Product Description

John Vince explains a wide range of mathematical techniques and problem-solving strategies associated with computer games, computer animation, virtual reality, CAD, and other areas of computer graphics.

Covering all the mathematical techniques required to resolve geometric problems and design computer programs for computer graphic applications, each chapter explores a specific mathematical topic prior to moving forward into the more advanced areas of matrix transforms, 3D curves and surface patches. Problem-solving techniques using vector analysis and geometric algebra are also discussed.

All the key areas are covered including: Numbers, Algebra, Trigonometry, Coordinate geometry, Transforms, Vectors, Curves and surfaces, Barycentric coordinates, Analytic geometry.

Plus – and unusually in a student textbook – a chapter on geometric algebra is included.

Customer Reviews (2)

Broad but cursory
This give a very broad overview of many topics from matrix transformations to analytic geometry, but in a paperback less than a half inch thick, the topics are only given a cursory introduction.

not a book to learn new material from
Vince takes you through what is hopefully a revision course on maths that you will need if you are going to program graphics. The topics include matrix algebra. (Of course.) This gives the essence of translation and scaling in a three dimensional space. Then analytic geometry and B splines are covered.

The book has no problem sets. Though it does have one chapter at the end devoted to sample problems with their answers. It is not a book to learn new material from. ... Read more

Product Description
This book, updated and improved, introduces the mathematics that support advanced computer programming and the analysis of algorithms. The book's primary aim is to provide a solid and relevant base of mathematical skills. It is an indispensable text and reference for computer scientists and serious programmers in virtually every discipline. ... Read more

Customer Reviews (30)

Actually delivers in a readable way
After having had a bad result from other Ronald L. Graham, Erdos on Graphs : His Legacy of Unsolved Problems, books and articles. I was surprised with this book. I think that Dr. Knuth seems to turn what he touches to gold? I kind of wish I had read this one several years ago when
I wasn't as familiar with the material.
I was amazed to find the recursion for the Eulerian numbers of the second type and a host of very useful identities as well.

Great, great math book ...
How often do you get to have two of the giants of mathematics Graham and Knuth co-author (with Patashnik) a book like this - even suitable for high-school students?

Don't let the binding or whatever fools you, this is a serious math book and serious thinking is required.The material is broad and interesting.I think the book can be used as a supplement text to any of the discrete math/algorithm course (or just leisure reading).It will serve you years to come.Extra bonus - the marginal notes.It may be annoying to you or not but I found it funny at times.

I echo the same feeling as some of the readers here - keep this one always within reach.This is a future classic!

enjoying the struggle
really good book, some times it's bit hard to comprehend, but I'm enjoying the struggle.

Long Live Concrete Mathematics!
I had the pleasure of taking the course "Concrete Mathematics" with Ron Graham as an undergrad engineering student at Princeton University in the late 1980s, and in retrospect it was quite possibly the highlight of my academic career. Likewise, this text has a cherished spot in my bookcase even to this day. The material is challenging, sometimes downright frustrating, but good stuff nonetheless... and as others have noted, very useful! The skills gained are specifically tailored for application in fields such as computer science, really a number of disciplines; and complement what one learns in the more "standard" math courses. How many academic texts have become must-haves even beyond your college years? For me, only this one. I'd give it fifteen stars if I could.

A difficult but worthwhile mathematics text
This book's title can be misleading. I would say it is more of an advanced textbook on the mathematics that is a foundation for computer science than a foundational book on the mathematics of computer science. I think this misreading of the title and thus the book's content is what is behind much of the heartache that readers have when trying to tackle it. This book expands on the "Mathematical Preliminaries" portion of "The Art of Computer Programming" series of books by Knuth, and thus this book has a style much like that series of books. The book is complete and clear, but it is also densely packed with lots of theory and proofs and will require much effort and time to understand well. It is really not meant to be an applied mathematics textbook at all. I show the table of contents next. Note that there are exercises at the conclusion of each chapter with solutions in the back of the book. However, most of the exercises are not so simple that you can just glimpse at the solution and figure out how to get from A to B. I recommend it if you have the time. It can really bring out thoughts and the beauty of mathematics that you may not have considered before.

1. Recurrent Problems.
The Tower of Hanoi.
Lines in the Plane.
The Josephus Problem.
Exercises.

2. Sums.
Notation.
Sums and Recurrences.
Manipulation of Sums.
Multiple Sums.
General Methods.
Finite and Infinite Calculus.
Infinite Sums.
Exercises.

