Colloquium Schedule
2000-2001 Colloquia
- Self-Reference and Fixed Points in Recursion Theory and
Goedel's Incompleteness Theorems
Bob Wolf, Mathematics Department, Cal Poly
Abstract
Goedel's incompleteness theorems, like the uncertainty principle in physics, are among the most profound and surprising "negative" scientific discoveries of the twentieth century. In 1929, at the age of 22, Kurt Goedel proved that formal mathematical systems cannot even determine the truth or falsity of all questions involving whole numbers.
He also proved that a formal system that includes a significant amount of mathematics cannot be shown to be consistent (free from contradictions) without using methods more powerful than what is included in the system itself. Goedel's work shattered an ambitious program that had been launched by David Hilbert, intending to find formal systems that would settle all mathematical problems and would be free from contradiction.
This talk will explain the ingenious ideas used by Goedel to prove these theorems, and will show how the same ideas were used to prove some of the most important results in recursion theory, the branch of mathematics that studies computers and their capabilities. - Fair Division Using Combinatorial Topology
Francis Edward Su, Harvey Mudd College
Abstract
You and your friends move into a house and find yourselves debating who should get what room and for what part of the total rent. Is it always possible to split the rent in such a way that everyone will choose a different room? If so, how?
In this talk, we'll show how ideas from combinatorial topology (such as Sperner's lemma, Tucker's lemma, and generalizations) can address this and other "fair division" questions. These yield constructive N-person procedures for the division of goods (such as the classical cake-cutting problem), burdens, and mixtures of goods and burdens (such as the rent problem). Stronger solution concepts are obtained from stronger combinatorial theorems; proofs exhibit interesting connections between combinatorics, analysis, topology and the social sciences.
Undergraduates are encouraged to attend; this talk features work by undergraduates, and no background in topology is assumed. - An Evacuation Model: Highway from the Danger Zone
Cal Poly Mathematics Modeling Team: Brian Morris, Aaron Newcomer, J.C. Price
Abstract
In the 2001 Mathematical Contest in Modeling, we were asked to model the evacuation of the coastal population of South Carolina in the face of an oncoming hurricane. We were also asked to suggest strategies for improving traffic flow from the area. We created a computer simulation program to test the effectiveness of lane reversals on major highways, staggered evacuation times by counties and restrictions on the number and type of vehicles each family might bring. Time restraints prohibited a more through investigation, however we determined that staggered evacuation times would ease traffic during an evacuation. We concluded our paper with a newspaper article to inform the public of our results. - Reconstructing Planar Domains from Moments
Mihai Putinar, U.C. Santa Barbara
Abstract
It is well known that X-ray data of a planar shape can be interpreted, via Radon transform, as a partial set of moments. In general these data do not suffice to reconstruct exactly the shape. However, for quadrature domains, a remarkable class of semi-algebraic domains which approximate every planar domain, it is possible to perform the reconstruction exactly. We will discuss this algorithm and the necessary approximation bounds. Methods of operator theory, complex analysis and approximation theory will be invoked. - Bicycle Wheel Aerodynamics: What a Drag
Cal Poly Mathematics Modeling Team: Joel Fish, Brian Miceli, Ryan Tully-Doyle
Abstract
In the 2001 Mathematical Contest in Modeling, we were asked to provide a table demonstrating the conditions for which the ideal rear wheel of a racing bicycle is a spoked wheel and those for which it is solid. We were also asked to present a method for using the tables. We wrote a spreadsheet program based on a simplified power-speed equation to generate the necessary tables. To improve the accuracy of wheel selection, we wrote a computer program to model bicycle races on approximated courses, taking into account wind direction and variable coefficients of drag. In the interest of accuracy, we employed the RK4 numerical method to approximate solutions to the speed equation. Using these solutions, we were able to effectively model a real race given various power curves. We wrote a robust computer program to incorporate our developments into our previous model and ran test cases on a simple hypothetical course. - Electrons on the Sphere
Michael Neubauer, CSU Northridge
Abstract
We consider n equally charged particles, say electrons, that are constrained to the sphere. The final configuration will be one that minimizes the Coulomb potential energy of the system. The questions are:
What are these minimal configurations?
What is the minimal Coulomb energy of the system?
