UNIVERSITY OF MIAMI
 

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
Solutions
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
Solutions
Fri Sept 24 Rings of Polynomials
Descartes' Factor Theorem
Concept of a Splitting Field
Exam 1: Fri Oct 1, in class
Solutions
Homework 3
Solutions
Fri Oct 21 Partial Fractions
Euclidean Domains
The Euclidean Algorithm
Unique Prime Factorization
Homework 4
Mon Nov 1 Equivalence Relations
Modular Arithmetic
The Group of Units (Z/nZ)^X
The Euler-Fermat Theorem





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