3. Integer Functions.
Floors and Ceilings.
Floor/Ceiling Applications.
Floor/Ceiling Recurrences.
'mod': The Binary Operation.
Floor/Ceiling Sums.
Exercises.

4. Number Theory.
Divisibility.
Factorial Factors.
Relative Primality.
'mod': The Congruence Relation.
Independent Residues.
Additional Applications.
Phi and Mu.
Exercises.

5. Binomial Coefficients.
Basic Identities.
Basic Practice.
Tricks of the Trade.
Generating Functions.
Hypergeometric Functions.
Hypergeometric Transformations.
Partial Hypergeometric Sums.
Mechanical Summation.
Exercises.

6. Special Numbers.
Stirling Numbers.
Eulerian Numbers.
Harmonic Numbers.
Harmonic Summation.
Bernoulli Numbers.
Fibonacci Numbers.
Continuants.
Exercises.

7. Generating Functions.
Domino Theory and Change.
Basic Maneuvers.
Solving Recurrences.
Special Generating Functions.
Convolutions.
Exponential Generating Functions.
Dirichlet Generating Functions.
Exercises.

8. Discrete Probability.
Definitions.
Mean and Variance.
Probability Generating Functions.
Flipping Coins.
Hashing.
Exercises.

9. Asymptotics.
A Hierarchy.
O Notation.
O Manipulation.
Two Asymptotic Tricks.
Euler's Summation Formula.
Final Summations.
Exercises.

A. Answers to Exercises.
B. Bibliography. ... Read more

Product Description
The mathematical knowledge needed for computer and information sciences­­including, particularly, the binary number system, logic circuits, graph theory, linear systems, probability and statistics­­get clear and concise coverage in this invaluable study guide. Basic high school math is all that's needed to follow the explanations and learn from hundreds of practical problems solved step-by-step. Hundreds of review questions with answers help reinforce learning and increase skills. ... Read more

Customer Reviews (4)

Well written but all over the map as far as subject matter
I found this Schaum's outline to be a very well written book on a variety of elementary mathematical subjects probably most suitable for someone who has just graduated high school and is a freshman starting some kind of technical degree. However, beyond that, I am not sure exactly who the target audience is supposed to be. The book contains some information on the very basic computer math that a college freshman engineering or ITstudent would need to know such as binary number systems and computer codes and math. However, some of the other material is very much oriented towards the aspiring computer engineer but is not really mathematical such as the sections on logic, flowcharts, sets and relations, and logic gates. Other sections are mathematical but don't necessarily have anything to do with computers and could be just as helpful to a student of applied mathematics such as the sections on linear algebra, linear equations, statistics, and graph theory.

Thus my recommendation would be that if you need a good tutorial on a variety of mathematical and pseudo-mathematical topics that tie in well with a technical degree of any kind, the low price of admission on this odd little outline is probably worth it. Just don't expect it to rescue you in any one course in particular. It will more likely rescue you in particular sections of several courses instead.

Great book which helped me tremendously
This book tremendously helped me understand computers and their relationship to mathematics and helped clear about doubts all through the semesters in college that I studied computer science. I strongly recommend this book to anyone majoring in computer science, information technologies, computer programming, etc ... as this book serves as a pillar to understanding the fundamentals of computer hardware and software.

A cheap and good book
The book is pretty much suitable for students who has finishedhigh school maths but requires revision on maths for computing. A few chapters are simple enough for students to run over quickly. There is asupplementary questions and solved questions with working for student tounderstand and practice on. Overall the book is good enough to refresh yourmemory on computer maths.

very poorly structured
For a start this book is never intended to be used by itself but as a supplement,so any attempt to use it as a textbook will only reslut in frustartion. Furthermore its not geared to teach as many VERY importantconcepts are simply ommited and the author makes far too many assumptionswhich all results in an incomplete book. The book attempts to cut studytime but also ends up cutting too much in clear and sufficent explanations.Use this book once you have completly mastered whathever topic you areinvolved in,and even then its only good for the practise problems at theend of each chapter. All in all DONT buy this book if you are trying tolearn something...use it ONLY for reviwing and just as a supplement. ... Read more

Product Description

Stein/Drysdale/Bogart's Discrete Mathematics for Computer Scientists is ideal for computer science students taking the discrete math course.

