Modern Algebra with Applications
Select Format
Select Condition 
Book Overview
Praise for the first edition "This book is clearly written and presents a large number of examples illustrating the theory . . . there is no other book of comparable content available. Because of its detailed coverage of applications generally neglected in the literature, it is a desirable if not essential addition to undergraduate mathematics and computer science libraries." -CHOICE As a cornerstone of mathematical science, the importance of modern algebra and discrete structures to many areas of science and technology is apparent and growing-with extensive use in computing science, physics, chemistry, and data communications as well as in areas of mathematics such as combinatorics. Blending the theoretical with the practical in the instruction of modern algebra, Modern Algebra with Applications, Second Edition provides interesting and important applications of this subject-effectively holding your interest and creating a more seamless method of instruction. Incorporating the applications of modern algebra throughout its authoritative treatment of the subject, this book covers the full complement of group, ring, and field theory typically contained in a standard modern algebra course. Numerous examples are included in each chapter, and answers to odd-numbered exercises are appended in the back of the text. Chapter topics include: Boolean Algebras Polynomial and Euclidean Rings Groups Quotient Rings Quotient Groups Field Extensions Symmetry Groups in Three Dimensions Latin Squares P?lya--Burnside Method of Enumeration Geometrical Constructions Monoids and Machines Error-Correcting Codes Rings and Fields In addition to improvements in exposition, this fully updated Second Edition also contains new material on order of an element and cyclic groups, more details about the lattice of divisors of an integer, and new historical notes. Filled with in-depth insights and over 600 exercises of varying difficulty, Modern Algebra with Applications, Second Edition can help anyone appreciate and understand this subject.
Format:Hardcover
Language:English
ISBN:0471414514
ISBN13:9780471414513
Release Date:November 2003
Publisher:Wiley-Interscience
Length:352 Pages
Weight:1.35 lbs.
Dimensions:0.8" x 6.3" x 9.8"
Customer Reviews
2 ratings
The best modern algebra text I have seen
Published by Thriftbooks.com User , 19 years ago
It has been some time since I taught a course in modern algebra, but if I were to teach it again, I would use this book. The first chapter covers the basics of binary operations and algebraic structures. Seven pages in length, it is a basic overview of what the students should already know. Chapter two covers what is arguably the simplest abstract algebra, Boolean algebra. Propositional logic, switching circuits, posets and lattices are the examples used. I am in strong agreement with the introduction of switching circuits this early in a course. It is an application of abstract algebra that students can easily understand and relate to. Switching circuits also immediately demonstrates that the inclusion of "with applications" in the title is not a misnomer. Basic group theory is the topic of chapter three, quotient and symmetry groups are covered in chapters four and five. The Polya-Burnside method of enumeration is the topic of chapter five, monoids and machines the focus of chapter seven, rings, fields, polynomial, Euclidean and quotient rings are examined in chapters eight, nine and ten. Field extensions are covered in chapter eleven, Latin squares in chapter twelve, geometrical constructions in chapter thirteen and error-correcting codes in chapter fourteen. The exposition is excellent, it is one of the more readable texts in advanced mathematics that you will find. There are many examples of the applications of modern algebra to the real world and a large number of exercises are included at the end of the chapters. Solutions to the odd numbered exercises are found in an appendix. Modern algebra is a difficult topic due to the abstract nature of the material. It is easy for students to get confused and lost when they are studying the book on their own. The risk of that is minimized if they are reading this book.
important computer applications
Published by Thriftbooks.com User , 20 years ago
This book is pitched at the level of a third or fourth undergraduate year in maths, or at a graduate level course. Gilbert assumes a solid background in maths, especially linear algebra. He expounds on groups and rings. You can certainly treat this book as a pure maths text on algebra. But there is a twist to it, for some of you. He discusses applications in engineering. Notably Boolean algebra. Boolean logic forms the conceptual and practical basis of computer hardware and software. Gilbert shows how to represent a Boolean expression in a normal form and how to simplify it. Very practical and vital to circuit design. Later on in the book, he gives a good but all too brief discussion of finite state machines. These can be used in control systems and even in the construction of computer languages like Java. Where the Java bytecode can be validated precisely because Java is a finite state machine. Finally, error correcting codes take up an entire chapter. Important in communications theory, and even in such common items as storing information on computer media like DVDs.
Copyright © 2025 Thriftbooks.com
Terms of Use | Privacy Policy | Do Not Sell/Share My Personal Information | Cookie Policy | Cookie Preferences | Accessibility Statement
ThriftBooks ® and the ThriftBooks ® logo are registered trademarks of Thrift Books Global, LLC
ThriftBooks ® and the ThriftBooks ® logo are registered trademarks of Thrift Books Global, LLC
