Abstract Algebra I

Here is is a textbook that I wrote for MTH 561 and 562.

Office Hours: via Zoom, Wed and Thurs at 3-4pm

Here is the syllabus.

This course has an optional writing credit.
Assignment Due Date Topics
Homework 1
Thurs, Aug 31 Introduction: Abel-Ruffini Theorem
Axioms of Groups
Old Notes on Matrices
Old Notes on Determinants
Homework 2
Thurs, Sept 14 Meet and Join of Subgroups
Cyclic Groups
Isomorphism of Groups
Dihedral Groups
Othogonal Groups
Exam 1: Thurs, Sept 21
Exam Solutions
Homework 3
Tues, Oct 10 Posets and Lattices
Kernel and Image of a Homomorphism
Correspondence Theorem for Groups
Fundamental Theorem of Cyclic Groups
The Euler-Fermat Theorem
Homework 4
Thurs, Oct 19 Equivalence Modulo a Subgroup
Cosets and Lagrange's Theorem
Direct Products
Chinese Remainder Theorem
Normal Subgroups
Exam 2: Thurs, Oct 26
Exam Solutions
Homework 5
Tues, Nov 14 First Isomorphism Theorem
Group Actions
Burnside's Lemma
Euler's Totient Function
Homework 6
Tues, Dec 12 "Hard" vs "Soft" Group Theory
Cauchy's Theorem
Second Isomorphism Theorem
Groups of Size p^2
Unsolvability of S_n