Schaum's Outline of Discrete Mathematics (Schaum's)

Book Description

The first edition of this book sold more than 100,000 copies—and this new edition will show you why! Schaum’s Outline of Discrete Mathematics shows you step by step how to solve the kind of problems you’re going to find on your exams. And this new edition features all the latest applications of discrete mathematics to computer science! This guide can be used as a supplement, to reinforce and strengthen the work you do with your class text. (It works well with virtually any discrete mathematics textbook.) But it is so comprehensive that it can even be used alone as a text in discrete mathematics or as independent study tool!

Customer Reviews:

Excellent study guide for students of discrete math and computer science.......2006-03-21

Discrete mathematics, or the study of finite systems, has become increasingly important for students of computer science, and this book is a good foundational text on the subject. This Schaum's outline is much more complete than the average Schaum's, and it is also very clear and instructive. It is not just a good text for discrete mathematics. It also covers the basics of abstract algebra and the basics of the theory of computation.
The first 3 chapters cover sets, relations, functions, and algorithms, including a very good section on the complexity of algorithms. Chapter 4 is on logic and propositional calculus, which is the foundation of artificial intelligence and digital logic. The next three chapters cover the basics of vectors, matrices, counting (permutations and combinations), and probability theory. This material is important in the design and analysis of operating systems. Next are chapters on graph theory, directed graphs, and binary trees, all of which should be covered in any good course on the analysis of algorithms. These chapters include discussions of planarity, traversibility, minimal paths, and Warshall's and Huffman's algorithms. There is a chapter on languages and machines that includes material on regular expressions, automata, Turing machines, and computable functions. There is also a chapter dedicated to the very basics of abstract algebra, and another chapter on boolean algebra.
This text is therefore a superset of what you will probably find in an upper level undergraduate class in discrete mathematics, and is definitely a book you want to keep around especially if you are a computer science student and need additional study material for your core courses of artificial intelligence, analysis of algorithms, operating systems, and theory of computation. Highly recommended.

Typical Schaum's.......2006-02-05

This is a very helpful outline whether you are taking the class and need a supplement or are just trying to learn the material on your own. The writing is clear and succinct, and there are hundreds and hundreds of practice problems all of which are answered. The topics covered are standard for the topic, so this book will cover everything in your class unless your teacher has some unorthodox lesson plan. My one caveat is that there are occasional errors in the answer keys. This can be frustrating especially if you don't feel confident in your own work. The errors are far and few between for the most part and if you can live with them then you will get much use out of this book. Highly recommended.

Very instructive.......2005-09-08

This math book simply helps and supports learning with good, specific examples and no jargon.

When some ppl make the already abstract more confusing ..........2005-06-20

This book can pull you out of confusion. After all, an abstract course in discrete structures which is supposed to be the fundamentals of learning computer hardware and software programming need not be made even more confusing. Grab this book and make learning discrete structures more enjoyable and less painful !

Not a 5 star!.......2002-04-26

I waited several weeks for this book to arrive, and was disappointed to see that its 'just another maths book', nothing special. I didn't find this book any easier to understand than any other maths book, I ended up refering to my other book more.

Dictionary on Lie Algebras and Superalgebras

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Dictionary on Lie Algebras and Superalgebras
Luc Frappat , Antonino Sciarrino , and Paul Sorba
Manufacturer: Academic Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0122653408

Book Description

This book is a detailed reference on Lie algebras and Lie superalgebras presented in the form of a dictionary. It is intended to be useful to mathematical and theoretical physicists, from the level of the graduate student upwards. The Dictionary will serve as the reference of choice for practitioners and students alike.

