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Modern Algebra with Applications 2nd Edition

4.3 out of 5 stars 3 customer reviews
ISBN-13: 978-0471414513
ISBN-10: 0471414514
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Editorial Reviews

Review

“…an ideal starter into algebra for all kinds of students, and a very useful addition to existing textbooks…” (Zentralblatt Math, Vol.1050, 2005)

From the Back Cover

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
  • Pólya—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.

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Product Details

  • Hardcover: 352 pages
  • Publisher: Wiley-Interscience; 2 edition (November 5, 2003)
  • Language: English
  • ISBN-10: 0471414514
  • ISBN-13: 978-0471414513
  • Product Dimensions: 6.5 x 0.8 x 9.5 inches
  • Shipping Weight: 1.3 pounds (View shipping rates and policies)
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #1,669,612 in Books (See Top 100 in Books)

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Top Customer Reviews

Format: Paperback
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.
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Format: Paperback Verified Purchase
I just bought this title after having the second edition checked out from university library most of the semester. Be careful not to confuse the two: Amazon's system didn't make it clear that this was the edition being sold. Both are fine books and the first ed is a steal at the price it is commonly offered at, but the the second ed is quite a bit more concise with a second author contributing to the updated materials. This version seems to have considerably more material dedicated to applications, and would be a good additional reference to have on hand whether for introductory abstract algebra at the undergrad level or grad, or an applications course.
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Format: Hardcover Verified Purchase
Came brand new as advertised.
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