Publisher's Synopsis
A new approach to abstract algebra that eases student anxieties by building on fundamentals.
Introduction to Abstract Algebra presents a breakthrough approach to teaching one of math's most intimidating concepts. Avoiding the pitfalls common in the standard textbooks, Benjamin Fine, Anthony M. Gaglione, and Gerhard Rosenberger set a pace that allows beginner-level students to follow the progression from familiar topics such as rings, numbers, and groups to more difficult concepts.
Classroom tested and revised until students achieved consistent, positive results, this textbook is designed to keep students focused as they learn complex topics. Fine, Gaglione, and Rosenberger's clear explanations prevent students from getting lost as they move deeper and deeper into areas such as abelian groups, fields, and Galois theory.
This textbook will help bring about the day when abstract algebra no longer creates intense anxiety but instead challenges students to fully grasp the meaning and power of the approach.
Topics covered include:
Rings
Integral domains
The fundamental theorem of arithmetic
Fields
Groups
Lagrange's theorem
Isomorphism theorems for groups
Fundamental theorem of finite abelian groups
The simplicity of An for n5
Sylow theorems
The Jordan-Hölder theorem
Ring isomorphism theorems
Euclidean domains
Principal ideal domains
The fundamental theorem of algebra
Vector spaces
Algebras
Field extensions: algebraic and transcendental
The fundamental theorem of Galois theory
The insolvability of the quintic
