Algebra 1: Groups, Rings, Fields and Arithmetic

Description

This is the first in a series of three volumes dealing with important topics in algebra. It offers an introduction to the foundations of mathematics together with the fundamental algebraic structures, namely groups, rings, fields, and arithmetic. Intended as a text for undergraduate and graduate students of mathematics, it discusses all major topics in algebra with numerous motivating illustrations and exercises to enable readers to acquire a good understanding of the basic algebraic structures, which they can then use to find the exact or the most realistic solutions to their problems. Front Matter....Pages i-xvii Language of Mathematics 1 (Logic)....Pages 1-12 Language of Mathematics 2 (Set Theory)....Pages 13-53 Number System....Pages 55-91 Group Theory....Pages 93-143 Fundamental Theorems....Pages 145-177 Permutation Groups and Classical Groups....Pages 179-217 Elementary Theory of Rings and Fields....Pages 219-268 Number Theory 2....Pages 269-309 Structure Theory of Groups....Pages 311-351 Structure Theory Continued....Pages 353-386 Arithmetic in Rings....Pages 387-419 Back Matter....Pages 421-433