SPRING 2003                                                                                                  FIFTY-EIGHTH SERIES

M*A*T*H

Colloquium

The Mathematics Department of Sonoma State University

presents a series of informal talks open to the public.

“Mathematics is the process of turning coffee into theorems” – Paul Erdös

This series is supported entirely by private donations.

New - Syllabus for Math 175/375 Students

 

Wednesdays at 4:00 p.m.

Darwin Hall Room 108

Coffee at 3:45 p.m.

 

 

FEBRUARY 5                  XOR, Ken Yanosko, Professor of Mathematics, Humboldt State University: In mathematics, when we use the word "or" we usually intend the "inclusive or", which has the meaning "and/or". But there are in fact many contexts in which "or" should be taken to denote the "exclusive or", with the meaning "or but not both". In this talk we will investigate some applications of the exclusive or, "xor", in logic, algebra, cryptography, and game theory.

 

FEBRUARY 12                 CREDIBILITY THEORY, Jerry Klenow, Professor of Mathematics, Sonoma State University, independent consultant and a Fellow of the Casualty Actuarial Society:  For how many years must a driver remain "claim free" in order to earn a meaningful discount on insurance rates? When new information becomes available, how much "weight" should be assigned to it relative to the broader, historical, data base? If two different sources of data are being used to answer the same question, how much "weight" should be given to each?  Actuaries address these issues using a set of procedures that have been developed under the topic known as Credibility Theory.

 

FEBRUARY 19                 MATHEMATICA TOOLKITS, Bill Barnier, Professor of Mathematics, Sonoma State University, and his Fall 2002 Math 180 Students (Jessica Doran, Vicente Duarte, Jennifer Flory, Sarah Minnick, Jason Murphy, Helene Nehrebecki, and Edward Roubal): Student projects done for the Fall 2002 Math 180 class will exhibit colorful and accessible Mathematica programs that demonstrate applications of mathematics in a variety of areas.  Pizza after Colloquium.

 

FEBRUARY 26                 HOW DOES THE BRAIN COMBINE DIFFERENT SOURCES OF INFORMATION?, Marty Banks, Professor of Vision Science, Optometry, & Psychology, UC Berkeley: We use more than source of sensory information when estimating properties of the environment. For example, the eyes and hands both provide relevant information concerning an object's shape. The eyes estimate shape using binocular disparity (differences in the images to the two eyes) and pictorial cues (also used by painters). The hands supply shape information by means of tactile and proprioceptive cues. One can show, using Bayes' rule, that there is a statistically optimal way to combine information from different sources. We find that the brain follows this statistically optimal strategy under a wide variety of situations.

 

MARCH 5              WHAT'S THE MATH ON RAP?, Helene Nehrebecki, Student in Mathematics, Sonoma State University: The math of rap and hip-hop begins with the math of music.  Experiments performed by Pythagoras show how frequencies are intentionally made so music is possible.  Included will be a demonstration on measuring frequencies on a chromatic scale.  Ratios of major musical chords, designing instruments, a brief history of pop music, and math behind non-offensive hip-hop lyrics and keyboard hooks will be discussed. COME FOR THE HIP-HOP, STAY FOR THE MATH!   Pizza after Colloquium.

 

MARCH 12            GAMMA AND A PRODUCT OF SINES, David Sklar, SOLA Optical and City College of San Francisco: This talk is about a surprising trigonometric identity that arises in the theory of Euler’s Gamma function.  We’ll look at a short, relatively elementary, proof using the geometry of the unit circle, cyclotomic polynomials, and some basic algebra of complex numbers. Then we’ll review enough of the theory of the Gamma function to see how our trig identity can be derived from Gauss’s multiplication formula.

 

MARCH 19            TEACHER’S PETS, Charles Biles, Professor of Mathematics, Humboldt State University: This is a little collection of some gems I've collected over the last couple of years. The talk is meant for undergraduates and should be accessible to sophomore math majors. Even freshpeople will get something out of it. This is not one of those heavy-duty talks whose intention is to blow people out of the water -- Just the opposite.

 

MARCH 26            THE BINOMIAL THEOREM, INDICATORS, AND THE BELL CURVE, Matthew Carlton, Professor of Mathematics, Cal Poly San Luis Obispo: In this talk, we will show how the binomial theorem plays a role in probability and exemplifies two important statistical tools: indicator variables and the Central Limit Theorem. The talk is geared toward undergraduates and doesn't assume prior statistics knowledge.

 

APRIL 2                DUALITY AND SYMMETRY OF HYPER-GEOMETRIC PROBABILITIES, James Jantosciak, Professor of Mathematics (Retired), Brooklyn College: The inherent duality and symmetry of the hypergeometric probability distribution is explained in the context of problems commonly encountered.  For instance, among 15 students, 12 are seniors and 9 are math majors.  What is the probability that 7 students are senior math majors?

 

APRIL 9                SPRING BREAK

 

MATH FESTIVAL
APRIL 16               COMPUTING WITH WORDS AND PERCEPTIONS – A PARADIGM SHIFT IN COMPUTING AND DECISION ANALYSIS, Lotfi A. Zadeh, Professor in the Graduate School, Computer Science Division, Department of Electrical Engineering and Computer Sciences, U C Berkeley: Computing with words and perceptions, or CWP for short, is a mode of computing in which the objects of computation are words, propositions and perceptions described in a natural language. Perceptions play a key role in human cognition. Humans — but not machines — have a remarkable capability to perform a wide variety of physical and mental tasks without any measurements and any computations. Everyday examples of such tasks are driving a car in city traffic, playing tennis and summarizing a book. One of the major aims of CWP is to serve as a basis for equipping machines with a capability to operate on perception-based information.

 

APRIL 23               THE CENTIMETER SOLUTION IN GPS SURVEY, William Poe, Professor of History, Sonoma State University:  A description of the mathematical aspects of achieving the centimeter level of precision in a GPS survey. Some preliminary description of the way that the GPS system works will be necessary. I will demonstrate the post-processing software that I use. The actual algorithms used by the software are proprietary to each manufacturer and are closely guarded trade secrets.

 

APRIL 30               THE MILLENIUM PROBLEMS, Keith Devlin, Stanford University, and author of The Millennium Problems: the seven greatest unsolved mathematical puzzles of our time, published by Basic Books (2002) .  In 2000, The Clay Mathematics Institute, a privately funded research center in Cambridge, Massachusetts, announced that $7 million in prize money awaited the individuals who first solved the seven most difficult open problems of mathematics: the Millennium Problems. The problems were selected by a small group of internationally acclaimed mathematicians, who felt that they are the most significant unsolved problems of contemporary mathematics. They lie at the center of major areas of mathematics and have resisted attempts at solution by many of the best mathematicians in the world. What are these problems, and what are your chances of solving one of them and pocketing the $1 million prize?

 

MAY 7                  IMAGE PROCESSING OF RADAR IMAGES USING MATLAB, Raquel Maderazo, Raytheon Corp, LA: Image processing applications for radar images will illustrate jobs available in engineering for math majors.  There will be a little pitch for Raytheon!

 

MAY 14                 COMBINATORICS OF STRING RE-WRITING SYSTEMS, Bala Ravikumar, Professor of Computer Science, Sonoma State University: String rewriting is a fundamental concept in linguistics, in computation and in proof theory. In this talk, we will look at some simple string rewriting systems and attempt to answer questions about characterization of reachable configurations, shortest path to reach a specific configuration, the number of reachable ones etc. Examples will be chosen that highlight specific techniques. Some of them are results are new, while others are well-known.  Pizza after Colloquium.

updated 2/12/03