ABSTRACT

Designed for an advanced undergraduate- or graduate-level course, Abstract Algebra provides an example-oriented, less heavily symbolic approach to abstract algebra. The text emphasizes specifics such as basic number theory, polynomials, finite fields, as well as linear and multilinear algebra. This classroom-tested, how-to manual takes a more narra

chapter 1|18 pages

The integers

chapter 2|32 pages

Groups I

chapter 3|14 pages

The players: rings, fields, etc.

chapter 4|20 pages

Commutative rings I

chapter 5|22 pages

Linear algebra I: dimension

chapter 7|8 pages

Some irreducible polynomials

chapter 8|16 pages

Cyclotomic polynomials

chapter 9|8 pages

Finite fields

chapter 10|28 pages

Modules over PIDs

chapter 11|14 pages

Finitely-generated modules

chapter 12|10 pages

Polynomials over UFDs

chapter 13|8 pages

Symmetric groups

chapter 14|14 pages

Naive set theory

chapter 15|6 pages

Symmetric polynomials

chapter 16|4 pages

Eisenstein’s criterion

chapter 17|10 pages

Vandermonde determinants

chapter 18|10 pages

Cyclotomic polynomials II

chapter 19|26 pages

Roots of unity

chapter 20|22 pages

Cyclotomic III

chapter 21|12 pages

Primes in arithmetic progressions

chapter 22|24 pages

Galois theory

chapter 23|10 pages

Solving equations by radicals

chapter 24|24 pages

Eigenvectors, spectral theorems

chapter 25|18 pages

Duals, naturality, bilinear forms

chapter 26|10 pages

Determinants I

chapter 27|26 pages

Tensor products27.1

chapter 28|30 pages

Exterior powers