology (such as "For Sale"). The most interesting games usually combine some or all of the above. We will have fun learning and playing the games but also spend some time discussing the mathematical content of these games. The first game this year is called "Set" (see http://www.setgame.com/ for more info), and is a great fun game about pattern-matching. No at all obvious at first, the game has clear connections to modular arithmetic and geometry which we will discuss. In addition there are some interesting questions of probability to discuss. Everybody is invited. Bring a friend! No prior experience or exposure to "Set" is necessary.

**October 17, 2007**

**Movie Night: ***"The Proof": A documentary about Andrew Wiles' work on Fermat's Last Theorem*

*"The Proof": A documentary about Andrew Wiles' work on Fermat's Last Theorem*

For over 350 years, some of the greatest minds of science struggled to prove what was known as Fermat's Last Theorem - the idea that a certain simple equation had no solutions in positive integers. The theorem has gained notoriety in part because of the following published statement by Pierre de Fermat: "It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers. I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain." Now hear from the man who spent many years of his life cracking the problem.

**October 24, 2007**

*How to Apply to Graduate School*

*How to Apply to Graduate School*

**Jen Mogel, Ph.D. Mathematics, UCSC with special guest Department Chair, Professor Richard Montgomery **

Ever feel overwhelmed by the thought of applying to Graduate School? Its no wonder! With everything else piling up, getting organized can seem a rather daunting task. This weeks Undergraduate Colloquium is designed to help you get the ball rolling. Jen Mogel, a Ph.D. student in Mathematics at UCSC, will be outlining the graduate application process from the ground up. She will be covering topics that range from: tips on what to include in your personal essay, to important deadlines you will need to meet. She will also provide insight into the life of a successful graduate student and what demands she faces on a regular basis. In addition to this, The Mathematics Department Chair, Professor Richard Montgomery, will be attending in order to field your questions. With vast experience serving on the acceptance panel this will be a rare opportunity to solicit some very skilled advice!

**November 7, 2007**

*When pi and Number Theory Collide*

*When pi and Number Theory Collide*

**Professor Martin Weissman **

Suppose you choose two whole (positive) numbers at random. What is the probability that they have no common factor? Surprisingly, the answer can be computed precisely, and involves pi. I'll explain the problem and it's solution, using only basic properties of whole numbers and factorization, and some multivariable calculus at the end.

**November 14, 2007**

*Cal Teach and The Math Major*

*Cal Teach and The Math Major*

**Cara M. Aguirre, Math Placement Coordinator, Cal Teach Program, and Andrea Gilovich, Math Department Undergraduate Advisor **

: Do you have an interest in teaching as a career? If so, come find out how the Cal Teach program can help you explore teaching as a career, while at the same time possibly satisfying some of your degree requirements. Cal Teach offers internships, advising, professional development, and teaching resources for math, science, and engineering majors who are interested in teaching at the middle or high school levels. All aspects of the program will be discussed as well as how the Cal Teach internships can possibly satisfy math degree requirements and education minor requirements. Current math teachers from local schools and fellow math majors currently participating with the Cal Teach program will also be present to answer your questions.

**November 28, 2007**

*On the uniqueness of the projective plane of order 4*

*On the uniqueness of the projective plane of order 4*

**Bruce Cooperstein **

A projective plane is a geometric object consisting of a set P of points and a collection L of special subsets of P, whose elements we call lines which satisfies the following: 1) Two points lie on a unique line. 2) Two lines meet in a unique point. 3) There exists four points no three of which are on the same line (non-colinear). An easy argument implies that all lines have the same cardinality. When this is finite and equal to n+1 we say this is a projective plane of order n. We will give some examples and show that all planes of order 4 are isomorphic.

**December 5, 2007**

**Games Night**

**Dr. Frank Bauerle **

This week we will be playing Ricochet Robots (originally published as the game Rasende Roboter in Germany), a fun and fast-paced strategy game. The idea is to move the game pieces (Robots) from their location on the game board to a selected location. The way to win is by minimizing the number of moves, given that the robots motion is restricted by certain rules. One of the great plusses of this game is that there is no set order of play (everybody plays simultaneously) and no set number of players (you can play alone or have as many people as you can fit around a table to see the board). Once we have played the game a few times and you have mastered the rules we will also work on some puzzles based on the game