The talk will feature lots of pictures of arrangements of points on the sphere and their convex hulls. Undergraduates encouraged to attend. - The Star Problem
Estelle Basor, Mathematics Department, Cal Poly
Abstract
Consider n x n matrices with ones below the main diagonal, plus or minus ones (randomly chosen) above the main diagonal and zeros elsewhere. If we plot all the eigenvalues for such matrices, what shape is formed as n approaches infinity? This problem was the topic of the senior project of Jeff Liese. His results will be described as well as some remaining questions. Undergraduates are especially encouraged to attend this talk. - Random Pick Matrices
Linda Patton, Mathematics Department, Cal Poly
Abstract
The Nevanlinna-Pick interpolation theorem describes when there exists an analytic function from the unit disk (in the complex plane) to itself which interpolates n specified data pairs. The necessary and sufficient condition is that a certain n x n "Pick" matrix which depends on the interpolation data is positive semidefinite.
Question: If the data points are independently uniformly distributed in the unit disk, what is the probability that the associated Pick matrix is positive semidefinite? This question will be answered when n = 2. A nice general conjecture which resulted from a senior project will be described. - The Poincare Conjecture, or How to Become a
Millionaire
Daryl Cooper, U.C. Santa Barbara
Abstract
If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction around a doughnut, then there is no way of shrinking it to a point without breaking either the rubber band or the doughnut. We say the surface of the apple is "simply connected", but that the surface of the doughnut is not. Poincare, almost a hundred years ago, knew that a two-dimensional sphere is essentially characterized by this property of simple connectivity, and asked the corresponding question for the three-dimensional sphere (the set of points in four-dimensional space at unit distance from the origin). This question turned out to be extraordinarily difficult, and mathematicians have been struggling with it ever since.
The Clay Mathematics Institute is offering one million dollars for the solution to any of seven famous problems. The Poincare conjecture is one of them. It is a basic question about the possible shapes for three-dimensional "universes." - Mathematics and Magic Tricks
Persi Diaconis, Stanford University
Abstract
Sometimes the way a magic trick works is more amazing than the trick itself. Professor Diaconis will illustrate this idea with the mathematics of shuffling cards. There are applications of these ideas to parallel processing, group theory and even to the ability to invent new card tricks. The content of the talk is joint work with bill Cantor and Ron Graham and all undergraduate mathematics and statistics majors are encouraged to attend.
Persi Diaconis is a Professor of Mathematics and Statistics at Stanford University. He is perhaps best known for his checkered past as a professional magician. He is also a winner of the McCarthy award and a member of the National Academy of Sciences. - Computational Algebra and (Non)Commutativity
Susan Hermiller, University of Nebraska
Abstract
For an ideal I in a polynomial ring R, the Ideal Membership Problem asks if there is a computational algorithm to determine, for any polynomial in R, whether or not the polynomial is in I. In general, if the polynomials are commutative, the answer is that a Groebner basis can be used to provide the algorithm, but if the polynomials are noncommutative, there may be no algorithm at all. In this talk Groebner bases for both commutative and noncommutative ideals will be described, as well as the correspondence between them. An integral part of this correspondence is captured in the commutator ideal in the noncommutative polynomial ring. Examples of several computational properties of this ideal will be given (this is joint work with J. McCammond). - Explosion and Quenching Problems
Colleen Kirk, Montclair State University, New Jersey
Abstract
Nonlinear heat equations (parabolic partial differential equations) will be examined for blow-up and quenching solutions. Blow-up explosion) occurs when the solution becomes unbounded in finite time. Quenching occurs when the solution of the equation remains bounded, while the first order time derivative becomes unbounded in finite time. One mathematical model will be examined in detail: A concentrated heat source moves within a reactive-diffusive medium. Of primary interest is the role that the speed of the source plays in determining whether or not blow-up occurs. - Situations That Facilitate the Development of
Skepticism
Stacy Brown, University of Illinois
Abstract
Researchers have shown that undergraduate mathematics majors experience difficulties understanding, producing and appreciating mathematical proofs. However, little is known about the types of didactical situations that lead to the development of mathematical skepticism, a prerequisite to justification. In this talk, some preliminary findings from a three-part teaching experiment in which the investigator attempted to facilitate the development of skepticism (on the students' behalfs) will be discussed. - A Survey of Algorithms in 3-Manifold Topology
David Bachman
Abstract
In 1961 Haken gave an algorithm which determines whether or not a given loop of string could be deformed (without cutting!) into a circle. Since then, his algorithm has been modified to solve many other interesting problems in 3-manifold topology. For example, in 1991 Rubinstein gave a modification which determines if a given 3-manifold is homeomorphic to the 3-sphere.
