Classic algebra

Fundamental to all areas of mathematics, algebra provides the cornerstone for the student's development. The concepts are often intuitive, but some can take years of study to fully absorb. For over twenty years, the author's classic three-volume set, Algebra , has been regarded by many as the most outstanding introductory work available. This work, Classic Algebra , combines a fully updated Volume 1 with the essential topics from Volumes 2 and 3, and provides a self-contained introduction to the subject. Complete and rigorous coverage of the important basic concepts Topics covered include sets, mappings, groups, matrices, vector spaces, fields, rings and modules Written in a lucid style, with each concept carefully explained Introduces more advanced topics and suggestions for further reading Contains over 800 exercises, including many solutions In addition to the basic concepts, advanced materials is introduced, giving the reader an insight into more advanced algebraic topics. The clear presentation style gives this book the edge over others on the subject. Undergraduates studying first courses in algebra will benefit from the clear exposition and perfect balance of theory, examples and exercises. The book provides a good basis for those studying more advanced algebra courses. Fundamental to all areas of mathematics, algebra provides the cornerstone for the student's development. The concepts are often intuitive, but some can take years of study to absorb fully. For over twenty years, the author's classic three-volume set, Algebra, has been regarded by many as the most outstanding introductory work available. This work, Classic Algebra, combines a fully updated Volume 1 with the essential topics from Volumes 2 and 3, and provides a self-contained introduction to the subject.In addition to the basic concepts, advanced material is introduced, giving the reader an insight into more advanced algebraic topics. The clear presentation style gives this book the edge over others on the subject.Undergraduates studying first courses in algebra will benefit from the clear exposition and perfect balance of theory, examples and exercises. The book provides a good basis for those studying more advanced algebra courses. 1 Sets and mappings......Page 001.djvu 2 Integers and rational numbers......Page 021.djvu 3 Groups ......Page 040.djvu 4 Vector spaces and linear mappings ......Page 066.djvu 5 Linear equations ......Page 106.djvu 6 Rings and fields ......Page 129.djvu 7 Determinants ......Page 183.djvu 8 Quadratic forms......Page 204.djvu 9 Further group theory ......Page 242.djvu 10 Rings and modules ......Page 290.djvu 11 Normal forms for matrices ......Page 340.djvu 1 The axiom of choice and Zorn's lemma ......Page 377.djvu 2 Countable and uncountable sets; transfinite induction ......Page 379.djvu Solutions to the exercises ......Page 381.djvu Some frequently used notations......Page 419.djvu Index......Page 421.djvu