Product Description
Logic and Complexity looks at basic logic as it is used in Computer Science, and provides students with a logical approach to Complexity theory. With plenty of exercises, this book presents classical notions of mathematical logic, such as decidability, completeness and incompleteness, as well as new ideas brought by complexity theory such as NP-completeness, randomness and approximations, providing a better understanding for efficient algorithmic solutions to problems. Divided into three parts, it covers: Model Theory and Recursive Functions - introducing the basic model theory of propositional, 1st order, inductive definitions and 2nd order logic. Recursive functions, Turing computability and decidability are also examined. Descriptive Complexity - looking at the relationship between definitions of problems, queries, properties of programs and their computational complexity. Approximation - explaining how some optimization problems and counting problems can be approximated according to their logical form. Logic is important in Computer Science, particularly for verification problems and database query languages such as SQL. Students and researchers in this field will find this book of great interest. ... Read more

Product Description
Discrete mathematics is quickly becoming one of the most important areas of mathematical research, with applications to cryptography, linear programming, coding theory and the theory of computing. This book is aimed at undergraduate mathematics and computer science students interested in developing a feeling for what mathematics is all about, where mathematics can be helpful, and what kinds of questions mathematicians work on. The authors discuss a number of selected results and methods of discrete mathematics, mostly from the areas of combinatorics and graph theory, with a little number theory, probability, and combinatorial geometry. Wherever possible, the authors use proofs and problem solving to help students understand the solutions to problems. In addition, there are numerous examples, figures and exercises spread throughout the book.

László Lovász is a Senior Researcher in the Theory Group at Microsoft Corporation. He is a recipient of the 1999 Wolf Prize and the Gödel Prize for the top paper in computer science. József Pelikán is Professor of Mathematics in the Department of Algebra and Number Theory at Eötvös Loránd University, Hungary. In 2002, he was elected Chairman of the Advisory Board of the International Mathematical Olympiad. Katalin Vesztergombi is Senior Lecturer in the Department of Mathematics at the University of Washington. ... Read more

Customer Reviews (3)

Review
Kinky introduction but has good problems that come inside the chapters not at the end.

unique in approach
I am really surprised at my fellow reviewer's statements indicating that you need to be a genius to understand this book. In fact, it is really the opposite; the authors took an effort to make the material approachable to the mathematically minded and provide motivating context for each example. While at the authors, you should note that these people are some of the most well known researchers in this area and Dr. Lovasz is also an exceptional lecturer. I believe all possess Erdos number 1 :) It is surely not a textbook, in the sense of Rosen's "Discrete Mathematics and its Applications" nor it strives for completeness like Reinhard Diestel's "Graph Theory". Instead it is a selection of topics that give a good introduction into discrete mathematics with carefully selected insightful problems with solution hints! So, yes, I think it is great for self study and especially for those (as the introduction suggests) who have had a more analysis-biased introduction into Mathematics. Instead of being a collection of theorems and proofs, the problems in this book build on the absolute necessary basics (often just high-school math) and, yes, skip unnecessary notation and pseudo-rigor. I should also note that I am basing this review on the Hungarian edition, which also reads well but I have not actually seen the original English text.

If You're Brilliant and Don't Mind a Lack of Rigor, Try It.
Ouch.I definitely made a mistake trying this book.From what I can see, the only set of people who might find this book useful would be genius non-Math-types.My handy-dandy way of explaining this is by mapping the universe of all possible readers onto a set of x-y axes.Let the x axis run from "non-Math-types" up through "Math-types."Let they y axis go from "non-geniuses" up through "geniuses:"

- Quadrant I:if you're a genius Math-type, you'll be aghast at the lack of rigor in the proofs and at all the steps missing from the few proofs given.But, you might be able to work through the material on your own.My guess, though, is that you'll throw the book across the room in disgust, instead.

- Quadrant II:if you're a genius non-Math-type, you might find the lack of rigor in the proofs tolerable.Plus, you, like the Quadrant Is, might be able to work through the material enough so that you can follow the author's explanations.If you're smart enough and have enough familiarity with the material before reading this book, you might find its terseness acceptable.

