Introduction to Abstract Algebra

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Introduction to Abstract Algebra

An introductory course from the School of Mathematics

Course Overview[edit | edit source]

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[edit | edit source]

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

Course outline[edit | edit source]

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[edit | edit source]

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

Assignments[edit | edit source]

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[edit | edit source]

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[edit | edit source]

not available yet

Sign Up List[edit | edit source]

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


Off-site lectures[edit | edit source]

With video[edit | edit source]

Without video[edit | edit source]

Reading[edit | edit source]