In this talk we will review Haken's original algorithm, and some of the more recent modifications. We will then discuss some of the many open topology questions which seem likely to fall to similar techniques. Also, we will mention some of the questions the algorithms themselves have generated, in regards to computational complexity issues. - Distance-Regular Graphs and the Taut Condition
Mark MacLean, University of Wisconsin
Abstract
Graphs that are distance-regular make an interesting subject of study because of their high degree of combinatorial regularity and symmetry. Perhaps the most familiar examples of distance-regular graphs are the vertices and edges for each of the platonic solids. In this talk, we'll define what it means for a graph to be distance-regular, and we'll see how they can be studied by examining a particular matrix algebra. We'll then define a certain algebraic property for distance-regular graphs called the *taut condition*, and we'll look at this condition in detail.
About the Speaker
Mark MacLean is a candidate for a tenure-track faculty position in the Mathematics Department. He is currently a graduate student at the University of Wisconsin. - Ergodic Theory, Geodesic Flows and Hyperbolic
Geometry
Florence Newberger, Pennsylvania State University at University Park
Abstract
Ergodic theory is the study of measure theoretic dynamical systems. These dynamical systems consist of a space (set) X, a measure m (and a Borel algebra of measurable sets B), and a transformation T:X -> X which preserves m. One goal in ergodic theory is to categorize the degree to which T "mixes up" X. We will begin by defining several such degrees of mixing. We will proceed by describing a measure theoretic dynamical system that is very geometric in nature. The space X in this system is a locally symmetric negatively curved manifold, in particular, one whose universal cover is hyperbolic space. The transformation is the geodesic flow on this manifold. We will discuss how properties of the manifold correspond to properties of the action of its fundamental group viewed as a group of isometries of hyperbolic space. The measure in this system is geometrically constructed from this group of isometries. Because the system is so inherently geometric, an understanding of the dynamics can reveal an understanding of the geometry and vice versa. We will finish by stating some ergodic theoretic results for these systems, including that they achieve a particularly high degree of mixing.
About the Speaker
Florence Newberger is a candidate for a tenure-track faculty position in the Mathematics Department. She is currently a S. Chowla Research Assistant Professor at Pennsylvania State University at University Park. - Low Dimensional Manifolds, Geometry, and Algebra
Matthew White, Mathematics Department, Cal Poly
Abstract
In this talk, we explore some of the interesting questions in low dimensional topology. Primarily, we consider closed 3-dimensional manifolds. These are (suitably nice) compact topological spaces that locally "look like" an open ball in Euclidean 3-space. The major unsolved problem in 3-manifolds research is that of classification; that is, can we list, up to homeomorphism, all of the closed 3-manifolds? Thurston has provided a conjectural classification which uses ideas developed from surfaces (closed 2-manifolds). Hence, to develop insight, we will spend some time discussing the analogous problems for surfaces. This is helpful since surfaces were classified in 1922. We will also build a few 3-manifolds. In the attempt to understand the issues in classification, there emerges a fascinating interplay between topology, geometry, and algebra. We will discuss how topologists exploit these connections. The author will also present some of his own work. - Quivers and Quotients of Path Algebras
Jessica Sklar, University of Oregon
Abstract
Let G be a quiver, that is, a finite directed graph. The paths in G form a semigroup; using this semigroup, we can create the C-path algebra of G. We first examine some common algebras from this perspective. Next, a lovely theorem tells us that any "nice" finite-dimensional C-algebra is isomorphic to a quotient of a path algebra; this is one reason to study path algebras! We end by discussing two important classes of such quotients. - Asymptotic and v-Asymptotic Expansions
Todor Todorov, Mathematics Department, Cal Poly
Abstract
The first part of this talk is a short introduction to asymptotic analysis and will be accessible to graduate students. We start with the definitions of Landau's asymptotic symbols, asymptotic series and asymptotic expansion of a function. With several examples we will try to demonstrate that an asymptotic expansion in a divergent series might be as useful as (or even more useful than) an expansion in a convergent series. There will also be examples of asymptotic formulas from calculus.