Written specifically for computer science students, this unique textbook directly addresses their needs by providing a foundation in discrete math while using motivating, relevant CS applications. This text takes an active-learning approach where activities are presented as exercises and the material is then fleshed out through explanations and extensions of the exercises.

Customer Reviews (1)

I did not find it suitable for my discrete math course
I evaluated this book for possible adoption in a course in introductory discrete mathematics. My decision was that I would not use it in the course. One primary reason is that there are no sections devoted to set theory and functions. Most of the introductory material in these areas is included in the book, but only in conjunction with other topics, such as counting, solving recurrences and computing probabilities. In my experience, students need to be exposed to the material as a point of emphasis, rather than embedded inside other topics.
The first chapter introduces the basic principles of counting, permutations, combinations, binomial coefficients and a section on equivalence relations that is considered optional. This is because it is not used again in later chapters, something I don't agree with. Chapter two deals with cryptography and number theory. While I have no objection to this material in a discrete mathematics course, I prefer that it be put off to the latter part of the course. In chapter three, the logic of propositions and predicates as well as the laws of inference are examined. I generally prefer more coverage of these areas. Chapter four is 84 pages and covers induction, recursion and recurrence relations. Taking up approximately one fourth of the book, the coverage is complete. Probability is covered in chapter 5 and graph theory in chapter 6. The coverage in both is fairly typical, so I have no positive or negative comments on either one. Relations are covered in depth in an appendix. Solutions to the odd exercises are included in an appendix.
Since I prefer to start my discrete mathematics course by covering set theory, functions and logic, I have removed this book for adoption consideration.
... Read more

Product Description
This book helps you write computer solutions to mathematical problems-at all levels. Supplies complete programs, complete subroutines, and fragments of code to be included directly within the user's program. 3 1/2 inch disk included. DLC: Engineering mathematics - Data processing. ... Read more

Customer Reviews (1)

Dated, but still a good introduction to some areas of computer science
In the 1980's, I was teaching mathematics at the college level and we made the decision to offer a course in discrete mathematics for computer science students. While I was trained in mathematics, I did not know the precise meaning of the term in this context. Therefore, I purchased this book and read through it. Shortly after that, I wrote the proposal to add a course in discrete mathematics to our curriculum and it passed all the confirmatory hurdles.
Since the definition of what is considered discrete mathematics for computer science students has changed over the years, the coverage here is not consistent with the modern approach. The chapters are:

*) Mathematical models
*) Mathematical reasoning
*) Sets
*) Binary relations
*) Functions
*) Counting and algorithm analysis
*) Infinite sets
*) Algebras

As you can see, there is no graph theory and there is no mention of switching theory and only one page devoted to Boolean algebra. Therefore, while this book was excellent at the time and remains a solid introduction to some areas of discrete mathematics, the field has moved somewhat beyond this coverage.
... Read more

Product Description
This completely updated second edition illustrates the mathematical concepts that a game programmer would need to develop a professional-quality 3D engine. Although the book is geared toward applications in game development, many of the topics appeal to general interests in 3D graphics. It starts at a fairly basic level in areas such as vector geometry and linear algebra, and then progresses to more advanced topics in 3D game programming such as illumination and visibility determination. Particular attention is given to derivations of key results, ensuring that the reader is not forced to endure gaps in the theory. The book assumes a working knowledge of trigonometry and calculus, but also includes sections that review the important tools used from these disciplines, such as trigonometric identities, differential equations, and Taylor series.

Key Features
* Includes four new chapters: the graphics pipeline, the stencil shadow rendering technique, curves & surfaces, and numerical methods
* Concentrates on key mathematical topics for programming 3D game engines
* Discusses applications in the context of the OpenGL architecture due to its cross-platform nature and long-standing industry acceptance. Sample rendering code is presented using ARB vertex programs and fragment programs
* Selected topics include quaternions, homogeneous coordinates, ray tracing, bump mapping, portal systems, polygonal techniques, shadows, and physics
* Includes exercise sets for use as a textbook

New to This Edition
The following are selected revisions in the second edition:
* A new preliminary chapter that provides a review of the 3D rendering pipeline
* A new chapter containing an advanced discussion of the stencil shadow rendering technique
* A new chapter covering various numerical methods pertinent to 3D graphics programming, including numerical solutions to linear systems, numerical eigenvalue determination, and numerical integration
* A new chapter covering curves and surfaces, including Bézier curves and B-splines
* New discussions of texture filtering, mipmapping, and infinite projection matrices
* Updated lighting method implementations and collision detection techniques
* Additional exercises in all chapters ... Read more

Customer Reviews (14)

Not available for Kindle PC !?!
Disapointing : this ebook doesn't seem to be allowed for Kindle PC.
I was interested to be able to check the book on my desktop machine at work at the same time I would read it from my Kindle...

