Advising

Spring 2009 Courses

M301 Real Analysis
TuTh 11-12:15, F 1:15-2:05
Giuliana Davidoff

Topics include the real number system, convergence of sequences and series, power series, uniform convergence, compactness and connectedness, continuity, abstract treatment of differential and integral calculus, metric spaces, and point-set topology.

Satisfies Science and Math II-A requirement.  Prereq. Mathematics 251 or permission of instructor.

M319 Topics in Algebra: A second course in Linear Algebra (or lots of the algebra an applied mathematician should know)
MW 8:35-9:50, F 9-9:50
Margaret Robinson

As Peter Lax wrote in the preface to the second edition of his Linear Algebra text: "If you can reduce a mathematical problem to a problem in linear algebra, you can most likely solve it, provided you know enough linear algebra...A sound undergraduate education should offer a second course on the subject, at the senior level."

In this class we will take a linear transformation of a finite dimensional vector space to itself and study how you choose a basis so that the matrix associated with the transformation has a nice form. Why might you want to do such a thing?

Topics will include: Vector spaces, subspaces, linear independence, basis and dimension, change of basis; Linear transformations, eigenvalues, eigenvectors and spectral theory, Jordan canonical form, operators on inner product spaces, dual spaces, bilinear and quadratic forms, module theory, the classification of finitely generated modules over a principal ideal domain with applications to abelian groups and canonical forms for matrices.

This is beautiful mathematics and I hope this course will highlight the richness of the mathematical ideas along with the algorithms and numerical work involved in the applications of linear algebra.

Satisfies Science and Math II-A requirement.  Prereq. Mathematics 311 or permission of instructor.

M333 Differential Equations
MW 11-12:15, F 11-11:50
Anthony Bak

This is an introduction to differential equations for students in the mathematical or other sciences. Topics include first-order equations, second-order linear equations, qualitative study of dynamical systems, and first- and second-order linear partial differential equations.

Satisfies Science and Math II-A requirement.  Prereq. Mathematics 202.

STAT344 Seminar in Statistics and Scientific Research: Applied Multivariate Statistical Analysis
TTh 11-12:15, F 2:15-3:05
Rebecca Horowitz

In this course students will learn about statistical methods for data that contains more than one variable. Tentative topics include multivariate distributions, Inference for the multivariate normal, Multivariate regression models, MANOVA, Principal component analysis, Factor analysis, Canonical correlation, Discriminant analysis, and Cluster analysis.

Satisfies Science and Math II-A requirement.  Prereq. Mathematics 211 or permission of instructor.