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This book presents a unified treatment of recently developed techniques and current understanding about solving systems of linear equations and large scale eigenvalue problems on high-performance computers. It provides a rapid introduction to the world of vector and parallel processing for these linear algebra applications. Topics include major elements of advanced-architecture computers and their performance, recent algorithmic development, and software for direct solution of dense matrix problems, direct solution of sparse systems of equations, iterative solution of sparse systems of equations, and solution of large sparse eigenvalue problems. This book supercedes the SIAM publication Solving Linear Systems on Vector and Shared Memory Computers, which appeared in 1990. The new book includes a considerable amount of new material in addition to incorporating a substantial revision of existing text. ... Read more

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Stressing the interplay between theory and its practice, this text presents the construction of linear models that satisfy geometric postulate systems and develops geometric topics in computer graphics. It includes a computer graphics utility library of specialized subroutines on a 3.5 disk, designed for use with Turbo PASCAL 4.0 (or later version) - an effective means of computer-aided instruction for writing graphics problems.;Providing instructors with maximum flexibility that allows for the mathematics or computer graphics sections to be taught independently, this book: reviews linear algebra and notation, focusing on ideas of geometric significance that are often omitted in general purpose linear algebra courses; develops symmetric bilinear forms through classical results, including the inertia theorem, Witt's cancellation theorem and the unitary diagonalization of symmetric matrices; examines the Klein Erlanger programm, constructing models of geometries, and studying associated transformation groups; clarifies how to construct geometries from groups, encompassing topological notions; and introduces topics in computer graphics, including geometric modeling, surface rendering and transformation groups. ... Read more

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Aimed at introductory college maths students, this text provides a clear exposition of the foundation of maths and an appreciation of the creative dimensions of some mathematical concepts. ... Read more

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Introduces engineers, computer scientists, and physicists to advanced math topics as they relate to practical problems. The material is arranged into seven independent parts: ODE; Linear Algebra, Vector calculus; Fourier Analysis and Partial Differential Equations; Complex Analysis; Numerical methods; Optimization, graphs; Probability and Statistics. ... Read more

Customer Reviews (2)

Helpful
I found this book to be more of a help than the student solutions manual. It covers the material in the beginnings of the chapters (6-12 covered in this review) well and will help you check your work to make sure you are getting it right. It is sparse on the applied sections but does have hints and references to help you through the material.

Advanced Engineering Mathematics (6 edition)
De los textos que conozco de matemáticas avanzadas para ingeniería, me parece que es el mejor. Da un excelente desarrollo de las ecuaciones diferenciales ordinarias y parciales, obviamente desde el punto de vistaelemental. La parte de variable compleja, es la que más me gusta, es unbuen tratado de variable compleja, comparable con los textos(elementales)especializados en el tema. Un estudiante que trabaje lo deecuaciones diferenciales, análisis de Fourier y ecuaciones en derivadasparciales, lo de análisis complejo y numérico, adquiere unas buenas basesen la matemática aplicada a las ciencias e ingeniería. Además tiene unagran variedad de ejercicios y problemas, los cuales ayudan a un mejorentendimiento de la materia estudiada. Me gustaría conocer la octavaedición, pues los comentarios son con base en la sexta, debe haber varioscambios entre estas ediciones. ... Read more

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State of the art survey presents the most relevant approaches to unifying Petri nets in a systematic and coherent way. Softcover. ... Read more

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This volume contains the proceedings of a highly successful AMS Short Course on Chaos and Fractals, held during the AMS Centennial Celebration in Providence, Rhode Island in August 1988. Chaos and fractals have been the subject of great interest in recent years and have proven to be useful in a variety of areas of mathematics and the sciences. The purpose of the short course was to provide a solid introduction to the mathematics underlying the notions of chaos and fractals. The papers in this book range over such topics as dynamical systems theory, Julia sets, the Mandelbrot set, attractors, the Smale horseshoe, calculus on fractals, and applications to data compression. The authors represented here are some of the top experts in this field. Aimed at beginning graduate students, college and university mathematics instructors, and non-mathematics researchers, this book provides readable expositions of several exciting topics of contemporary research. ... Read more

Customer Reviews (1)

Somewhat dated, but still a good introduction to chaos and fractals
This material is the collection of lecture notes used for a short course presented by the American Mathematical Society in 1988. Therefore, the material is somewhat dated. The topics are:

