# Math 521B: Abstract Algebra B

Schedule number: 21905
Spring 2010
MWF, 10:00 -10:50.
EBA-258
San Diego State University
Final Exam: Fri. May 14, 10:00-12:00

Professor: Mike O'Sullivan
Email: m.osullivan@math.sdsu.edu
Office: GMCS #579, 594-6697
Office Hours: MW 11:00-12:00, 1:00-1:30, 3:15-4:00.
F: 11:00-12:00 (most weeks).
You may also stop by on Tu or Th afternoon. If I am in and available, we can talk.
Other times: by appointment.

## Text

Hungerford, Abstract Algebra: An Introduction 2nd ed.

## Detailed Information

Review for the first exam.
Review for the second exam.
Review for the third exam.
 SCHEDULE ASSIGNMENTS

## Course Description

The focus of this course is the theory of groups. This is one of the core topics in pure mathematics, displaying beauty, elegance, simplicity and depth. The notion of a group developed over two hundred years ago, as a way to understand the symmetry of other mathematical objects. In the 20th century, group theory became one of the foundational topics in pure mathematics. By the end of the century, one of the major challenges in group theory was eventually solved, due to the work of dozens of mathematicians in hundreds of papers. By the end of this course you will understand what this challenge means: classify all finite simple groups. You will also appreciate some pieces of the answer.

In the last third of the semester we will study fields. There are two principal topics, constructing a field from an integral domain (Section 9.4) and constructing fields by adjoining roots of an equation (Chapter 10). The culmination of this portion of the course will be finite fields, which we will characterize completely. Finite fields are of great interest nowadays since they are used in error correction coding and cryptography.

## Prerequisites

The prerequisite for this course is Abstract Algebra 521A. You should already have some experience with fields from 521A, but we will review Chapters 4 and 5 as needed.

You should be conversant with the fundamentals of logic ("and", "or", "implies", "for all", "there exists", and negation). We will use a variety of proof methods in this course: direct proof, proof by contradiction, and mathematical induction. We use equivalence relations. This material is all covered in Discrete Mathematics, Math 245.

When we cover fields we will use some linear algebra, but just basic notions: linear independence, span, basis and dimension. We will spend some time in Section 10.1, which reviews this material.

## Schedule

I expect to spend about 9 weeks on groups, Chapters 7 and 8. We will continue with 5 weeks on fields, Section 9.4, and Chapter 10.