ABSTRACT ALGEBRA

    ONLINE STUDY GUIDE

INTRODUCTION

Some history

Biographies (from the MacTutor History of Mathematics archives)

Some help with logic and proofs

Links to some algebra sites

        Introduction

1.1   Divisors     Problems     Solutions

1.2   Primes     Problems     Solutions

1.3   Congruences     Problems     Solutions

1.4   Integers Modulo n     Problems     Solutions

        Review problems     Solutions

        Introduction

2.1   Functions     Problems     Solutions

2.2   Equivalence relations     Problems     Solutions

2.3   Permutations     Problems     Solutions

        Review problems     Solutions

        Introduction

3.1   Definition of a Group     Problems     Solutions

3.2   Subgroups     Problems     Solutions

3.3   Constructing Examples     Problems     Solutions

Some group multiplication tables

3.4   Isomorphisms     Problems     Solutions

3.5   Cyclic Groups     Problems     Solutions

3.6   Permutation Groups     Problems     Solutions

3.7   Homomorphisms     Problems     Solutions

3.8   Cosets, Normal Subgroups, and Factor Groups     Problems     Solutions

        Review problems     Solutions

        Introduction

4.1   Fields; Roots of Polynomials

4.2   Factors

4.3   Polynomials with Integer Coefficients

4.4   Existence of Roots

        Review problems     Solutions

5.1   Commutative rings; Integral Domains

5.2   Ring Homomorphisms

5.3   Ideals and Factor Rings

5.4   Quotient Fields

        Review problems     Solutions

6.1   Algebraic Elements

6.2   Finite and Algebraic Extensions

6.3   Geometric Constructions

6.4   Splitting fields     Problems     Solutions

6.5   Finite Fields     Problems     Solutions

6.6   Irreducible Polynomials over Finite Fields

6.7   Quadratic Reciprocity

        Review problems     Solutions

        Introduction

7.1   Isomorphism Theorems; Automorphisms     Problems     Solutions

7.2   Conjugacy     Problems     Solutions

7.3   Groups Acting on Sets     Problems     Solutions

7.4   The Sylow Theorems     Problems     Solutions

7.5   Finite Abelian Groups     Problems     Solutions

7.6   Solvable Groups     Problems     Solutions

7.7   Simple Groups     Problems     Solutions

        Introduction

8.1   The Galois Group of a Polynomial     Problems     Solutions

8.2   Multiplicity of Roots     Problems     Solutions

8.3   The Fundamental Theorem of Galois Theory     Problems     Solutions

8.4   Solvability by Radicals     Problems     Solutions

8.5   Cyclotomic Polynomials

8.6   Computing Galois Groups

9.1   Principal Ideal Domains

9.2   Unique Factorization Domains

9.3   Some Diophantine Equations

Index of Definitions

Index of Theorems

© 2000 by John A. Beachy and William D. Blair.

If you would like a printed copy of the solved problems, rather than printing the html pages you should download and print one of these supplements, which are typeset using LaTex and are available in either pdf or postscript format.

Abstract Algebra: A Study Guide for Beginners

Abstract Algebra: Review Problems on Groups and Galois Theory

"Introduction" to Abstract Algebra | Abstract Algebra Online