Key Features:
* Compiles and presents material currently scattered throughout numerous textbooks and specialist journal articles
* Dictionary format provides an easy to use reference on the essential topics concerning Lie algebras and Lie superalgebras
* Covers the structure of Lie algebras and Lie superalgebras and their finite dimensional representation theory
* Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras

A Course in Abstract Harmonic Analysis (Studies in Advanced Mathematics)

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A Course in Abstract Harmonic Analysis (Studies in Advanced Mathematics)
Gerald B. Folland
Manufacturer: CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 0849384907

Book Description

Abstract theory remains an indispensable foundation for the study of concrete cases. It shows what the general picture should look like and provides results that are useful again and again. Despite this, however, there are few, if any introductory texts that present a unified picture of the general abstract theory. A Course in Abstract Harmonic Analysis offers a concise, readable introduction to Fourier analysis on groups and unitary representation theory. After a brief review of the relevant parts of Banach algebra theory and spectral theory, the book proceeds to the basic facts about locally compact groups, Haar measure, and unitary representations, including the Gelfand-Raikov existence theorem. The author devotes two chapters to analysis on Abelian groups and compact groups, then explores induced representations, featuring the imprimitivity theorem and its applications. The book concludes with an informal discussion of some further aspects of the representation theory of non-compact, non-Abelian groups.

Customer Reviews:

Review.......2006-07-27

A very good exposition of this beautiful subject. As a student just entering the field, I had to get a copy of my own!

Homogenization of Reticulated Structures (Applied Mathematical Sciences)

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Homogenization of Reticulated Structures (Applied Mathematical Sciences)
Doina Cioranescu , and Jeannine Saint Jean Paulin
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0387986340

Book Description

This book presents recent works on lattice type structure. Its aim is to give continuous simple models for thin reticulated structures which may have a very complex pattern. For this reason, the authors treat partial differential equations depending on several small parameters, and give the asymptotic behavior with respect to these parameters. Attention has been paid to mathematical rigor, convergence results and error estimates.
Chapter 1 gives an introduction to homogenization methods in perforated domains. Chapter 2 offers the main ideas to study thin reticulated structures. Chapters 3 and 4 are dedicated to the study of networks in thermal and elasticity problems. Chapter 5 and 6 treat similar problems to those in Chapter 3 and 4, but in this instance, the structure is thin and tall, tower-like.

Modern Algebra with Applications (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)

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The best modern algebra text I have seen
important computer applications

Modern Algebra with Applications (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)
William J. Gilbert , and W. Keith Nicholson
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Hardcover

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Elementary Analysis

ASIN: 0471414514

Book Description

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. Filled with in-depth insights and over six hundred exercises of varying difficulty, this invaluable text can help anyone appreciate and understand this subject.

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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 new areas of mathematics such as combinatorics. This book contains the essentials of abstract (or modern) algebra together with a wide variety of applications.

Customer Reviews:

The best modern algebra text I have seen.......2006-07-22

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.......2005-01-01

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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Abstract Algebra vol 2 by Spindler
A thorough, accessible and indispensable resource on algebra

Abstract Algebra with Applications
Karlheinz Spindler
Manufacturer: CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 0824791444

Book Description

A comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.

Customer Reviews:

Abstract Algebra vol 2 by Spindler.......2000-08-03

Page 174 volume 2 the author did not follow completely the proof of Nagell theroem as in Algebraic Number Theory by Stewart & Tall Instead He introduced the matrix [1 1, -2 0], We may name it here for short S, The author claims that S**42k = [-1 -1, -1 -1] mod 3 which is wrong S**42k = +-[1 0, 1 0] 4|k or 2|k respectively and = +-S 4|k-1 or 2|k-1 respectively in both cases the first entery in the total matrix as S**(42k +13) * [0 1] would be -1 and destroy the logic of the author in his argument However it deos not violate the theory for -1 in a field of chratersistic 3 need not be -1 in the integral domain Z[sqrt(-7)] I do here thank Amazon.com for the chance to report that for neithe the author nor the editorial at the publisher has an address to communicate with. Abdu Shokr 35-17 Ditmars blvd suite 202 NY NY 11105 August 3 2000

A thorough, accessible and indispensable resource on algebra.......1999-03-11

This two volume set is by far the most complete text on abstract algebra available. Rich in detail, a wealth of examples and clear yet concise explanations provide the reader an accesible source to deepen his understanding of abstract algebra. Spindler conveys his love of algebra and a desire to reveal its riches to the average student. If you've relied on Hungerford's / Lang's Algebra or Warner's Modern Algebra, this text is the last text you will need.

