-
Chapter 1:
Why Abstract Algebra?
-
Chapter 2:
Operations
-
Chapter 3:
The Definition of Groups
-
Chapter 4:
The Elementary Properties of Groups
-
Chapter 5:
Subgroups
-
Chapter 6:
Functions
-
Chapter 7:
Groups of Permutations
-
Chapter 8:
Permutations of a Finite Set
-
Chapter 9:
Isomorphism
-
Chapter 10:
Order of Group Elements
-
Chapter 11:
Cyclic Groups
-
Chapter 12:
Partitions and Equivalence Relations
-
Chapter 13:
Couting Cosets
-
Chapter 14:
Homomorphisms
-
Chapter 15:
Quotient Groups
-
Chapter 16:
The Fundamental Homomorphism Theorem
-
Chapter 17:
Rings: Definitions and Elementary Properties
-
Chapter 18:
Ideals and Homomorphisms
-
Chapter 19:
Quotient Rings
-
Chapter 20:
Integral Domains
-
Chapter 21:
The Integers
-
Chapter 22:
Factoring into Primes
-
Chapter 23:
Elements of Number Theory (Optional)
-
Chapter 24:
Rings of Polynomials
-
Chapter 25:
Factoring Polynomials
-
Chapter 26:
Substitution in Polynomials
-
Chapter 27:
Extensions of Fields
-
Chapter 28:
Vector Spaces
-
Chapter 29:
Degrees of Field Extensions
-
Chapter 30:
Ruler and Compass
-
Chapter 31:
Galois Theorey: Preamble
-
Chapter 32:
Galois Theorey: The Heart of the Matter
-
Chapter 33:
Solving Equations by Radicals