Introduction to Modern Algebra and Its Applications

The book is a comprehensive introduction to modern abstract algebra and its applications,covering classical theory,number theory,finite fields,and finite dimensional algebras. It also provides modern applications in cryptography,coding theory,computer science,and physics,including the RSA algorithm,secret sharing algorithms,Diffie-Hellman Scheme,and ElGamal cryptosystem. It features examples,exercises,and a detailed construction of the Cayley-Dickson construction for finite dimensional algebras.

Format: Paperback / softback
Length: 394 pages
Publication date: 30 May 2022
Publisher: Taylor & Francis Ltd

The book serves as an comprehensive introduction to modern abstract algebra and its diverse applications. It delves into all major aspects of classical theory, encompassing numbers, groups, rings, fields, and finite dimensional algebras. Moreover, it presents intriguing and significant modern applications in fields such as cryptography, coding theory, computer science, and physics. Specifically, it examines algorithm RSA, secret sharing algorithms, the Diffie-Hellman Scheme, and the ElGamal cryptosystem, which are based on the discrete logarithm problem. Additionally, it introduces Buchbergers algorithm, a crucial tool for constructing Gröbner bases.

Key Features:

The book comprehensively covers all major topics of classical theory in modern abstract algebra, including groups, rings, fields, and their applications. In addition, it provides an introductory foray into number theory, finite fields, finite dimensional algebras, and their practical applications.

The book presents numerous examples and illustrations to elucidate the theory and its applications. It also includes a wide range of exercises of varying difficulty levels, aiding in the comprehension and mastery of the subject matter.

In detail, the book explores the construction of the Cayley-Dickson construction for finite dimensional algebras, particularly focusing on algebras of quaternions and octonions. It demonstrates their applications in number theory and computer graphics, highlighting their significance in modern mathematics and computing.

By offering a thorough and comprehensive exploration of modern abstract algebra and its applications, this book serves as an invaluable resource for students, researchers, and practitioners in the fields of mathematics, computer science, and related disciplines.

Weight: 730g
Dimension: 234 x 156 (mm)
ISBN-13: 9780367609085