Abstract Algebra I

There is no required textbook. All lecture notes will be posted here. For further reading I recommend Michael Artin's Algebra and Charles C. Pinter's Book of Abstract Algebra.

Office Hours: Mondays 4-5pm and Wednesdays 1-2pm

Here is the syllabus.
Course Notes
Item Date Information
Homework 1
Solutions in the Notes
Fri Aug 31 Quadratic and Cardano Formulas
Lagrange's Method
Permutations
Definition of Group and Subgroup
Homework 2
Solutions in the Notes
Fri Sept 14 Subgroup Generated by a Subset
Intersection and Join
Examples of Cyclic Groups
Definition of Isomorphism
Exam 1
Solutions
Fri Sept 21 Total = 21
Average = 16.8
Median = 17
St Dev = 4.8
Homework 3
Solutions in the Notes
Fri Oct 5 Posets and Lattices
Subgroups of Z
Galois Connections
Fundamental Theorem of Cyclic Groups
Homework 4
Solutions in the Notes
Mon Oct 22 Equivalence Modulo a Subgroup
Lagrange's Theorem
Normal Subgroups and Quotients
First Isomorphism Theorem
Definition of Group Actions
Exam 2
Solutions
Fri Oct 26 Total = 24
Average = 18.5
Median = 20.5
St Dev = 4.6
Homework 5
Solutions in the Notes
Fri Nov 16 Multiplication of Groups
Direct and Semidirect Products
Isometries of Euclidean Space
Simple and Solvable Groups
The Orbit-Stabilizer Theorem
Homework 6
Thurs Nov 29 Free and Transitive Group Actions
The Class Equation
Groups of Size p and p^2
S_n is Not Solvable
A_5 is Simple
Exam 3
Solutions
Mon Dec 3 Total = 24
Average = 18.1
Median = 29.0
St Dev = 5.2