TABLE OF CONTENTS

Integers

Functions

Groups

Basic group theory

Factor groups and homomorphisms
Some group multiplication tables

Polynomials

Rings

Commutative rings; integral domains
Localization, noncommutative examples

Fields

Structure of Groups

Sylow theorems; abelian groups; solvable groups
Nilpotent groups; groups of small order

Galois Theory

Unique Factorization

Modules

Sums and products; chain conditions
Composition series; tensor products; modules over a PID

Structure of Noncommutative Rings

Ideal Theory of Commutative Rings

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