*) Dynamics of simple maps
*) Nonlinear oscillations and the Smale horseshoe map
*) Fractal basin boundaries and chaotic attractors
*) Julia sets
*) The Mandelbroit set
*) Introduction to fractals
*) Iterated function systems

However, despite the passage of almost twenty years, this material is still an excellent introduction to these subjects. At the time of the conference, the material was new, exciting and it seemed that new applications of chaos and attractors were being discovered on a daily basis. At the time, I was a regular reader of the weekly "Science News" magazine and hardly an issue went by without a mention of chaos or fractals. Since it was so new, the material had to be presented at a level that led to understanding. Therefore, the modern reader that is relatively ignorant of the topics can get a great deal of benefit from this book.
... Read more

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This guide book to mathematics contains in handbook form the fundamental working knowledge of mathematics which is needed as an everyday guide for working scientists and engineers, as well as for students. Easy to understand, and convenient to use, this guide book gives concisely the information necessary to evaluate most problems which occur in concrete applications. In the newer editions emphasis was laid on those fields of mathematics that became more important for the formulation and modeling of technical and natural processes, namely Numerical Mathematics, Probability Theory and Statistics, as well as Information Processing. For the 5th edition, the chapters “Computer Algebra Systems” and “Dynamical Systems and Chaos” were fundamentally revised, updated and expanded. In the chapter “Algebra and Discrete Mathematics” a section on “Finite Fields and Shift Registers” was added.

Customer Reviews (18)

Fantastic, comprehensive reference manual.
Picking up this book gives you a great feeling.The density of the material, the finish of the cover, the slickness of the pages, and the crisp font can't help but make you feel like you made the right purchase.Delving into the content doesn't dissatisfy either.This is one of the most comprehensive math books I've ever found, and will be used for my personal and professional studies for years to come.

Best Handbook
Best handbook on mathematics. Both concise and comprehensive. Yet, there are some mistakes on basic physical examples such as classifying power as a vector quantity.

Used Book in Wonderful Condition
The vendor described the book as in very good condition. This was an understatement because the book is virtually pristine; it seemed as if it were never opened and it was delivered in a timely way. The one drawback to a handbook like this is that it's printed in a very small font and is difficult to read (for readers of a certain age). Of course, this is not the vendor's fault and I would gladly patronize this site again.

Best Mathematics Handbook
This work is, by far, the best mathematics handbook I've purchased.It is extremely well organized and well-written.The typeography is very clear.In the 1153 pages there are 745 figures and 142 tables.All areas of mathematics are covered in detail:arithmetic, functions, geometry, linear algebra, algebra and discrete mathematics, differentiation, infinite series, integral calculus, differential equations, calculus of variations, linear integral equations, functional analysis, vector analysis and vector fields, function theory, integral transformations, probability theory and mathematical statistics, dynamical systems and chaos, optimization, numerical analysis, computer algebra systems, and tables.A detailed bibliography and index are provided.Recommended for all mathematicians, scientists, and engineers!

Very good reference.
Product was "as expected".I am very satisfied with the quick response to my order. ... Read more

Customer Reviews (1)

not outdated
Don't be put off by the book being printed in 1985. The algorithms it explains are scarcely outdated. It talks at the level of these algorithms; independent of any particular computer language or hardware.

So we see the derivation of Legendre polynomials, complex integration and interpolation methods, as some examples of the book's topics. On the issue of solving systems of differential equations, difficult questions of numerical stability arise and the reader gets enough exposure to appreciate this. ... Read more

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This is a mathematics book, not a programming book, although it explains Pascal to beginners. It is aimed at high school students and undergraduates with a strong interest in mathematics, and teachers looking for fresh ideas. It is full of diverse mathematical ideas requiring little background. It includes a large number of challenging problems, many of which illustrate how numerical computation leads to conjectures which can then be proved by mathematical reasoning. It is assumed that readers have a PC at their disposal. ... Read more

Customer Reviews (1)

Great book when published, now very much out of date
When this book was published in 1993, it was a great book, suitable for use in many different math classes. Engel uses programs written in the language Pascal to solve many different math problems to the extent that Pascal could handle them. At that time, the size of integers was rather limited, so solutions could be found only as long as they were small. The problems and solutions are split into the following categories:

a) Number theory.
*) Probability
*) Statistics
*) Combinatorial algorithms
*) Numerical algorithms