I strongly recomend for the ones that want to seriously go into game development!
When I received this book I couldn't wait to start reading it. I didn't finish it yet but so far all explanations, mathematical rules are so clear and understandable. It's incredible to model world with usage of equations and numbers. Don't hesitate! Get it. Enjoy.

Little more than an outline
I was disappointed in how little explanations were included in this math book.It seemed more like a dictionary.It was as if someone listed all the math concepts that could be included and then put the list into a hard cover binder.
I did read some of the other reviews thinking I had missed something.One suggested spending a year on the book.But there is so little there.My college book on linear algebra did a much better job of explaining the material.Theorems were explained, samples worked out and 10 to 20 problems were given at the end of each section.This book as 50 problems for the entire book.This book spends eight pages on quaternions.Studying these pages over an extended period of time would not give the understanding you could get from a book like Kuipers' Quaternions and Rotation Sequences.It took 75 pages but one is able to understand the system and how it relates to game programming.
With all the colleges now offering game programming degrees, their must be a book written by someone who is use to explaining the material.That person would know the best way to present the material and could anticipate questions and include the answers in his or her explanations.

a disappointment
the second edition brings a new chapter on the graphics pipeline. Well done, except that it is extremely obscure, for those who already understood the arcanes of the graphics pipeline.
Chapter 5 on "ray tracing": 6 pages on root finding of quadratic, cubic and quartic polynomials;
to compare with Chapter 7: "Visibility determination": The spatial partitioning deserves solely 4 pages.
What's the point on dwelling so much on something that is trivial and botching something that is hard to grasp and of paramount importance ?

One of a kind

As a professional 3D graphics programmer, I can not stress enough the quality of this book. This book covers 3D math fundamentals, algorithms, and it is complete with easy to understand (!) proofs. The math is difficult because there is so many problems to be solved in 3D (and they draw from many different branches of mathematics), but it is written in such a clear way that every topic is made approachable. Unlike esoteric Ph. D papers, you aren't assumed to have any specific knowledge of math idioms or jargon. You simply need a decent grasp of college calculus and trigonometry to make the most of it. There are a few samples too to test your knowledge.

Expect to spend at least a solid year to really make the use of this book. Treat it as you would a two - three semester course in college. During this process, you'll find yourself occasionally wanting to get more practice and referring to a respective book on it.

If you could only own two books for 3D programming, buy this first and buy Ericson's book on collision detection next.

In summary, Eric Lengyel's attention to detail and mastery of 3D math / algorithms really shines and this book is an example of it.



... Read more

Product Description
Numerical analysis is the branch of mathematics concerned with the theoretical foundations of numerical algorithms for the solution of problems arising in scientific applications. Designed for courses in numerical analysis and as a reference for practicing engineers and scientists, this book presents the theoretical concepts of numerical analysis and the practical justification of these methods through computer examples with the latest version of MATLAB. The book addresses a variety of questions ranging from the approximation of functions and integrals to the approximate solution of algebraic, transcendental, differential and integral equations, with particular emphasis on the stability, accuracy, efficiency and reliability of numerical algorithms. The CD-ROM which accompanies the book includes source code, a numerical toolbox, executables, and simulations. FEATURES*Presents each numerical method by first providing examples and geometric motivation, then the steps to perform the computation, and finally the mathematical derivation of the process *Provides short programs in MATLAB that can be used for scientific applications with or without modifications *Shows the visual representation of mathematical concepts in 2D graphics and is compatible with the current MATLAB v.7.5. *Accompanied by a CD-ROM featuring source code, executables, figures, and simulations *Includes an introduction to MATLAB commands *Features an Instructor s Resource Disc for use as a textbook BRIEF TABLE OF CONTENTS 1. Number Systems and Errors. 2. Nonlinear Equations. 3. Systems of Linear Equations. 4. Approximating Functions. 5. Numerical Differentiation and Integration. 6. Ordinary Differential Equations. 7. The Eigenvalue problems. Appendix A. Mathematical Preliminaries. B. Introduction to MATLAB. ... Read more