- Quadrant III:if you're a non-genius non-Math-type (i.e., "normal"), you'll be lost.You (we) won't understand what the point of this is, won't be able to work thru all the missing steps in the few proofs given, and will rant and rave when the authors "prove" one thing, give one example, and then ask the reader to prove the several follow-up theorems as an exercise.With, essentially, one example to work from in a subset of each topic, you'll never be able to work through the few questions with answers (which answers are short to the point of worthlessness) and will throw up your hands in dismay when attempting to solve the non-answered end-of-chapter questions.

- Quadrant IV:if you're a non-genius Math-type, you will join the Quadrant Is in horror at the lack of rigor, but, like the Quadrant IIIs, will be horribly frustrated since you won't be able to force your way through the material on your own.A definite lose-lose situation, here.

The really odd thing with this book is that, in the universities, Discrete Math (the subject) is usually a required course for Computer Science majors and is a PRE-CALCULUS course.There's absolutely no way that any such student at that point in his degree could get through this book.I received my B.S. in Mathematics from the University of Michigan well over 20 years ago (so I've forgotten most everything, plus I was a Quadrant IV type but figured it out much later and migrated to Quadrant III), but there are entire chapters in this book where I only understand words like "the" and "and."The authors assume an extremely in-depth degree of mathematical knowledge on the part of the reader.Also, there's nothing to tie the subject matter back to anything a CS person (or any non-math-type) could use in his degree, profession, or life.So, once again, this book is very poorly matched against any intended audience.

I'd also like to point out that I doubt this book would ever be chosen by any academic institution for teaching.It just doesn't follow the established norms on how to teach.Specifically, it should:1) tell the readers what it's going to say, 2) tell them, and 3) tell them what it just told them.Each chapter and section in this book just starts out talking about something.You really have no idea where the authors are going until they actually get there.What the book really, REALLY needs is for the authors to state exactly what they're going to do in a section and chapter, do it, and then summarize it.Ditto for the book as a whole.The preface needs some kind of overall game plan so the people reading the book know where they're going.

Since the publisher hasn't provided the information on Amazon, I've put a scanned copy of the book's Table of Contents in the "User Images" area at the top of the page.

I rate this book 2 stars out of 5. ... Read more

Product Description

Here is an accessible, algorithmically oriented guide to some of the most interesting techniques of complexity theory. The book shows that simple algorithms are at the heart of complexity theory. The book is organized by technique rather than by topic. Each chapter focuses on one technique: what it is, and what results and applications it yields.

Customer Reviews (1)

Good idea, but badly executed
The aim of this book is to introduce complexity theory using a more technique-oriented approach, which is not seen in other complexity theory textbooks. Techniques covered are:
- self-reducibility
- one-way function
- tournament divide and conquer
- isolation technique (aka. isolation lemma)
- witness reduction
- polynomial interpolation
- nonsolvable group (used in Barrington's theorem to show that width-five branching program can simulate any Boolean formula and thus the complexity class NC1)
- random restriction technique
- polynomial technique
This seems like an awesome approach and I can't agree with the authors more about the organization of techniques. This was the reason why I bought the book.

Unfortunately, the results are badly presented in a lot of places. Proofs are extremely tedious with unnecessary details and notations. This overly formal approach prevents readers from seeing the big strategy or ideas behind the proofs. For example, Barrington's theorem has a very elegant and readable 1-page proof (cf. Boppana-Sipser survey "The Complexity of Finite Functions", 1989). But in this book they decided to include an ugly 6 page proof!

The students will learn more from "Computational Complexity" by Arora and Barak, where only the most elegant and readable versions of proofs are selected. Papadimitriou does not cover recent results, but is also a solid textbook with full of excellent exercises. ... Read more

Product Description
Essential Mathematics for Games and Interactive Applications, 2nd edition presents the core mathematics necessary for sophisticated 3D graphics and interactive physical simulations. The book begins with linear algebra and matrix multiplication and expands on this foundation to cover such topics as color and lighting, interpolation, animation and basic game physics. Essential Mathematics focuses on the issues of 3D game development important to programmers and includes optimization guidance throughout.

The new edition Windows code will now use Visual Studio.NET. There will also be DirectX support provided, along with OpenGL - due to its cross-platform nature. Programmers will find more concrete examples included in this edition, as well as additional information on tuning, optimization and robustness.

The book has a companion CD-ROM with exercises and a test bank for the academic secondary market, and for main market: code examples built around a shared code base, including a math library covering all the topics presented in the book, a core vector/matrix math engine, and libraries to support basic 3D rendering and interaction.

