Math 497A - Honors MASS Algebra

Finite Fields and Applications

Instructor:  Gary Mullen, Professor of Mathematics
TA:  Daniel Droz

113 McAllister Building,  MWRF 10:10 - 11:00 a.m.

Description:  This course will consist of an introduction to the theory of finite fields. We will also discuss some of the many practical applications of finite fields. These applications will include algebraic coding theory for the error-free transmission of information and cryptology for the secure transmission of information. Finite fields are also of great use in the construction of various kinds of combinatorial designs.

Reading:  G. Mullen and C. Mummert:  Finite Fields and Applications.   ISBN: 978-0-8218-4418-2.

Math 497B - Honors MASS Analysis

An Introduction to Dynamical Systems

Instructor:  Victoria Sadovskaya, Associate Professor of Mathematics
TA:  Kurt Vinhage

113 McAllister Building,  MWRF 11:15 a.m. - 12:05 p.m

Description:  The theory of dynamical systems is a modern branch of mathematics. Its main objective is to analyze long-term behavior of systems that evolve over time. In this course, we will introduce the fundamental concepts and tools of dynamics and discuss an array of examples with gradual increase in complexity. The topics will include contractions, linear maps, differential equations, recurrence, equidistribution, hyperbolic systems, symbolic systems and coding, fractals, entropy, and chaos.

Reading:  B. Hasselblatt and A. Katok:  A First Course in Dynamics with Panorama of Recent Developments.   ISBN: 978-0-5215-8750-1.

Math 497C - Honors MASS Geometry

Affine and Projective Geometries

Instructor:  Yakov Pesin, Distinguished Professor of Mathematics
TA:  Alena Erchenko

113 McAllister Building,  MTWF 1:25 - 2:15 p.m.

Description:  This course is an introduction to Geometry and its goal is to describe Geometry following Felix Klein’s Erlangen program, that is as the action of the group of isometries. The emphasis is on Affine, Projective and non-Eucleadian (Lobachevsky-Poincare hyperbolic) geometries.

Reading:  A. B. Sossinsky:  Geometries.   ISBN: 978-0-8218-7571-1.