There is also a section of miscellaneous problems. Each problem is explained in detail and there is a functioning Pascal program that will identify any solutions.
Time and the several swimlanes of advancement in technology have rendered this book obsolete. Pascal is no longer the primary language of computer science instruction and the limits on the size of integers are now almost laughable. The power of symbolic mathematics packages such as Mathematica has rendered the writing of a program in any other way an act of foolishness. With their ability to store numbers almost unlimited in size and the ease and simplicity of writing programs inside them, symbolic mathematics packages give you almost unlimited power to perform mathematical tests. The associated ease and quality of display render the simple dot diagrams in this book almost useless.
A significant achievement in its time, this book is now largely of historical interest. Engel was a trailblazer with an axe and a shovel, only now even the programming novice can use bulldozers and chainsaws. ... Read more

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The volume discusses issues at the crossroads of molecular biology, linguistics, computer science and mathematics.The first section contains papers related to one of the fundamental concepts of the theory of formal languages, namely that of grammar.Results are presented in 'classical' as well as new and modern areas of grammar theory.The automation concept of the theory of formal languages is discussed in the second section: different types of automata are investigated either in search of new theoretical properties or for potential applications in software engineering, linguistics and ecology.The third section discusses languages for picture descriptions, semilinear and DOL power series, relationships between different classes of languages and the languages associated with rewriting systems.The last section is devoted to computing with molecules, and both experiments and theoretical models are described.Operations inspired by gene recombination and DNA strand assembly are considered as formal operations on strings and languages. ... Read more

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Constrained Coding and Soft Iterative Decoding is thefirst work to combine the issues of constrained coding and softiterative decoding (e.g., turbo and LDPC codes) from a unified pointof view. Since constrained coding is widely used in magnetic andoptical storage, it is necessary to use some special techniques(modified concatenation scheme or bit insertion) in order to applysoft iterative decoding. Recent breakthroughs in the design and decoding of error-control codes(ECCs) show significant potential for improving the performance ofmany communications systems. ECCs such as turbo codes and low-densityparity check (LDPC) codes can be represented by graphs and decoded bypassing probabilistic (a.k.a. `soft') messages along the edges of thegraph. This message-passing algorithm yields powerful decoderswhose performance can approach the theoretical limits on capacity.This exposition uses `normal graphs,' introduced by Forney, whichextend in a natural manner to block diagram representations of thesystem and provide a simple unified framework for the decoding ofECCs, constrained codes, and channels with memory. Soft iterativedecoding is illustrated by the application of turbo codes and LDPCcodes to magnetic recording channels. For magnetic and optical storage, an issue arises in the use ofconstrained coding, which places restrictions on the sequences thatcan be transmitted through the channel; the use of constrained codingin combination with soft ECC decoders is addressed by themodified concatenation scheme also known as `reverseconcatenation.' Moreover, a soft constraint decoder yields additionalcoding gain from the redundancy in the constraint, which may be ofpractical interest in the case of optical storage. In addition, thismonograph presents several other research results (including thedesign of sliding-block lossless compression codes, and the decodingof array codes as LDPC codes). Constrained Coding and Soft Iterative Decoding will prove usefulto students, researchers and professional engineers who are interestedin understanding this new soft iterative decoding paradigm andapplying it in communications and storage systems. ... Read more

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Numerical linear algebra is far too broad a subject to treat in a single introductory volume. Stewart has chosen to treat algorithms for solving linear systems, linear least squares problems, and eigenvalue problems involving matrices whose elements can all be contained in the high-speed storage of a computer. By way of theory, the author has chosen to discuss the theory of norms and perturbation theory for linear systems and for the algebraic eigenvalue problem. These choices exclude, among other things, the solution of large sparse linear systems by direct and iterative methods, linear programming, and the useful Perron-Frobenious theory and its extensions. However, a person who has fully mastered the material in this book should be well prepared for independent study in other areas of numerical linear algebra. ... Read more

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This self-contained book provides a systematic account of the main algorithms derived from the simplex method and the means by which they may be organized into effective procedures for solving practical linear programming problems on a computer.The book begins by characterizing the problem and the method used to solve it, going on to deal with the practicalities of the subject, emphasizing concerns of implementation. The final section of the book discusses the basic principles of optimization: duality, decomposition, and homotopy.In conjunction with the simplex method, they each lead to other key algorithms of linear programming. The author's approach is distinguished by his detailed exploration of ideas and issues that center on the need to structure data suitably, and to organize calculations in an efficient and numerically stable manner.Unlike many liner programming texts, the author's overall perspective is grounded in nonlinear programming rather than combinatorics. ... Read more

