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: Thurs, 3-5pm on Zoom. Also by appointment.

Here is the syllabus.
There is also an optional writing project.
Course Notes
Item Date Information
Homework 1
Fri Sept 10 Cardano's Formula
C as a ring and a field
C as a vector space
C as linear functions and matrices
Roots of Unity
Homework 2
Fri Sept 24 Rings of Polynomials
Descartes' Factor Theorem
Concept of a Splitting Field
Exam 1: Fri Oct 1, in class
Homework 3
Fri Oct 21 Partial Fractions
Euclidean Domains
The Euclidean Algorithm
Unique Prime Factorization
Homework 4
Solutions in the notes
Mon Nov 1 Equivalence Relations
Modular Arithmetic
The Group of Units (Z/nZ)^X
The Euler-Fermat Theorem
Exam 2: Fri Nov 5, in class
Homework 5
Fri Nov 19 Chinese Remainder Theorem
Partial Fractions
Homework 6
Fri Dec 3 Field of Fractions
Statements of the FTA
Exam 3: Wed Dec 8, in class