--Simple game enginewith math, rendering, and input libraries on the CD-ROM, so that game developers can immediately start applying the techniques they learn in a basic codebase.
--Exercises on the CD-ROM for educators to use for course material
--Code samples shown throughout the book for real-world application
... Read more

Customer Reviews (14)

Kindle Edition is a rip-off
This is a great book, however, with the Kindle version being priced only 5 dollars less than the hardcover, one would expect that you would get the same value.

However, you do not, as the CD-ROM that is included with hardcover is not included with the kindle edition.This is an issue, when for instance, you look up line segment to line segment, and find out that source code isn't listed in the book to save space.This doesn't make the book worthless, but it makes it pretty worthless.

If you are thinking about getting the Kindle edition - don't.Get the hardcover edition instead.

Essential Math a good basis
As a novice game programming hobbyist, I've written applications using the DirectX SDK to render 3D visuals without really understanding what's happening behind the scenes. Applying a transformation matrix to a model and illuminating it with a spotlight just seemed to be magic beyond my understanding. This book has delivered enough information to get a good foundation in the understanding of the mathematics involved to bring points and images into a visual representation to the screen while going even further to discuss collision detection, interpolation, and rigid body dynamics.

If the reader wanted to develop a 3D application on a platform with no native support or SDK, there's enough material in this book to give the reader a core background to develop a software solution. Even though portions of the graphics pipeline are automatically handled by an SDK or hardware, the concepts are presented so the reader is taken every step of the way.

The reader should know algebra (of course), trigonometry, and calculus if they want to get something out of it. A history of linear algebra also helps, but it isn't necessary since the chapter on matrices that goes over the essential operations. The later chapters on collision detection and physics start getting more math-heavy. Having previously read a couple other books in the Morgan Kaufmann series: Real Time Collision Detection and Game Physics, I was expecting the discussions to be very similar; however, the reader would only get a basic understanding of the topics and would greatly benefit from continuing their reading into the aforementioned books.

Overall, I enjoyed this book very much and it gets my approval for anyone wanting to get into game programming and 3D simulation. The author also provides many resources and accompanies the book with a CD of precompiled visual examples that should better solidify the user's understanding. As previously mentioned, Real Time Collision Detection and Game Physics make fantastic supplements to this book.

Very complete textbook for game math
This textbook seems to adequately cover all the major formulas used for game engines pretty well. It's not easy to read, but then these are difficult concepts. I showed this to my upcoming professor, and he was impressed; ended up making it the required textbook for the course.

For high school graduates
Respectable publisher, respectable series. I was expecting presentation level, scope and depth similar to Eberly's "Game Physics". Unfortunately, mistake. This is a book for someone who just graduated from American high school and knows only so called "algebra" (+, -, *, / with calculator, no fractions). No question, there are such individuals, they have to learn, and for them this is pretty good book. I was fooled by impressive Table of Contents and number of pages. Was useless for me. Lesson learned: if you want Eberly's quality, buy Eberly's books

One of the most useful books on my shelf
This has been one of the most interesting and useful books on my bookshelf. It's great for people trying to learn the kind of math that's needed in computer game development or for people who just want a refresher. This book is such a great help and so clearly written that it would be worth it at $100, for this price it's a huge bargain. Everyone interested in programming games should own a copy. ... Read more

Product Description

Taking an approach to the subject that is suitable for a broad readership, Discrete Mathematics: Proofs, Structures, and Applications, Third Edition provides a rigorous yet accessible exposition of discrete mathematics, including the core mathematical foundation of computer science. The approach is comprehensive yet maintains an easy-to-follow progression from the basic mathematical ideas to the more sophisticated concepts examined later in the book. This edition preserves the philosophy of its predecessors while updating and revising some of the content.

New to the Third Edition
In the expanded first chapter, the text includes a new section on the formal proof of the validity of arguments in propositional logic before moving on to predicate logic. This edition also contains a new chapter on elementary number theory and congruences. This chapter explores groups that arise in modular arithmetic and RSA encryption, a widely used public key encryption scheme that enables practical and secure means of encrypting data. This third edition also offers a detailed solutions manual for qualifying instructors.

