Program Overview

Course Overview

The course is titled "Topics in Algebra" and is often referred to as "modern algebra." It covers the development of groups, rings, and fields, which are generalizations of familiar integers. The course will explore both the theory and applications of these concepts, particularly in signal and image processing. Examples of applications include digital cryptography and error correction.

Course Description

This course is an investigation of the theory and applications of modern algebra. It will delve into the notions of groups, rings, and fields, and their applications in various fields, including signal and image processing.

Textbook

The textbook for the course is "Contemporary Abstract Algebra, sixth edition," by Joseph Gallian. Additional materials include online resources provided by J. Gallian.

Course Requirements

• Students are expected to attend class and participate.
  • Regular attendance and active participation in class discussions are required.
• There will be regular homework that will be graded.
  • Homework assignments will be given regularly and will be graded based on completeness and accuracy.
• Students will give a short presentation on a topic of their choice.
  • Many suggestions for presentation topics are available from the textbook.
• There will be a final take-home exam.
  • The final exam will be a take-home exam that will test students' understanding of the course material.

Grading

• Homework: 40%
• Presentation: 10%
• Participation: 10%
• Final: 40%

Instructor Information

The instructor for the course is Dan Rockmore, Professor of Mathematics and Computer Science. The course will be held in Moore 150, Period 11 (MWF 11:05-12:20; x-hour T 12:00-12:50).

First Class

The first class will be held on Monday, June 27.