In the second part of the talk we define a non-Archimedean metric and the concept of v-asymptotic series (v stands for "valuation") in the class of functions with moderate growth. We show that a function is an asymptotic sum of a v-asymptotic series iff the function is the sum of the series in the metric topology. As an application (whose origin is in quantum statistics) we calculate the v-asymptotic expansion of an integral with a large parameter. This work is a simplified and shortened version of a recent article on nonstandard asymptotics (jointly with Bob Wolf). - Identifying Spaces from Groups of Transformations
Joe Borzellino, Penn State University
Abstract
Given a geometric object X (a topological space X), one can look at the group of transformations (homeomorphisms) of that space. A transformation is a bijective map of the space to itself which is continuous and has continuous inverse. If the space X carries an additional structure (e.g. differentiable), we may wish to look at those transformations that also preserve that structure (diffeomorphisms). An idea of Klein was to study a topological or geometric space by investigating properties of its group of transformations. One of the main questions is to determine whether or not a topological space is completely identifiable by its group of transformations. In other words, can two different topological spaces have the same group of transformations? For manifolds of dimension larger than one, the answer is no. I will begin by looking at some specific low dimensional examples, and give some history of the work done on this problem. Finally, I will introduce the notion of an orbifold (which is a generalization of the concept of a manifold), and show why Klein's program when applied to orbifolds offers some surprising results. - God Help the State of Maine When Mathematics Reach for Her: A
Mathematical Peculiarity of the Constitution
John Alongi, Carleton College
Abstract
What does mathematics have to do with the first presidential veto? Why does the House of Representatives have 435 members? The United States Constitution requires that "Representatives shall be apportioned among the several states according to their respective numbers, counting the whole number of persons in each State ...". How does geometry wreak havoc with this seemingly innocuous requirement? My talk will address these questions and expose the power and complexity of mathematics in the social sciences. - On the Leray-Schauder principle in the ANR spaces
Andrzej Granas, University of Montreal
Abstract
The topic of the talk lies on the borderline of geometric topology (theory of ANRs) and nonlinear analysis. In the first part of the talk we shall recall the definition and basic properties of the ANR spaces (these spaces include, for example, polyhedra, Banach manifolds, and finite unions of closed convex sets in Banach spaces). Then we address the question of compact extendability of a compact map into an ANR space; we show that this problem depends only on the compact homotopy class of a given compact map. Precisely, in the context of the theory of compact maps, we establish an analogue of the classical Homotopy Extension Theorem of Borsuk.
In the second part of the talk, the above extended result is applied to obtain a Generalized Schauder fixed point theorem and the Leray-Schauder principle in arbitrary ANRs will be established. The classical Schauder theorem and the classical Leray-Schauder principle in Banach spaces are special cases of the above theorems.
The methods used in the proofs of the above results are elementary and no use is made of the fixed point index for ANRs. - Comparing Writing with Interviews and Traditional Forms of
Assessment of Students' Understanding of the Derivative
Gwen Fisher, University of Wisconsin, Madison
Abstract
Many scholars agree that the daily writing journal is not a prohibitive tool of assessment for a class of moderate size, and the journal can provide a continuous source of data describing each student's understanding about the material. This study compares the use of open-ended writing tasks with interviews and traditional calculus assessments to assess students' understanding of the concept of the derivative. This study was designed to test the hypotheses: students can be taught to write what they would say in an interview, and daily, focused writing assignments can provide a continuous source of data that are qualitatively different from data obtained from written, in-class tests. The data for this study consists of 14 students' responses to (a) two one-hour interviews, (b) a subset of the 39 writing tasks, and (c) three in-class exams. An example of the writing tasks is, "What does the derivative have to do with limits and vice-versa?" The theoretical framework for the data analysis depicts the derivative as a ratio, as a limit, and as a function, each of which may be referenced as a recognition, as a dynamic process, and as a static object. Also, each reference can be coded in any of four representations: numeric, graphical, symbolic, and concrete. - Joint Math/Stat Colloquium
If Statistics Isn't Mathematics, We Can't Go On Meeting Like This
Ann Watkins, Mathematics Department, California State University, Northridge
Abstract
Over the last several decades, the statistics and mathematics communities have diverged, acknowledging little in common other than a claim to John Tukey. Recently, however, the Mathematical Association of America and the American Statistical Association have begun to collaborate. This is partly a result of developments in the schools, and partly because the weaknesses within each discipline have analogues in the strengths in the other. Common interests include the content of the respective undergraduate majors, the dearth of actual majors in mathematics and statistics, equitable treatment for statisticians in mathematics departments, the secondary school curriculum and the Advanced Placement Program, and training the mathematicians who teach statistics.