Customer Reviews (1)

An outstanding reference.
College-level courses strong in numerical analysis as well as those catering to engineers and scientists will appreciate this introduction: the first to present the theory of numerical analysis and the practical justifications of methodology using the latest version of MATLAB. This will also make a fine college-level text for primary or supplemental reading: it provides short programs in MATLAB to be used for scientific applications, surveys MATLAB commands and processes, includes a CD-ROM featuring source code and simulations, and reinforces theory with applications. An outstanding reference. ... Read more

Product Description
Master the fundamentals of discrete mathematics with DISCRETE MATHEMATICS FOR COMPUTER SCIENCE with Student Solutions Manual CD-ROM! An increasing number of computer scientists from diverse areas are using discrete mathematical structures to explain concepts and problems and this mathematics text shows you how to express precise ideas in clear mathematical language. Through a wealth of exercises and examples, you will learn how mastering discrete mathematics will help you develop important reasoning skills that will continue to be useful throughout your career. ... Read more

Product Description

University studies in computing require the ability to pass from a concrete problem to an abstract representation, reason with the abstract structure, and return with useful solutions to the specific situation.

The tools for developing these skills are in part qualitative – concepts such as set, relation, function, and structures such as trees and well-founded orders. They are also in part quantitative – notably elementary combinatorics and finite probability. Recurring in all of these are instruments of proof, both purely logical ones (such as proof by contradiction) and mathematical (the various forms of induction).

Features:

• Explains the basic mathematical tools required by students as they set out in their studies of Computer or Information Science

• Explores the interplay between qualitative thinking and calculation

• Teaches the material as a language for thinking, as much as knowledge to be acquired

• Uses an intuitive approach with a focus on examples for all general concepts

• Provides numerous exercises, solutions and proofs to deepen and test the reader’s understanding

• Includes highlight boxes that raise common queries and clear away confusions

• Tandems with additional electronic resources including slides on author's website

http://david.c.makinson.googlepages.com

This easy-to-follow text allows readers to carry out their computing studies with a clear understanding of the basic finite mathematics and logic that they will need. Written explicitly for undergraduates, it requires only a minimal mathematical background and is ideal for self-study as well as classroom use.

Customer Reviews (1)

Great introductory maths textbook for CS students
This is a great maths book for first year Computer Science undergraduates. It assembles in a single text most of the basic mathematical tools required in the study of Computer Science, ranging from sets and relations, to combinatorics and probabilities, to trees and logic.

Most importantly, the book is easy to follow even for someone who is not a great fan of mathematics; in fact, these are the people that will probably benefit most from this book. Concepts are presented very clearly, in a lively prose, with extra care in providing an intuitive grasp of formal notions, and attention in clarifying subtle details. This is further assisted by an on-going dialog spread throughout the book between two fictional characters, Alice and Mad Hatter (borrowed from Lewis Carroll's classical novel), discussing subtleties in the text. Carefully selected exercises in each chapter help to reinforce students understanding of the text.

Overall, a great introductory textbook. I strongly recommend it to anyone starting studies in Computer Science.
... Read more

Product Description
Best-selling author Nigel Cook's new second edition of Introductory Computers Mathematics provides a complete math course for those learning computer technology. Employing an “integrated math applications” approach, this book reinforces all math topics with extensive applications to show readers the value of math as a tool.Specific chapters in the section on Basic Math discuss fractions; decimal numbers; positive and negative numbers; exponents and the metric system; algebra, equations and formulas; geometry and trigonometry; and logarithms and graphs. Computer Math topics cover analog to digital, number systems and codes, logic gates, Boolean expressions and algebra, binary arithmetic, and an introduction to computers and programming.For individuals preparing for a career in computer technology. ... Read more

Customer Reviews (2)

Well thought out and applicable introduction... Great Refresher.
I spent a long time looking for a resource like this.As someone who clearly did not pay enough attention in high school or college and someone who then rarely used mathematics I find this book a great refresher.It is easy to understand with some of the best explanations I've ever seen of the principles behind why algebraic expressions are the way they are.Recently I have been trying to learn to program (verses learn a programming language) and realized that in even some of the more basic introductions there were many things assumed about my mathematical knowledge that sadly did not hold true for me.While I knew there was an order of operations I could not have told you what it was or why.And when they began to talk about algorithms I became completely lost.But this book walked me back through much of this and I am now able to move forward again.I highly recommend this book to anyone wanting a practical and applicable knowledge of basic mathematics.

