Abstract Algebra
Ages 18–22
Grade Reference
| 🇺🇸 United States | College Freshman |
| 🇬🇧 United Kingdom | University Year 1 |
| 🇮🇳 India | Undergraduate Year 1 |
| 🇳🇬 Nigeria | University Year 1 |
| 🇿🇦 South Africa | University Year 1 |
| 🇦🇺 Australia | University Year 1 |
| 🇨🇦 Canada | University Year 1 |
About This Textbook
This textbook is intended for a one or two-semester undergraduate course in abstract algebra. Though there are no specific prerequisites for a course in abstract algebra, students who have had other higher-level courses in mathematics will generally be more prepared than those who have not.
Table of Contents
Preliminaries — The Integers — Groups — Cyclic Groups — Permutation Groups — Cosets and Lagrange’s Theorem — Introduction to Cryptography — Algebraic Coding Theory — Isomorphisms — Normal Subgroups and Factor Groups — Homomorphisms — Matrix Groups and Symmetry — The Structure of Groups — Group Actions — The Sylow Theorems — Rings — Polynomials — Integral Domains — Lattices and Boolean Algebras — Vector Spaces — Fields — Finite Fields — Galois Theory