About the Speaker
Ann Watkins is Professor of Mathematics at California State University, Northridge. In January, she will become president of the MAA, having served previously as second vice-president, governor of the Southern California Section, chair of the Coordinating Council on Education, and co-editor of the College Mathematics Journal. Her field is statistics education. She is a former chair of the Advanced Placement Statistics Development Committee and the co-author or co-editor of thirteen books including Activity-Based Statistics and Exploring Data. She was selected as the 1994-1995 Cal State Northridge Outstanding Professor and won the 1997 Cal State Northridge Award for the Advancement of Teaching Effectiveness. She was recently elected a Fellow of the American Statistical Association. - Special Undergraduate Mathematics
Colloquium
Numbers, Nimbers, and Numberless Wonders: An Introduction to Combinatorial Game Theory
Jason Lee, U.C. San Diego
Abstract
Loosely speaking, a combinatorial game is a two-player game with perfect information (both players always know what is going on) and with no chance moves such as rolling dice or drawing cards. The two players take turns making clearly defined moves. We require that the game terminate after finitely many moves, and the winner is the last person able to make a move. NIM is probably the most well known example of a combinatorial game.
Examples of combinatorial games and their arithmetic will be given, most notably, how to add and subtract games. I'll prove that 1/2 + 1/2 = 1 (numbers) and say why this needs proof. I'll mention some of the bizarre objects that arise in the arithmetic system, including up, down, star, tinies, minies, the ever important nimbers, and really baffling things like infinitesimals (numberless wonders).
Some of the basic theorems and techniques include the Number Avoidance Theorem, the Enough Rope Principle, the powerful Sprague-Grundy Theorem, and the simple but effective and oft used Tweedledee and Tweedledum Argument. - Joint Math/Stat Colloquium
Screening Test Methodology
Wesley Johnson, Chair, Graduate Group in Epidemiology
Professor, Dept. of Statistics, University of California, Davis
Abstract
In this talk, we will discuss some recent progress in screening test methodology. The standard goals are to find individuals in a population that have a particular characteristic of interest, such as HIV infected blood units that have been donated for transfusion, or drug users in the transportation industry, for example. We can also estimate various parameters of interest, like the sensitivity and specificity of the screening tests, the prevalence of the characteristic in the population, and the prevalence in the screened population. Prediction may also be of interest, e.g. we may want to make inferences about the number of drug users in an, as yet, unscreened company,or about the number of drug users that will be missed by the screening procedure. We consider situations both with and without a gold standard.
About the speaker
Dr. Johnson is a professor in the Division of Statistics at U.C. Davis, and also the Chair of the Graduate Group in Epidemiology there. He is the author of numerous publications, and in 1995 was given the Most Outstanding Faculty/Staff Award. - Partitions
Lawrence Sze, Mathematics Department, Cal Poly
Abstract
A partition of a positive integer n is a non-increasing sequence of positive integers that sum to n. For example, the 5 partitions of 4 are (4), (3,1), (2,2), (2,1,1), and (1,1,1,1). The number of partitions of n grows rapidly with n. For example, there are 304,801,365 partitions of 104. The numbers of partitions satisfy many interesting properties. For instance, consistent with the above two example partition numbers, the Ramanujan Congruences state that the number of partitions of 5N+4 is always divisible by 5.
I will discuss these and other properties of general partitions along with more specialized types of partitions such as t-core and (e,r)-core partitions. Furthermore, I will try to point out areas suitable for possible undergraduate research.
This talk should be of interest to mathematically inclined undergraduates and faculty, especially those with an interest in number theory and combinatorics. - The Chain Rule and Other Combinatorial Ideas
Art DeKleine, Mathematics Department, Cal Poly
Abstract
Calculus is a study of rates of change, and combinatorics is a study of counting techniques, two seemingly different areas of mathematics. A formula for differentiating composite functions, called the Chain Rule, is established in all beginning calculus classes, as are higher-order derivatives (position, velocity, acceleration, jerk, etc.). Question: Is there a "nice" formula for higher-order derivatives of composite functions? This question prompts a discussion of techniques studied in the combinatorics class, hence the title. - Kernels of Hankel Operators and Hyponormality of Toeplitz
Operators
Jonathan Shapiro, Mathematics Department, Cal Poly
Abstract
Dr. Shapiro will discuss formulas for kernels of products of Hankel operators and identities involving kernels of Hankel operators. He will use properties of the kernels of Hankel operators to explore the hyponormality of certain Toeplitz operators, including those whose symbol is of circulant type. In addition, he will discuss formulas for and estimates of the rank of the self-commutator of a hyponormal Toeplitz operator. - Algorithmic Roots of Goedel's Incompleteness
Theorem
Vladimir Uspenskiy, Lomonosov University of Moscow
Abstract
Given any proof system, there is a true statement that cannot be proven within the system. This fact is the content of Goedel's famous incompleteness theorem - one of the deepest theorems in mathematics. It is amazing that Goedel found a precise formulation and a proof of his theorem. It is no less amazing that the theorem actually is of a rather simple nature. An attempt will be made in this talk to unearth the roots of the theorem, which lie in computability theory.
