FALL 1997 FORTY-SEVENTH SERIES

WEDNESDAYS
         
Lecture at 4:00 PM in Darwin 108, Coffee in Darwin 108 Foyer at 3:40 PM 

M*A*T*H COLLOQUIUM




SEPTEMBER 10	

MYTHS OF MATHEMATICS

 

Morris W. Hirsch, Mathematics, U C Berkeley, will discuss the notion that Mathematicians, like members of any community, have certain beliefs about what they do, which they take for granted and rarely examine critically. Occasionally these myths run up against harsh reality. In this talk I will examine such myths, including the Myth of Truth (that every mathematical statement is true or false); the Myth of Proof (that there is a well-defined notion of correct proof); and the Myth of Computers (that a good approximate answer to any problem can be found by a computer calculation).


SEPTEMBER 17 WHO SOLVED THE PROBLEM, YOU OR YOUR COMPUTER?

Clement Falbo, Mathematics, SSU, will tell of the LOVE-HATE relationship between one mathematician and his "Symbolic Math Processing" software. We will have an open discussion on how this software changes the type of problems we should ask students to solve. What do we mean by a Problem? a Solution? Is Understanding still important? What, if anything, should we ask students to Memorize? Is Drill dead? Are Proofs passˇ?



SEPTEMBER 24 HILBERT'S THIRD PROBLEM

Dan Wheeler, Mathematics, San Francisco State and formerly Sonoma State, will discuss the following question: Given two tetrahedra of equal bases and altitudes, is it always possible to dissect one into a finite number of parts in such a way that these parts may be reassembled to form the other?



OCTOBER 1 STUDENT PROJECTS IN CALCULUS

Bill Barnier, Mathematics, and Doug Martin, Chemistry, SSU, will describe several student projects in calculus. The presentation will be graphic and should appeal to anyone with an interest in mathematics and its applications. Calculus background is not necessary.



OCTOBER 8 COMPLEX CURVATURE

Tristan Needham, Mathematics, USF, will discuss a new type of (complex) curvature which can be associated with conformal mappings of the plane. This concept provides an elegant method of recognizing an harmonic function just by looking at a picture of its level curves. The talk should be accessible to any undergraduate who has taken complex analysis.



OCTOBER 15 WEIGHTED VOTING, MEASURES OF POWER, AND EQUAL REPRESENTATION

Jim Pedgrift, Mathematics, SSU, will consider mathematical consequences of a series of one-person-one-vote decisions handed down in the 1960's by the U.S. Supreme Court, setting forth a new standard of constitutional fairness for systems of elected representation at the state and local level. Some very interesting mathematical problems were created in the attempt to quantify and measure power and representation.



OCTOBER 22 CRYPTOGRAPHY: THE ART AND SCIENCE OF CODE-BREAKING

Karen Fraser, Learning Skills Services, SSU, will explain how the power of secret codes has saved lives, won wars, and made fortunes! She will help you learn to encode and decode secret messages. A mathematical and historical exploration of several types of ciphers, this lecture will demonstrate how to crack monoalphabetic, polyalphabetic, and product ciphers, as well as many others.



OCTOBER 29 POLYHEDRAL TRIGONOMETRY

Jeff Hrdlicka, MatheMagician, of Starmast Multimedia, will take trigonometry, a useful two-dimensional tool, and use it to examine two-dimensional sections of three-dimensional polyhedra. The relationships among the various sections reveal a variety of elegant formulae, including the miter-bevel settings for cutting polygonal picture frames, methods for creating tunnels through polyhedra, rectangular and spherical coordinates for the Platonic and Archimedean polyhedra, and an n-spherical distance formula.



NOVEMBER 5 INVENTING 'WHEN': MATHEMATIZING TIME

Nelson (Buzz) Kellogg, Hutchins, SSU, will discuss some of the fascinating philosophical problems that arise in quantifying time.



NOVEMBER 12 CHAOS FROM SIMPLE TRIG

Rick Luttmann, Mathematics, SSU, will examine a simple trigonometric function, and show how iteration can lead to chaos. The example illustrates all of the characteristic phenomena of chaos theory.



NOVEMBER 19 A SIMPLIFIED AXIOM SYSTEM FOR CHAOS

Eldon Vought, Mathematics, Chico State, will discuss a recent discovery in Chaos Theory by five mathematicians in Australia. A common definition of chaos in a dynamical system is that the system possesses (1) transitivity, (2) a dense set of periodic points, and (3) sensitive dependence on initial conditions. Now it appears that (3) is a consequence of (1) and (2). The talk examines the proof and some of the motivations that led to this discovery. The topic involves elementary topology with a nice application of the triangle inequality.



NOVEMBER 26 THANKSGIVING RECESS



DECEMBER 3 THE INDOOR SPORT OF PRIME NUMBER HUNTING

Landon Curt Noll, cryptographer, Information Security Infrastructure Team, Silicon Graphics Inc, Mountain View, and two-time holder of the world's record for largest known prime, will discuss the search for larger and larger primes. Today, hunters seek prime numbers that approach a million digits in size. We will survey the mathematics as well as the tricks of the trade used by those who seek new large primes.



DECEMBER 10 BAYESIAN vs CLASSICAL STATISTICS: AN OVERVIEW

Brian Jersky, Mathematics, SSU, will present the underlying assumptions of Classical Statistical theory and compare them to those underlying Bayesian Statistics. Both reveal interesting and enlightening insights into uncertainty, and so there is no real disagreement between the two schools of thought. Applications to confidence intervals and hypothesis testing will be shown. This talk is appropriate for most students.



Parking permits ($1.50) are required Monday through Thursday 6am -10pm. No public parking is permitted in reserved spaces at any time.