### SPRING 2003 FIFTY-EIGHTH SERIES

M*A*T*H

#### Colloquium

## 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.****
**

** **

### 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

###