Introduction to Computer Mathematics!?
I got this book as an assistant for programming and additional mathematics. The book is written more like an introduction to mathematics. It starts with basic fractions, multiplication, and exponents. It briefly covers advanced algebraic expressions and trig. Though the good side of it is that it covers logic gates pretty good. I would suggest buying a series of books instead of one brief one. Whether you are going into computer science or information technology, get something more in depth. ... Read more

Product Description
Computing is an exact science and the systematic study of any aspect necessarily involves the use of mathematical models. Moreover, the rate at which the subject is evolving demands a facility for developing new mathematical systems to keep pace with new computing systems and this requires an appreciation of how mathematics works. An understanding of the underlying mathematical structure facilitates the construction of suitable computer programs to perform computations. Assuming no specific knowledge of mathematics, the authors describe all the basic concepts required and progress from sets (rather than numbers) through a variety of algebraic structures that permit the precise description, specification and subsequent analysis of many problems in computing. The material included provides the essential mathematical foundations for core topics of computer science and extends into the areas of language theory, abstract machine theory and computer geometry. Computer Mathematics will be of interest to undergraduate students of computer science and mathematics, post-graduate computing 'conversion' course students and computer professionals who need an introduction to the mathematics that underpins computer science theory. ... Read more

Product Description

Discrete mathematics and theoretical computer science are closely linked research areas with strong impacts on applications and various other scientific disciplines. Both fields deeply cross fertilize each other. One of the persons who particularly contributed to building bridges between these and many other areas is László Lovász, a scholar whose outstanding scientific work has defined and shaped many research directions in the last 40 years. A number of friends and colleagues, all top authorities in their fields of expertise and all invited plenary speakers at one of two conferences in August 2008 in Hungary, both celebrating Lovász’s 60^th birthday, have contributed their latest research papers to this volume. This collection of articles offers an excellent view on the state of combinatorics and related topics and will be of interest for experienced specialists as well as young researchers.

Product Description
Confusing Textbooks? Missed Lectures? Not Enough Time?

Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

This Schaum's Outline gives you:

• Practice problems with full explanations that reinforce knowledge
• Coverage of the most up-to-date developments in your course field
• In-depth review of practices and applications

Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores!

Schaum's Outlines-Problem Solved. ... Read more

Customer Reviews (10)

Incomplete
This book does not cover college level discrete math well enough. Recursion and induction are given only a cursory paragraph. Proofs are not adequately covered.

Good Book
This book is a good exercise book. It has tons of solved and review problems most of which are proofs of the theories explained through the chapters. Despite that, I do not see the book adequate for an undergraduate course by itself. It as of great use in tutorials and as a supporting reading.

Excellentstudy guide for students of discrete math and computer science
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
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
This math book simply helps and supports learning with good, specific examples and no jargon. ... Read more

Product Description
This book provides an elementary "hands-on" presentationof important mathematical logic topics.Explores topics thatare at the cutting edge of developments in computer science, while preserving the integrity of traditional logic. Stresses several self-contained proofsystems of interest to mathematical logic, some more suitable than others forparticular kinds of questions.For anyone interested in ComputerScience or Mathematics. ... Read more

Customer Reviews (3)

Great as preparation for automated reasoning, not so hot otherwise
In terms of the coverage of logic for mathematics and computer science, the target here is really the area of automated theorem proving. The book is split into two sections:

*) Quantifier-free logics
*) Logic with quantifiers

While the basic coverage of the propositional and predicate calculi is typical of what is done in other logic books, chapter three deals with equational logic and there is some coverage of abstract algebra. In particular, the representation of algebraic structures such as groups and fields. There is also extensive coverage of term rewrite systems (TRSs), which are constructed using replacement rules that resemble those of formal grammars.
If you are looking for a text in a course in basic mathematical logic, in my opinion this one is unsuitable. The extensive coverage of representations of structures including graphs takes you down a path not normally taken in a course in mathematical logic. In terms of computer science, it would have been helpful if more effort were spent in tying the logic into more mainstream areas covered in the computer science major. I also would not consider using this book as a text in a course in computation theory.

A logician from holland
I used this book as a course book and I can say that it is quite difficult to follow the book. All the proofs are either intuitive or very shortwithout much explanation or example. So, if you want to take this book as aguide for this field think twice!

gives basics for automated reasoning
I found this book to be an excellent reference for automated reasoning. It covers resolution and unification in great detail. It also covers Knuth-Bendix procedure for equational logic. I used this book as a startingpoint to learning about automated reasoning and logic in AI.

