Undergraduate Colloquium Winter 2008

Wednesdays 5:00p-6:00pm in 301A Jack Baskin Engineering
Refreshments will be served at 4:45pm
For further information, please contact
Dr. Frank Bauerle, bauerle@ucsc.edu,
or Andrea Gilovich, gilovich@ucsc.edu

January 16, 2008

Modeling complex dynamical systems: a test case -- global climate warming

Professor Ralph Abraham 

Is global climate warming threatening a planetary catastrophe within a few decades, or not? We will discuss this question in the context of Chaos Theory, paying special attention to the daisyworld models of James Lovelock, the founder of Gaia Theory, and the leading climate pessimist.

January 30, 2008

There is always room at Hotel Infinity

Dr. Frank Bauerle, Lecturer, UCSC Mathematics Department 

In this talk we use Hilbert's idea of Hotel Infinity to explain Cantor's approach to the cardinality of a set. This will naturally lead us to countable and uncountable sets and some surprising properties of infinite sets. Cantor's theorem is explained and how it leads us to a whole hierarchy of different infinities (rather than just one). We will also discuss the connections to the axiom of choice and some possible definitions of what it means for a set to be infinite.

February 6, 2008

Games Night: The Game of Pigs

Dr. Frank Bauerle 

The "Game of Pigs" is a simple dice game. The first player to 100 points wins. You score points as long you don't roll a one. At any time you can stop rolling (and end your turn) and "bank" your current score to get you closer to the target. But if you roll a one, you lose all the points of your current turn (you keep your "banked" points). We will play the game with dice and on-line against a computer a few times to get a feel for the game. Then we will dicuss the mathematics behind the strategy that will maximize your chance of winning. Time permitting, we can play some other dice games.

February 13, 2008

The History of Number and Numeration

Professor Tony Tromba 

We will trace the long struggle to find an adequate system of counting. Human societies have developed many different ways of writing numbers, but all but one civilization failed to discover our modern number system. Why was this so hard and what were the difficulties that had to be overcome before this system could be discovered?

February 20, 2008

Games Night: Settlers of Catan

Dr Frank Bauerle 

This week we will be playing Settlers of Catan, a multiplayer board game designed by Klaus Teuber. It was first published in 1995 in Germany by Franckh-Kosmos Verlags-GmbH & Co. (Kosmos) under the name Die Siedler von Catan. Briefly, The players in the game represent the eponymous settlers, establishing a colony on the previously uninhabited island of Catan. The island itself is laid out randomly at the beginning of each game from hexagonal tiles ("hexes") of different land types. Numbered tokens are then placed on each of the tiles, except for one desert hex.

February 27, 2008

Games Night

Dr. Frank Bauerle 

This week we will be mixing things up a bit. Instead of focusing on a single game we will be playing a variety of Games, exploring new and different strategies. A few examples of some we may choose to tackle are: Settler's of Catan, Ricochet Robots, Quoridor, and Set.

March 5, 2008

A Gentle Introduction to Quantum Geometries

Mathematics Undergraduate, Stanley Bishop 

Historically, it is when the frontiers of physics and geometry coincide that both subjects have made the most dramatic steps forward. 

Perhaps the best example of this interplay was Einstein's realization that gravity is a feature of geometry: objects do not fall, they follow the natural curvature of space-time. Developing these ideas and the language needed to express them has lead to a deeper understanding of space for both mathematicians and physicists. 

Einstein further envisioned a unified theory in which all of physics could be understood geometrically, yet with the advent of quantum mechanics this program seemed to hit a wall. The Heisenberg uncertainty principal says that any attempt to isolate the position of a particle is doomed to failure, how is one to consider geometrically a system with no coherent notion of position? 

Is it possible to mathematically extend our idea of what space is and realize quantum physics as a feature of some strange geometry? It is one possible answer we will consider by looking at a basic example and then discussing the connection between a space and the functions of that space which may exist. 

March 14, 2008

Movie Night - Infinite Series: Archimedes and Pi

Dr. Frank Bauerle, Lecturer, UCSC Mathematics Department 

In celebration of Pi Day, we will be showing Infinite Secrets, a NOVA episode on Archimedes and Pi. Archimedes is the most famous of the ancient mathematicians and the first to discover the value for Pi. He wanted to find a value as close as reasonably possible to the ratio of the circumference of a circle to its diameter. He devised an ingenious method using straight lines to measure a circle, finding the value for Pi. It has become one of the most widely used mathematical values today.