Exploring the relationship between mathematics and computer science, this text continues to provide a secure grounding in the theory of discrete mathematics and to augment the theoretical foundation with salient applications. It is designed to help readers develop the rigorous logical thinking required to adapt to the demands of the ever-evolving discipline of computer science.

Product Description
From one of our most acclaimed novelists, a  David-and-Goliath biography for the digital age.

One night in the late 1930s, in a bar on the Illinois–Iowa border, John Vincent Atanasoff, a professor of physics at Iowa State University, after a frustrating day performing tedious mathematical calculations in his lab, hit on the idea that the binary number system and electronic switches, com­bined with an array of capacitors on a moving drum to serve as memory, could yield a computing machine that would make his life and the lives of other similarly burdened scientists easier. Then he went back and built the machine. It worked. The whole world changed.

Why don’t we know the name of John Atanasoff as well as we know those of Alan Turing and John von Neumann? Because he never patented the device, and because the developers of the far-better-known ENIAC almost certainly stole critical ideas from him. But in 1973 a court declared that the patent on that Sperry Rand device was invalid, opening the intellectual property gates to the computer revolution.

Jane Smiley tells the quintessentially American story of the child of immigrants John Atanasoff with technical clarity and narrative drive, making the race to develop digital computing as gripping as a real-life techno-thriller. ... Read more

Customer Reviews (2)

RICK "SHAQ" GOLDSTEIN SAYS: THE BATTLE OF WHO REALLY INVENTED THE COMPUTER & THE REAL INTRIGUE OF WORLD WAR II"
This is the life story of John Atanasoff the man who many credit with inventing the first computer. (The ABC Computer) Though there are still disputes to this day involving who truly did invent the *FIRST* computer with some touting John Mauchly (Who is accused of stealing ideas from Atanasoff due to Atanasoff's exuberance during development.) and J. Presper Eckert with the more famous ENIAC computer, the fact remains as stated in this book that in 1973 Judge Larson ruled on a case involving Honeywell (On Atanasoff's side.) and Sperry Rand (On Mauchly and Eckert's side.) in the favor of Honeywell and according to the author: "SPERRY NEVER APPEALED THE DECISION, AND SO THEY MUST HAVE ACCEPTED IT." This eternal dispute should not influence a potential reader in making a decision on whether to read this book or not. This is a fascinating look at not only Atanasoff who was an Iowa State College professor of physics... and between 1937 and 1942 developed the concept... and with meager funds built the ABC Computer... but also other geniuses who were separated by countries and war. What I want to stress is that I found in the journey of not only Atanasoff, but of all the now famous names involved in the early quest to create/invent a computer device... that the quest was just as educationally exhilarating... as the actual creation. The individual personality tics of these geniuses are quite interesting to the average eye. The fact that Atanasoff helped his Father wire their entire home for electricity when he was ten-years-old... and *HE MASTERED THE OWNER'S MANUAL OF HIS FATHER'S NEW FORD MODEL T, AND AT ELEVEN HE WAS DRIVING IT." Accomplishments such as these, along with his constant inquisitive nature at school as well as at home signaled very early that he was capable of some very unique things. Along with John, you will learn about Von Neumann... Turing... Flowers... Aiken... Zuse... Babbage... Bush... et al... the entire who's who in the quest for a computer.

The most utterly fascinating part of this story is the need for computer intelligence and power during World War II. The need for the allies to bust the German's secret encoding system called *ENIGMA* was of utmost importance. Because of the war the race for inventing a computer in the civilian world was put on hold. The ?"computer-like"? devices that these geniuses developed named *BOMBES, BOMBAS AND COLOSSUS* literally changed the course of the war and the fact that the German's were so arrogant, that when the code busters were striking gold and saving lives, the German's didn't change their tactics because they couldn't believe anyone could accomplish what was being done by these machines. Some of this equipment was so revolutionary and *TOP-SECRET-CLASSIFIED* that the technology not only couldn't be used in other equipment... but it eventually had to be destroyed. One of the developers couldn't even list his accomplishments on a resume.

At times some of the technical explanations will not be understood by everyone. If I count the time I was involved with computers for over three years in the military as well as my civilian work, I have made my living in this industry for the last forty-one years. I have installed computers, used computers, sold computers, trained people on computers, and designed systems (systems analysis-not programming) from the punched card and tape days... to mainframes... to mini-computers... to today's microscopic systems... and yet when the author discussed diodes andother internal electronic components... I was lost. I just wanted to point out that deep technical knowledge is not a requirement to enjoy this book.

