Further Algebra And Applications
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Further Algebra and Applications
Author: Paul M. Cohn
language: en
Publisher: Springer Science & Business Media
Release Date: 2011-06-27
Further Algebra and Applications is the second volume of a new and revised edition of P.M. Cohn's classic three-volume text "Algebra" which is widely regarded as one of the most outstanding introductory algebra textbooks. For this edition, the text has been reworked and updated into two self-contained, companion volumes, covering advanced topics in algebra for second- and third-year undergraduate and postgraduate research students. The first volume, "Basic Algebra", covers the important results of algebra; this companion volume focuses on the applications and covers the more advanced parts of topics such as: - groups and algebras - homological algebra - universal algebra - general ring theory - representations of finite groups - coding theory - languages and automata The author gives a clear account, supported by worked examples, with full proofs. There are numerous exercises with occasional hints, and some historical remarks.
Algebra for Applications
This book examines the relationship between mathematics and data in the modern world. Indeed, modern societies are awash with data which must be manipulated in many different ways: encrypted, compressed, shared between users in a prescribed manner, protected from an unauthorised access and transmitted over unreliable channels. All of these operations can be understood only by a person with knowledge of basics in algebra and number theory. This book provides the necessary background in arithmetic, polynomials, groups, fields and elliptic curves that is sufficient to understand such real-life applications as cryptography, secret sharing, error-correcting, fingerprinting and compression of information. It is the first to cover many recent developments in these topics. Based on a lecture course given to third-year undergraduates, it is self-contained with numerous worked examples and exercises provided to test understanding. It can additionally be used for self-study.
Abstract Algebra
Author: Thomas Judson
language: en
Publisher: Orthogonal Publishing L3c
Release Date: 2023-08-11
Abstract Algebra: Theory and Applications is an open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many non-trivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.