I recommendthis book for anyone who is just beginning to learn about automatedreasoning.

The one suggestion that I have to anyone reading this book isto review your abstract algebrea and set theory. Although this books doesintroduce and cover abstract algebra basics, anohter reference is useful.As for set theory, try Schaum's Outline on Set Theory as an intro or arefresher. ... Read more

Product Description
This book provides a quick, concise introduction to the most important mathematics used in computer graphics. In ten chapters readers will discover the mathematical techniques required to solve problems and design computer programs for computer graphic applications. From trigonometry to coordinate geometry, each chapter explores a specific mathematical topic. Step-by-step, readers are lead through the fundamentals to such advanced areas as 3D curves, surface patches, and vectors.

Accessible coverage helps make the concepts easy to understand, so that a non-mathematician can quickly grasp the math that lies behind computer animation. ... Read more

Customer Reviews (3)

Great refresher
I love that the author was able to fit so much into so few pages. If I had to carry my old math books from college, I would have to hire a chiropractor.

It's important to point out that this isn't really the text to learn math from; however, it's a great little refresher that's to the point. So if you're rusty, get this book... if this is all new to you, I'd look into more indepth books.

Terrific Book!
This book is terrific. The word "fast" in the title hints that you are only going to get a superficial overview of various topics, but this is not the case: you actually come away with an UNDERSTANDING of the topics. The chapter on interpolation is a case in point... I came away being able to derive cubic interpolants, which means that I UNDERSTOOD cubic interpolants. The discussion on quaternions paved the way for me to be able to use them, and the chapter on Bezier curves and patches also gave me an excellent foundation on which to begin using them in OpenGL. In short, I guess this is just one of those magical books in which the author knows how to explain complex subjects in a simple, direct manner. This book is excellent, and I heartily recommend it.

Concise, tight mathematics reference.
First off, here is what you should expect when buying this book: it's a mathematical quick-reference book, and as such, it contains absolutely no code.What it does contain is background information and formulas for a bunch of the most common situations you'll encounter in computer graphics.

This book covers a lot of ground in relatively few pages, making it a tight read.It moves through Algebra, Trig, and Geometry, along the way covering such topics as 2D and 3D transforms, perspective, and Beziers.Most of the topics in the book are explained in sufficient detail in a small amount of space.The author makes great and liberal use of diagrams and pictures, which I find particularly helpful to understanding the material since math isn't one of my strong points.

There are also straightforward examples that demonstrate the mathematical principles, although there is usually only one or two examples per topic.This can be difficult if, like me, you have problems "getting it" without lots of examples to chew on.

As a software engineer, I enjoy figuring out how things work.And in that respect, this book is great.I have some experience dabbling in OpenGL, and I've read several other computer graphics texts that were laden with code examples but lacking in adequate explanations of the math being used.I have also read basic math books that were not geared towards computer programming topics, which made application and transfer of the mathematical threory difficult.This book filled the gap for me, taking me from thinking things like "Hey, look what I can do with OpenGL" to "Hey, I know how OpenGL is doing that!!"Well, maybe I don't know *exactly* how OpenGL works behind the scenes, but because of this book I have a much better understanding of basic computer graphics.

Highly recommended, especially if you don't have a strong math or computer science background. ... Read more

Product Description
Useful guide covers two major subdivisions of combinatorics--enumeration and graph theory--with emphasis on conceptual needs of computer science. Each part is divided into a "basic concepts" chapter emphasizing intuitive needs of the subject, followed by four "topics" chapters that explore these ideas in depth. Invaluable practical resource for graduate students, advanced undergraduates, and professionals with an interest in algorithm design and other aspects of computer science and combinatorics. Unabridged republication of original 1985 edition. References for Linear Order & for Graphs, Trees, and Recursions. 219 figures.
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Customer Reviews (2)

Suitable for a graduate level course
While most computer science departments require their students to take calculus, with few exceptions it is a skill that they will not use. The mathematics used by computer scientists is almost exclusively discrete in nature. In fact, assumptions concerning continuity can often lead to subtle errors in programming, the laws of algebra do not universally apply in computing. This book presents most of the key ideas of discrete mathematics applied to computing and the coverage is thorough and detailed.
It is split into two parts, linear order and graphs, trees and recursion. The emphasis is on detailed problem solving rather than explanations of the foundations. For example, there is a detailed example of a lexicographic bucket sort on page 16. The material is presented using higher level mathematical notation, so it is best suited for graduate level courses. A large number of exercises are included, but no solutions are given.
If you are looking for a text to be used in classes that have significant discrete mathematics prerequisites, then this book is certainly appropriate. It would be best suited for students with a great deal of programming experience.

