UNIVERSITY OF MIAMI
 

Abstract Algebra II

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 3:00-5:00pm on Zoom. Also by appointment.

Here is the syllabus.
Course Notes
Item Date Information
Homework 1
Solutions
Fri, Feb 4 Intermediate Value Theorem
Multivariable Polynomials
Permutations
Symmetric Polynomials
Laplace's Proof of the FTA
Homework 2
Solutions
Fri, Feb 18 Preview of Kronecker's Theorem
Congruence Modulo a Subgroup
Lagrange's Theorem
Orbit-Stabilizer Theorem
Exam 1: Wed Feb 23, in class
Solutions
Homework 3
Solutions
Fri, Mar 11 Normal Subgroups
Quotient Groups
First Isomorphism Theorem
Homework 4
Solutions
Mon, Mar 28 Isomorphism Classes of Groups
Cyclic Groups
Cyclotomic Polynomials
Exam 2: Fri Apr 1, in class
Solutions
Homework 5
Solutions
Fri, Apr 15 Ideals and Quotient Rings
First Isomorphism Theorem for Rings
Minimal Polynomials
Homework 6
Solutions
Fri, Apr 29 Existence of Splitting Fields
Existence of Finite Fields
Uniqueness of Splitting Fields
Uniqueness of Finite Fields
Exam 3: Mon May 2, in class
Solutions





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