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This text offers a unique treatment of discrete mathematics; it is organized by technique rather than topic focusing students on the construction and computation of objects. The text introduces algebras that directly apply to computer science; in addition to Boolean algebra, abstract data types are introduced as algebras and computational algebras. ... Read more

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The book deals with computer arithmetic in a more general sense than usual. Advanced computer arithmetic requires that all computer approximations of arithmetic operations - in particular those in the usual vector and matrix spaces - differ from the correct result by at most one rounding. The implementation of advanced computer arithmetic by fast hardware is examined in the book. The new expanded computational capability is gained at modest cost. It increases both, the speed of a computation and the accuracy of the computed result. Fast multiple precision arithmetic can be easily provided with it. All this strongly supports the case for implementing advanced computer arithmetic on every CPU. It is also shown in the book that on superscalar processors interval operations can be made as fast as simple floating-point operations with only very modest additional hardware costs. ... Read more

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One of the most fundamental concepts influencing the development of human civilization is numbers. While societies today rely on their understanding of numbers for everything from mapping the universe to running word processing programs on computers to buying lunch, numbers are a human invention. Babylonian, Roman, and Arabic societies devised influential systems for representing numbers, yet the story of how numbers developed is far more complicated. Concepts such as zero, negative numbers, fractions, irrational numbers, and roots of numbers were often controversial in the past. Numbers deals with the development of numbers from fractions to algebraic numbers to transcendental numbers to complex numbers and their uses. The book also examines in detail the number pi, the evolution of the idea of infinity, and the representation of numbers in computers. The metric and American systems of measurement as well as the applications of some historical concepts of numbers in such modern forms as cryptography and hand calculators are also covered.Illustrations, thought-provoking text, and other supplemental material cover the key ideas, figures, and events in the historical development of numbers. ... Read more

Customer Reviews (1)

Best book I've ever read!
The author, John J. Tabak, is the brother of a US Marine.John leads the reader to think about the meaning and mystery of numbers.Further, the incomplete foundation of mathematics is revealed along with some if its implications.Finally, the role of computers in the expanding frontier of mathematical knowledge is explored.Everybody should read this book.It leads the reader to deep insights while staying accessible to readers of all backgrounds and levels.
Sincerely, James J. Tabak USMC ... Read more

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Visualization is one of the most active and exciting areas of Mathematics and Computing Science, and indeed one which is only beginning to mature. Current visualization algorithms break down for very large data sets. While present approaches use multi-resolution ideas, future data sizes will not be handled that way. New algorithms based on sophisticated mathematical modeling techniques must be devised which will permit the extraction of high-level topological structures that can be visualized.

For these reasons a workshop was organized at the Banff International Research Station, focused specifically on mathematical issues. A primary objective of the workshop was to gather together a diverse set of researchers in the mathematical areas relevant to the recent advances in order to discuss the research challenges facing this field in the next several years. The workshop was organized into five different thrusts: - Topology and Discrete Methods; - Signal and Geometry Processing; - Partial Differential Equations; - Data Approximation Techniques; - Massive Data Applications. This book presents a summary of the research ideas presented at this workshop.

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Far more "user friendly" than the vast majority of similar books, this volume is truly written with the unsophisticated reader in mind.  The pace is leisurely, but the authors are rigorous and maintain a serious attitude towards theorem proving throughout. Emphasizes "Active Reading" throughout, a skill vital to success in learning how to write proofs. Offers two sections on probability (2.4 and 2.5). Moves material on depth-first search, which previously comprised an entire (very short) chapter, to an earlier chapter where it fits more naturally. Rewrites section on RNA chains to include a new (and easier) algorithm for the recovery of an RNA chain from its complete enzyme digest. Provides true/false questions (with all answers in the back of the book) in every section. Features an appendix on matrices.  A useful reference for mathematics enthusiasts who want to learn how to write proofs.

Customer Reviews (14)

Horrible!!!!
The concepts taught in this is fairly straight forward, but the Author makes every attempt to confuse and make it difficult. I have never seen such a horrible math book in all of my years as a student. I'll break down a typical chapter:

Chapter organization (i.e. are the topics covered related?): Pretty good as as whole. Each topic is introduced bit by bit and the flow from one section to the next makes sense.