Before you drink the Kool-Aid, there is one thing
I admit an underdog story is always appealing, and Smiley does a fantastic job of making the dry topic intriguing.But please understand, this is a highly fictionalized account.It is not "fact" that Atanasoff's machine was a computer at all!The controversy over the importance of Atanasoff's work has been debated, at length, in computer history circles for 35 years.And it has been debunked.This is not news.

(If you know enough about computers to know that they "run a program" then you are capable of understanding why historians consider the ABC more of a calculator than a computer; it had no program!Please look at a real computer history book or at least Wikipedia if you want to know more.)

The legend of Mauchly's treachery seems to grow richer with each telling.Smiley did no original research to find out about him, but instead propagated the evil intent that was ascribed him posthumously by the scorned Arthur Burks.And the author also parrots Burks' highly questionable list of fundamental computer ideas that Atanasoff had, and supposedly Mauchly stole.Binary System? Really? Leibniz might have something to say about that.When push comes to shove, there is no trace of the ABC in the ENIAC.But that would ruin the story.Apparently the author neglected to talk to anybody who actually knew Eckert or Mauchly.She did interview people from Ames, Iowa, where the Kool-Aid is manufactured.

So be forewarned.A gripping story, well-told indeed.But while it pretends to be technically savvy, it sacrifices a lot of truth in order to make a good yarn. ... Read more

Product Description
This book will be released simultaneously with Release 2.0 of Mathematica and will cover all the new features of Release 2.0. This new edition maintains the format of the original book and is the single most important user guide and reference for Mathematica--all users of Mathematica will need this edition. Includes 16 pages of full-color graphics. ... Read more

Product Description

Describes most popular computational methods used to solve problems in electromagnetics

Matlab code is included throughout, so that the reader can implement the various techniques discussed

Exercises included

Customer Reviews (1)

Review of "Computational Electromagnetics"
This is an excellent introduction to the field of computational electromagnetics, from a reasonably mathematical perspective - but in a very readable form, well suited to electronic engineers. It's obviously a book on a specialist topic; assuming you want to understand the mathematics behind finite approximations of Maxwell's equations (FEM, FDTD, Mom) - at least at introductory level - this is certainly one of the best to start with. As the authors state, although there are a number of books covering one of these methods in detail, only a couple of others (in particular, those by Sadiku, and myself) -and of course this text - cover all three of these methods. Strongly recommended. ... Read more

Product Description
This completely revised Second Edition of "ComputerGraphics" introduces the mathematics that is the foundation of many oftoday's most advanced computer graphics applications, includingCAD/CAM and geometric modeling. It features thoroughly updated subjectmatter, major organizational changes, and several new topics. Chapterson symmetry, limit and continuity, constructive solid geometry, andthe Bezier curve have been added, with many new figures andexercises. This highly diversified book can be utilized as a primarytextbook, supplemental teaching resource, individual tutorial oron-the-job reference text.New Features includes: New solutionsmanual for instructors; Each chapter contains an annotated suggestedreading list and exercises with answers; Expanded to appeal to bothacademics and professionals through new topicalcoverage. Professionals and students of computer science, engineering,or applied mathematics, as well as non-professional computer graphicshobbyists will find this book useful. ... Read more

Customer Reviews (8)

Good geometry and few computer stuff
This 2nd edition of a 1989 book maintains its mathematic approach with few or no relation to computers. The long title suggests a book with practical examples, but what it contains is pure math. Just to give an idea, the word "pixel" appears just in one page. However, the basics on hypernumbers, introduction on matrix methods, limits, points, lines, CSG spend half of book.

Computer Graphics today is much more than geometry, by the way solved by powerful graphics cards and APIs like OpenGL. Scientific visualization uses intensively colors, transparencies, movements, animation and none of these subjects are even touched. Nowadays mathematics apply also to fog, antialianing, specular, caustics, LOD, transparencies, reflexes, lightning. Unfortunately these math applications aren't tackled in this book. So, don't expect to find computer graphics in this book, as we understand it today. This is still a 1989 book.

If the title was just "Computer Graphics: An Introduction to the Mathematics and Geometry", as in its first edition, it was more related to its content. Unfortunately, just extending the book's title doesn't make it up-to-date.

