Introduction to Abstract Algebra

## Introduction to Abstract Algebra

### An introductory course from the School of Mathematics

## Course Overview

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The main topic of the course is to introduce students to Group Theory, including the Sylow theorem. We'll also cover the structure of abelian groups and various permutation groups. If we have time, I'll also give a brief introduction to rings and fields including polynomial rings, factorization, the classical geometric constructions, and Galois theory.

## Course requirements

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The following knowledge is required or desirable on commencement of study of this course:

* School of Mathematics:Introduction to Proofs
* Linear Algebra

## Course outline

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We're going to follow a number of different sources for ths course. Primarily, we will follow Wikibooks' Abstract Algebra textbook. A good textbook to pick up is Topics in Algebra by I.N. Herstein. Another is Abstract Algebra by W.E. Deskins.

* Set Theory, Mappings and some Number Theory
* Introduction to Groups
* Subgroups
* Cosets
* The Lagrange Theorem
* Normal Subgroups
* Homomorphisms
* Automorphisms
* Cayley's Theorem
* Permutation Groups and Class Equations
* Sylow's Theorem
* Direct Products
* Intro to Rings, Fields and Galois Theory

I will not assign grades unless you ask me to. If you would like to have your work graded, your grade will be the best of weighted averages of the three exams.

## Lecture series

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Lecture 1 - Introduction/Set Theory
Lecture 2 - Relations and Mappings
Lecture 3 - Groups

## Assignments

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Problem sets will be posted here after every lecture. These problem sets are designed to prepare the student for the exams. These will not be graded.

Problem Set #1
Problem Set #2
Problem Set #3

## Examinations

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The plan is to have two 'midterm' exams and a comprehensive 'final' exam. Exam questions will be based on questions from the problem sets and the lectures. I'm debating on how to implement the exams, more information will be available soon. More than likely a link to the exam will be posted here, and you will post the answers on your user page or other page.

## Recommended student evaluation scheme

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not available yet

## Sign Up List

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If you are interested in taking this course, please indicate so here.

## Off-site lectures

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### With video

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* Verity Seeker, Basic abstract algebra, Youtube.
* Benedict Gross, Abstract Algebra, Open Learning Initiative, Harvard University Extension School.
* Bob Donley, Abstract Algebra, Math Doctor Bob, Youtube

### Without video

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* Scott Williams, Introduction to Abstract Algebra, University of Arizona, Fall 2013.

## Reading

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* Wikibooks: Abstract Algebra
* Thomas W. Judson, Abstract Algebra: Theory and Applications
* Samir Siksek, Lecture Notes, Introduction to Abstract Algebra, Mathematics Institute, University of Warwick -- Also see associated homework sets, listed under the appropriate section here.