Excellent reference for data structure algorithm complexity.
This excellent reference has numerous examples, definitions and exercises covering trees, graphs, linked lists etc.This book provides a great companion to any data structures text. ... Read more

Customer Reviews (1)

A Must Read
An awesome book on Discrete Math. A must read for an undergrad CS student. ... Read more

Product Description

The two-volume textbook Comprehensive Mathematics for Computer Scientists, of which this is the first volume, is a self-contained comprehensive presentation of mathematics including sets, numbers, graphs, algebra, logic, grammars, machines, linear geometry, calculus, ODEs, and special themes such as neural networks, Fourier theory, wavelets, numerical issues, statistics, categories, and manifolds. The concept framework is streamlined but defining and proving virtually everything. The style implicitly follows the spirit of recent topos-oriented theoretical computer science. Despite the theoretical soundness, the material stresses a large number of core computer science subjects, such as, for example, a discussion of floating point arithmetic, Backus-Naur normal forms, L-systems, Chomsky hierarchies, algorithms for data encoding, e.g., the Reed-Solomon code. The numerous course examples are motivated by computer science and bear a generic scientific meaning.

For the second edition the entire text has been carefully reread, and many examples have been added, as well as illustrations and explications to statements and proofs which were exposed in a too shorthand style. This makes the book more comfortable to handle for instructors as well as for students.

Customer Reviews (2)

Not suitable for use as an introductory textbook
As the title of this book suggests, it covers a broad range of topics in mathematics; it is intended for use as an introductory textbook for computer science undergraduates. The topics covered include sets, numbers, graphs, logic, grammars, automata, algebra, and geometry. Many of those topics can be found in books on discrete mathematics and linear algebra.

This book is part of a larger e-learning project, which also includes a companion Web site [...]The Web site contains slides, errata, and modular courses, as well as other information about the e-learning project. Although the book contains a broad range of topics in 26 chapters, it is relatively compact compared to other mathematics textbooks designed for computer science students.

The book has the following shortcomings. First, many important concepts are not clearly explained. Most of the definitions and theorems are listed without detailed explanations. Second, many figures in the book are not referred to in the text; they just appear close to some definitions, theorems, or examples. Third, the book does not contain enough examples for students to practice after definitions and theorems are stated, nor does it contain a collection of exercises at the end of each chapter. Teachers who use this as a textbook may need to find other complementary materials or come up with their own exercises in order for students to practice the techniques described in the book. Generally speaking, this book looks like a collection of handouts since it lacks detailed information throughout.

The book is also weak in terms of the depth of its coverage. For example, it discusses graph theory, but does not mention the graph coloring problem or the shortest path problem. It covers trees, but does not include Huffman trees or sorting. Many of topics covered have a close relationship to data structures and algorithms, but the book does not discuss them clearly.

In my opinion, the book is not suitable for use as an introductory textbook for computer science undergraduates. It may be suitable for people who are already familiar with the subject and need a reference to quickly check definitions and theorems.

Set high standards
This book is very exciting and motivating, as it sets high standards both with respect to the contents and the style.

It contains the main topics of modern math from the beginning, with applications to Computer Science: Sets, Relations, Logic, Numbers, Groups, Rings, Modules, Linear Algebra, Geometry, Quaternions.

The style is extremely compact, precise and readable, with a professional notation. The book is optimal designed (modularized)
which results in a moderate size (360 p.)

The objective of his approach is to provide a better formal competence for computer scientists by a sound mathematical education:

"Improved formal competence is urged by the object-oriented paradigm which progressively requires a programming style and a design strategy of high abstraction level in conceptual engineering."

The accompanying online course contains illustrations and animations, which at the moment don't go far beyond the book's contents.
Nevertheless, the online part has a great potential for further applications, e.g. programming projects (Moebius-Strip, Raytracing, 3D Stereo, ...)

We hope, this book will establish itself as a standard for ambitious schools and students. ... Read more