Don't. No, no, no.
I can't understand the raving reviews. It is weak on math, and has no practical example on CG.
Let me give you an example: Chapter 2 (allegedly on "Matrix Methods"), exercise 2.20 (there are 25): Compute the determinant of the following matrix (I'll use Matlab/Scilab notation): M = [ 2 0; -3 2] Are you serious? What about learning Limits and Continuity in one short chapter? No comments...Seriously, if you don't already know this stuff, should you be looking at CG in the first place?
After I got this book, I got F.S. Hill's Computer graphics Using OpenGL, which is much thicker, mathematically oriented, and has practical examples in C++, and Parberry's and Dunn's 3D Math Primer for Graphics and Game Development which doesn't attempt so much as Hill's and Mortenson's, but has nice code in C++. There might be better options. Not to mention that one has to buy and study real math books.
I give it 1 star as the book falls short of its stated goals of preparing the reader for more advanced study.

Not bad, but not the best
Though the book covers a broad range of mathematics present in the field of computer graphics, I found it lacking in certain respects.The plentiful diagrams and figures greatly assisted comprehension of stated materials, yet I would like to see written proofs of methods used.In addition, such topics as quaternions are only briefly mentioned in historical references.Although this is an excellant mathematics book, I strongly recommend the purchase of Mathematics for 3D Game Programming & Computer Graphics in addition to this title.

great math book (did i really say that!)
if you want to learn the mathematics behind computer graphics buy this book.

it is well written and the explanations are first rate.i'm studying on my own with the book and hardly have need to ask others for any help with understanding topics.

i'm not sure what else to say, except I first tried Mathematics for Computer Graphics and Game Programming and it was pretty horrible compared to this book.

It's cheap, so get it.

Good resource for game developers
This is a good book that is better suited as a reference than a text book. The book seems to be set up with that in mind as the format allows for each concept covered to be easily found. For example, I have taken a course in Linear Algebra. I was still a little shakey about the rotation matricies that are commonly used in game programming. This book brought me up to speed in no time, but if I hadn't taken Linear Algebra, I'm not so sure that I would have fully understood that section. But again, overall this is a great reference to have around! ... Read more

Product Description
Provides an introduction to the fundamental concepts of applied mathematics through the use of realistic physical models. Paper. DLC: Engineering mathematics - Data processing. ... Read more

Product Description
This book is a clear and self-contained introduction to discrete mathematics. Aimed mainly at undergraduate and early graduate students of mathematics and computer science, it is written with the goal of stimulating interest in mathematics and an active, problem-solving approach to the presented material. The reader is led to an understanding of the basic principles and methods of actually doing mathematics (and having fun at that). Being more narrowly focused than many discrete mathematics textbooks and treating selected topics in an unusual depth and from several points of view, the book reflects the conviction of the authors, active and internationally renowned mathematicians, that the most important gain from studying mathematics is the cultivation of clear and logical thinking and habits useful for attacking new problems. More than 400 enclosed exercises with a wide range of difficulty, many of them accompanied by hints for solution, support this approach to teaching. The readers will appreciate the lively and informal style of the text accompanied by more than 200 drawings and diagrams. Specialists in various parts of science with a basic mathematical education wishing to apply discrete mathematics in their field can use the book as a useful source, and even experts in combinatorics may occasionally learn from pointers to research literature or from presentations of recent results. Invitation to Discrete Mathematics should make a delightful reading both for beginners and for mathematical professionals.

The main topics include: elementary counting problems, asymptotic estimates, partially ordered sets, basic graph theory and graph algorithms, finite projective planes, elementary probability and the probabilistic method, generating functions, Ramsey's theorem, and combinatorial applications of linear algebra.General mathematical notions going beyond the high-school level are thoroughly explained in the introductory chapter. An appendix summarizes the undergraduate algebra needed in some of the more advanced sections of the book. ... Read more

Customer Reviews (5)

excellent textbook
"An Invitation to Discrete Mathmatics" is an excellent textbook for college students, advanced high school students, and curious post-grads like myself. The text is engaging and clear, and the content reveals much of the wonderful capabilities of mathematics for a broad variety of sub-disciplines.

Worst Textbook I've Ever Had
I had this textbook in my undergraduate Discrete Math course.I have never written an Amazon review but I feel the need to in this case.The reviews I could find deal with the Czech version and are glowing.The English translation is not useful for those who are trying to learn the material for the first time.

