MA 521 - Abstract Algebra

MA 521 - Abstract Algebra Spring 2005

Office Hours: Tuesdays and Thursdays 1:00 - 2:30 in HA 235.

Book:

Algebra by Michael Artin, Prentice Hall

Prerequisites:

  1. MA 405, a basic undergraduate linear algebra course covering topics such as solutions of systems of linear equations, linear independence of vectors, basis and dimension of a vector space, determinants, and calculation of eigenvalues and eigenvectors.
  2. Math 407, a basic undergraduate abstract algebra course covering topics such as equivalence relations, groups, homomorphisms, cosets, rings and polynomials.

Basic Grading Scale:

90%-100%: A, 80%-89%: B, etc.
I will also use the + and - system when appropriate)

Date Topic

Jan. 11 Groups, Subgroups, Isomorphisms, Homomorphisms, Co-sets.
Jan. 13 Quotient Groups, Modular Arithmetic and Product of Groups.
Jan. 19 Vector Spaces, Linear Transformation, Representation of a Linear Transformation by Matrices.
Jan. 21 Linear Operations and Eigenvectors
Jan. 25 Review for the Test
Jan. 27 Test # 1

Feb. 01 Symmetry, the Group of Motions of the Plane, Finite Group of Motions
Feb. 03 Abstract Symmetry, the Operations on Co-sets, the Counting Formula
Feb. 08 The Sylow Theorems, Computation in the Symmetric Group.
Feb. 10 The Free Group, Generators and Relations.
Feb. 15 Linear Groups, the Classical Linear Groups, the Special Unitary Group SU2,
The Special Linear Group SL2(_)
Feb. 17 One-Parameter Subgroups, Translation in a group, Simple Groups.
Feb. 22 Review for the Test.
Feb. 24 Test # 2

Mar. 01 Group Representation, G-invariant Forms and Unitary Representation.
Mar. 03 Compact Groups
Mar. 15 Irreducible Representations, Characters.
Mar. 17 Permutation Representations and the Regular Representation
Mar. 22 Schur's Lemma, Representations of SU2
Mar. 29 Review for the Test # 3
Mar. 31 Test # 3

Apr. 05 Rings, Homomorphisms and Ideals
Apr. 07 Quotient Rings and Relations in a Ring
Apr. 12 Integral Domains and Fraction Fields, Maximal Ideals
Apr. 14 Factorization of Integers and Polynomials, Gass's Lemma
Apr. 19 Primes in the Ring of Gauss Integers, Algebraic Integers
Apr. 21 Fields, Finite Fields, Algebraic and Transcendental Elements
Apr. 26 Reviews
Apr. 28 Reviews