Each individual section:

Each section and chapters too, are prefaced with some nonsensical garbage that kind of relates to the chapter; sometimes it's some stupid fictional story the author wish would happen with his fictitious friends, and other times it would be a situation that could maybe might happen in real life, assuming you're a total loser, and have nothing better to do than to count things. Or maybe you're the count, from Sesame Street. I don't know, whatever.

Then the author introduces the concept, and makes it has hard as possible to get and understand.

After that, he has 'Pauses' where you're suppose to suddenly understand what he's suppose to be teaching you. These pauses make no sense, and might as well be at the end of the chapter or section.

The book does do a decent job in highlighting key concepts and definitions, but I still find some important information and key concepts buried deep in some example.

After that, you may still be wondering why this book is not even worth 1 star. This is why:

Proofs are INSANELY hard to flow.
Examples are also INSANELY hard to flow.
That's because the author thought it would be best solve the problem as if he's talking you through it. The only way he can do this is by putting the BOTH proofs AND examples in a paragraph INSTEAD of showing the steps LINE BY LINE. Every good math book worth its salt has the examples shown clearly line by line. They may never show every obvious step they make, but it's at least easy to see what you understand and what you don't understand. This book uses one paragraph to explain the answer. And it's not even a long paragraph. So this MATH book ends up being a wall of text. Most of the symbols are just bold alphabet charaters, so it makes it even harder to find what you're looking for and follow the text.

What broke the straw on the camels back is the fact that his text is setup like this: (periods added for clarity)
Example 11: BLAH BLAH BLAH BLAH BLAH
............BLAH BLAH BLAH
............_______________
............ Problem 12: Stupid problem here.

I am not sure what the difference is between Example and Problem, but he uses PROBLEM to describe an example and exercise to describe the problems you're suppose to work out. Then occasionally he will have an 'exercise' refeer to a 'problem' and you looking at the wrong thing for five minutes before you realize. Also he will do this:

problem 12 blah blah blah sets up problem whatever.
...refeer to exercise 32 for more.

Of course, the exercise doesn't have the answer, and they just say 'work problem 12 blah blah'. But then puts the answer in the back of the book.

Overall this book is extremely terrible, and you should shame your professor if he tells you to buy this god awful book. If your professor tells you to buy this book, then he probably also sucks at teaching the material, and I would strongly consider dropping the class.

Not the best book for Discrete Mathematics
I have used this book for my Discrete Math class.

Pros: Has a lot of Exercises to work on. Pretty Advanced style of Explanation.If you have a good professor this book will help.

Cons: If you are just starting to learn Discrete Math, this is not the book for you. The examples and the explanation are pretty advance sort .
It is hard to understand Discrete Math byreading this book only .So if you are depending on your self i would suggest you look for a different book.

Gerry
This book is the worse math textbook I have ever encountered.There is not enough explanation regarding the theory and the examples are not helpful.The exercises in each chapter can not be referred back to the chapter reading at all.The chapter pages are structured to save paper.Everything is jammed together.I am currently taking the course and between the instructor and the book little knowledge is being passed to the less than ten people in the class.This book should NEVER be used!

Accessible, Friendly
I'm currently taking a Discrete Math class with this textbook.I don't have any background in the subject, and my theoretical math background is limited to a Proofs course and a Non-Euclidan Geometry class.(Other than that I have the usual amount of undergraduate calculus and so on.)

I think this book is fantastic.It is written in an engagingly casual style, and it uses a lot of examples and detail to work out the material.The other theoretical math texts I've used really don't do this - they expect you to treat their material more as hints to do your own work, which can be really hard for students (and is why you have a professor, after all).

I can't address how well this book actually covers the various topics of discrete math, since I only know what I've learned in the course so far, but I'm very impressed with how well it spells things out.It's not exactly "light reading" (it's not Discrete Math for Dummies) but it is quite accessible.

Discrete? More like hidden and vague...
I do not recommend this book. While yes, it provides clearly marked definitions and formulas, when giving examples, the work shown leaves out some key steps that leave the reader grasping into thin air trying to figure out the method to their madness. Some exercise questions are vaguely written, leaving the student to interpret the meaning, which may result in differing answers.

If you have a teacher who uses this book, get it. Otherwise, if you are teaching yourself (or just have that bad of a teacher), either pass on buying this book or buy a supplement. Or find a good math tutor, you'll need it. ... Read more