# Undergraduate Colloquium Fall 2010

Wednesdays at 5:00 p.m. in Jack Baskin Engineering Room 301A

Refreshments served at 4:45 p.m.

For further information please contact Professor Frank Bauerle, bauerle@ucsc.edu.

**October 6, 2010**

**Games Night**

**Dr. Frank Bauerle Continuing Lecturer, Mathematics Department**

Games nights are an informal get-together of people interested in playing and learning about games with depth that will happen occasionally during the year. Each night will feature a new game or a collection of games. 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. Some games are two-player games (such as "Quoridor") and some will be multi-player such as ("Ricochet Robots" or "Pit"). 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" (seehttp://www.setgame.com/ for more info), and is a great fun game about pattern-matching. Not 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 13, 2010**

*Cal Teach and the Math Major -- with Pizza!*

*Cal Teach and the Math Major -- with Pizza!*

**Gretchen Andreasen, Cal Teach Director and David DelMundo, Mathematics Department Undergraduate Program 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 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 satisfy math degree requirements or education minor requirements (including the new STEM education minor). We'll have pizza for students who attend.

**October 20, 2010**

**Games Night - ***Richochet Robots*

*Richochet Robots*

**Frank Bauerle **

This week we will be introducing and playing Ricochet Robots. The premise is as follows: robots of different colors are scattered about a game board. Robots move laterally until they hit an obstacle (a wall or another robot). The goal is to find the shortest number of moves to move a particular robot to a particular space on the board. This game is one of those with simple rules but with interesting and often quite surprising solutions. One reason why this game is so much fun is that everybody plays simultaneously, i.e. there are no turns! Also you can play alone or with really any number of players (as long as the players can see the board). You can play the game on-line at http://www.wickle.com/weblog/index.php?content=ricochet

**October 27, 2010**

*Education Abroad (EAP) for Science and Mathematics Majors*

*Education Abroad (EAP) for Science and Mathematics Majors*

**EAP Peer Advisors and Continuing Lecturer Frank Bauerle **

Ever consider studying abroad? Worried about what this will mean for your studies or your bank balance? At this week's colloquium we will be discussing the opportunities and options for math and other science majors to study abroad. Some recent Education Abroad Program (EAP) participants and a peer counselor from the Office of International Education will lead the discussion and offer advice on program and course selection. Continuing Lecturer Frank Bäuerle and possibly Professor Debra Lewis will also share their views and personal experiences.

**November 3, 2010**

**Games Night: ***Hex*

*Hex*

**Dr. Frank Bauerle **

Hex is typically played on a 11x11 rhombus-shaped board made up of hexagons. Hex is an abstract strategy game independently invented by Piet Hein (1942) and Steve Nash (1947) that belongs to the general category of 'connection' games. Each player has an allocated color and players take turns placing a stone of their color on a single cell within the overall playing board. The goal is to form a connected path of your stones linking the opposing sides of the board marked by your colors, before your opponent connects his or her sides in a similar fashion. The first player to complete his or her connection wins the game. The four corner hexagons each belong to two sides. We will also discuss some of the interesting underlying logic such as that there are no ties in this game and that consequently there exists a winning strategy for the first player (even though the game is so complex that nobody and no computer program actually knows the winning strategy). For more information on this deep and rich game see http://en.wikipedia.org/wiki/Hex_(board_game)

**November 10, 2010**

**No Colloquium - Veteran's Day on Thursday**

**November 17, 2010**

*Singularities: cusps, coffee cups, and roots of polynomials.*

*Singularities: cusps, coffee cups, and roots of polynomials.*

**Professor Richard Montgomery, UCSC Mathematics Department **

Take a cup of liquid, preferably coffee, preferably with cream in it, in a shiny mug. Stand outside with it on a bright day and move it around gently. On the surface you will see bright curves of light, with sharp points in them. Those are called `caustics' and, typically are cubic cusps, represented by x^3 = y^2. We will describe the general notion of a singularity in algebraic and analytic geometry, describe a few. Time permitting, I will describe the singularities arising from multiple roots of polynomials, and also Newton's algorithm for solving a polynomial equation such as x^3 + 3 x^2 y^2 + 5 y^4 = 7 x^3 y^2 for y as a function of x.

**December 1, 2010**

*Informational Session about applying to Graduate School in Mathematics as well as Research Experience for Undergraduates (REU) and other opportunities for Math majors*

*Informational Session about applying to Graduate School in Mathematics as well as Research Experience for Undergraduates (REU) and other opportunities for Math majors*

Panel of Experts including faculty representatives Prof. Debra Lewis and Prof. Jie Qing (current Vice Chair of Graduate affairs), Staff members Sandra Yates (Graduate Coordinator) and David Del Mundo (Undergraduate Advisor), plus Kayden Krauel (current grad student) and Wyatt Howard and Michael Campbell (current grads, REU participants).