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Applied Abstract Algebra
David Joyner , Richard Kreminski , and Joann Turisco
Manufacturer: The Johns Hopkins University Press
ProductGroup: Book
Binding: Hardcover

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Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills

ASIN: 0801878225

Book Description

With the advent of computers that can handle symbolic manipulations, abstract algebra can now be applied. In this book David Joyner, Richard Kreminski, and Joann Turisco introduce a wide range of abstract algebra with relevant and interesting applications, from error-correcting codes to cryptography to the group theory of Rubik's cube. They cover basic topics such as the Euclidean algorithm, encryption, and permutations. Hamming codes and Reed-Solomon codes used on today's CDs are also discussed. The authors present examples as diverse as "Rotation," available on the Nokia 7160 cell phone, bell ringing, and the game of NIM. In place of the standard treatment of group theory, which emphasizes the classification of groups, the authors highlight examples and computations. Cyclic groups, the general linear group GL(n), and the symmetric groups are emphasized.

With its clear writing style and wealth of examples, Applied Abstract Algebra will be welcomed by mathematicians, computer scientists, and students alike. Each chapter includes exercises in GAP (a free computer algebra system) and MAGMA (a noncommercial computer algebra system), which are especially helpful in giving students a grasp of practical examples.

Computer Algebra Recipes for Mathematical Physics

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Computer Algebra Recipes for Mathematical Physics
Richard H. Enns
Manufacturer: Birkhäuser Boston
ProductGroup: Book
Binding: Paperback

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Computer Algebra Recipes: An Introductory Guide to the Mathematical Models of Science

ASIN: 0817632239

Book Description

Over two hundred novel and innovative computer algebra worksheets or "recipes" will enable readers in engineering, physics, and mathematics to easily and rapidly solve and explore most problems they encounter in their mathematical physics studies. While the aim of this text is to illustrate applications, a brief synopsis of the fundamentals for each topic is presented, the topics being organized to correlate with those found in traditional mathematical physics texts. The recipes are presented in the form of stories and anecdotes, a pedagogical approach that makes a mathematically challenging subject easier and more fun to learn.

Key features:

* Uses the MAPLE computer algebra system to allow the reader to easily and quickly change the mathematical models and the parameters and then generate new answers

* No prior knowledge of MAPLE is assumed; the relevant MAPLE commands are introduced on a need-to-know basis

* All recipes are contained on a CD-ROM provided with the text

* All MAPLE commands are indexed for easy reference

* A classroom-tested story/anecdote format is used, accompanied with amusing or thought-provoking quotations

* Study problems, which are presented as Supplementary Recipes, are fully solved and annotated and also provided on the CD-ROM

This is a self-contained and standalone text, similar in style and format to Computer Algebra Recipes: A Gourmet's Guide to Mathematical Models of Science (ISBN 0-387-95148-2), Springer New York 2001 and Computer Algebra Recipes for Classical Mechanics (ISBN 0-8176-4291-9), Birkhäuser 2003. Computer Algebra Recipes for Mathematical Physics may be used in the classroom, for self-study, as a reference, or as a text for an online course.

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Perfect for Beginning Algebra Students

Algebra: Pure and Applied
Aigli Papantonopoulou
Manufacturer: Prentice Hall
ProductGroup: Book
Binding: Paperback

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ASIN: 0130882542

Book Description

This book provides thorough coverage of the main topics of abstract algebra while offering nearly 100 pages of applications. A repetition and examples first approach introduces learners to mathematical rigor and abstraction while teaching them the basic notions and results of modern algebra. Chapter topics include group theory, direct products and Abelian groups, rings and fields, geometric constructions, historical notes, symmetries, and coding theory. For future teachers of algebra and geometry at the high school level.

Customer Reviews:

Perfect for Beginning Algebra Students.......2003-01-20

I used this as a textbook for an Abstract algebra course I took recently. It was surprisingly readable, and more importantly, there are plenty of examples that illustrate the definitions and theorems they've given.

Book Description

Learn to apply abstract algebra to practical real-world problems with TOPICS IN APPLIED ABSTRACT ALGEBRA! With coverage of interesting applications such as designing block designs to conduct statistical experiments for unbiased study of samples and designing secret-key cryptosystems and public-key cryptosystems for secure transmission of sensitive or secret data, this mathematics text makes the study of abstract algebra more exciting and meaningful. The opening chapter provides a brief refresher on the basic algebraic systems so that you are fully prepared to learn.

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