Groups, Matrices, and Vector Spaces

James B. Carrell

ISBN 10: 1493979108 / ISBN 13: 9781493979103

Published by Springer New York, 2018

About this Item

Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Emphasizes the interplay between algebra and geometryAccessible to advanced undergraduates/graduate students, in a variety of subject areas, including mathematics, physics, engineering, and computer science&nbsp.

Seller Inventory # 458517514

Bibliographic Details

• Title: Groups, Matrices, and Vector Spaces
• Publisher: Springer New York
• Publication Date: 2018
• Language: English
• ISBN 10: 1493979108
• ISBN 13: 9781493979103
• Binding: Soft cover
• Condition: New

About this title

Synopsis

This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group.

Applications involving symm

etry groups, determinants, linear coding theory and cryptography are interwoven throughout. Each section ends with ample practice problems assisting the reader to better understand the material.  Some of the applications are illustrated in the chapter appendices. The author's unique melding of topics evolved from a two semester course that he taught at the University of British Columbia consisting of an undergraduate honors course on abstract linear algebra and a similar course on the theory of groups. The combined content from both makes this rare text ideal for a year-long course, covering more material than most linear algebra texts. It is also optimal for independent study and as a supplementary text for various professional applications. Advanced undergraduate or graduate students in mathematics, physics, computer science and engineering will find this book both useful and enjoyable.

About the Author

James B. Carrell is Professor Emeritus of mathematics at  the University of British Columbia. His research areas include algebraic transformation groups, algebraic geometry, and Lie theory.