About the Speaker
Professor Vladimir Uspenskiy is a Russian mathematician in the fields of mathematical logic, theory of algorithms, foundations of mathematics, non-standard analysis, axiomatic probability theory and other areas. For many years, he has been the Chair of the Department of Mathematical Logic and Theory of Algorithms in the Moscow State University (he "inherited the Chairmanship" of this department from the famous Kolmogorov). - Introduction to Groebner Basis
Mark Stankus, Mathematics Department, Cal Poly
Abstract
Is there a procedure for solving systems of polynomial equations which is in some way similar to Gaussian elimination for linear equations? The answer is a qualified yes. Just as Gaussian elimination yields a matrix in echelon form which can be used to solve the system, there are algorithms for a system of polynomial equations which yield a "Groebner basis". This basis can be used to answer some questions about the solutions to the system.
There are also similar techniques which can be used for matrix equations. Applications include simplifying matrix expressions, creating new matrix equations from given equations (which can be helpful when trying to prove a theorem), and studying the solutions to a collection of matrix equations. For example, a collection of matrix equations from a problem in engineering may not be initially amenable to numerical solution, whereas our methods could give an equivalent collection of equations which is numerically solvable. Examples will be given.
The algorithms for computing Groebner basis (for polynomials) are implemented on Mathematica and Maple. The computations are exact (meaning there is no round-off error). No previous knowledge of Groebner bases is assumed. - Fermat's Last Theorem: As Easy as ABC
Michael Mossinghoff, Department of Mathematics, UCLA
Abstract
Fermat's famous "last theorem'' states that there are no solutions to the equation a^n + b^n = c^n in positive integers a, b, and c when n > 2. Posed by Fermat more than 360 years ago, this statement was proved only recently by Andrew Wiles. The study of problems like this one belongs to a branch of mathematics called Diophantine analysis. In this talk, we will introduce this subject and the kinds of problems it treats. We will then describe what is often called the most important open problem in the subject: the abc conjecture, and talk about its relation to Fermat's last theorem and other interesting problems in Diophantine analysis. Only knowledge of calculus and familiarity with polynomials is needed. - Clutching for Survival: The California Condor Restoration
Project
Tom O'Neil, Mathematics Department, Cal Poly
Abstract
For the last two years several Cal Poly students and I have been providing support to the Ventana Wilderness Society in their effort to establish a flock of California condors in the Big Sur area. Any attempt to develop a good recovery strategy requires an accurate population projection program. Unfortunately, there are several condor traits that make construction of such a program difficult. We will discuss these traits and how we have overcome many of the problems. Additionally, there is a lack of data. Critical to any population projection program is the survival rate data. No one knows the correct values, although there are estimates that can be used for first approximations. However, this data is based on observations of small populations of wild condors. No one wants to guess how the captive bred and reared birds will fare in the wild. To help in this area, we have created a database of every California condor in captivity or in the wild, living or dead since 1987 the year the last wild condor was brought into captivity. Here again, we will discuss the problems encountered in creating this database and getting it into a format that has made it a useful tool for the biologists in the condor recovery project.
About the Speaker
Thomas O'Neil received A.B. and M.S. degrees from San Diego State College and a Ph.D. in mathematics from The University of Wyoming. He is Professor of Mathematics at California Polytechnic State University, San Luis Obispo, where he has taught since 1973. His interests include problem solving, modeling, applications of mathematics and the pedagogical issues of computing in the mathematical classroom. His background includes ten years as technician and engineer in electronic research and development, with the U.S. Navy, General Dynamics/Astronautics and the Boeing Company.
1999-2000 Colloquia
1998-1999 Colloquia