1.The text uses analogies and metaphors that don't seem to be translated to English correctly.
2.It is organized as if the lecture was transcribed directly into this book.It is not organized for reading.
3.Possibly the worst thing about this book is that there are virtually no examples.The authors use formal proofs to explain the material.
4.Often the finial pieces of the proofs are "left as an excersize for the reader" (meaning homework at the end of the chapter).Too make matters worse only "hints" are provided at the back of the book and only for selected excersizes.

This is not a book to learn from, even with a very good lecturer I found that referring to this book for topics that were already explained was pointless.The school (Univ of CT) agreed dropping this text in favor of another after only one semester of its use.

To get through the course I ended up finding "Discrete Mathematics and Its Applications" by Kenneth H. Rosen and I highly recommend it.If you're forced to use "Invitation to Discrete Mathematics" in a course I'd suggest you buy a copy of Rosen's text (even an older edition).

The most witty introduction to discrete mathematics
If you expect to find only dull books on the subject of discrete mathematics then try this one.
When I was a child there were always the most hilarious Czech TV series on Children's television.

One was called Pan Tau. This series was about a bowler hat wearing genius Alphons Urban living under the roof top of his brother's family's house in a Prague suburb. Alphonswas an ordinary human. But he had a double: a small doll named Pan Tau which could, when twisting its hat, turn into a real life Alphons lookalike. Pan Tau, of course had suprahuman abilities, and he could play a lot of tricks to the nuisance of his real life equivalent Alphons, who had always a hard time to keep the existance of his mute supranatural lookalike a secret. In particular Alphons' nice and nephew were always amazed by their uncle's "practicality"...... .
Professors Matousek's and Nesetril's book is like Pan Tau --it always finds the right answer to otherwise intractable (mathematical) problems. Discrete mathematics can be extremely tough at times, but with Pan Tau's little genius incorporated into this book, suddenly Discrete Mathematics turns out to be extremely funny.Anyway, there is nothing but praise to spare for this most brilliant and witty book guiding the reader through the pitfalls of mathematics rendering her/him, like myself, a proficient connoisseur of discrete math.

A witty introduction to discrete mathematics
If you expect to find only dull books on the subject of discrete mathematics then try this one.
When I was a child there were always the most hilarious Czech TV series on Children's television.

One was called Pan Tau. This series was about a bowler hat wearing genius living under the roof top of his brother's family's house. Pan Tauwas an ordinary human. But he had a double: a small doll which could, when twisting its hat, turn into a real life Pan Tau lookalike. Pan Tau two, of course had suprahuman abilities, and he could play a lot of tricks to the nuisance of his real life equivalent, who had always a hard time to keep the existance of his mute supranatural lookalike a secret. In particular Pan Tau's nice and nephew were always amazed by their uncle's "practicality"...... .
Professor Matousek and Professor Nesetril's book is like Pan Tau's double -- as it always finds the right answer to otherwise intractable situations. Discrete mathematics can be extremely tough at times, but with Pan Tau's double's little genius incorporated in this book suddenly Discrete Mathematics turns out to be extremely funny.Anyway there is nothing but praise to spare for this most brilliant book guiding the reader through the pitfalls of mathematics rendering her/him, like myself, a proficient connoisseur of discrete math.

Excellent book (at least in Czech version)
This is one of the best books introducing to mathematics I've ever seen. It is fun to read and solve excercises. Contains beutifull and surprising results in combinatorics and graph teory but still don't require anymathmatical background. I've even used it as textbook for highschool. Butstill not as good as to see Nesetril lessons personally. ... Read more

Product Description
Advances in fields such as bioengineering, industrial engineering, and robotic design now require engineers to have a sound background in statistical methods to optimize performance and minimize error in problem-solving applications. By joining statistical analysis with computer-based numerical methods, this book bridges the gap between theory and practice with software-based examples, flow charts, and applications. Designed for engineering students as well as practicing engineers and scientists, the book has numerous examples with in-text solutions. In terms of content, it covers the sequence of mathematical topics needed by the majority of university courses, including calculus, error-handling, and ODEs; in addition, the book covers statistical computation and testing of hypothesis usually omitted from numerical methods texts. Using flow charts and computer programs, the authors demonstrate how the mathematical concepts will be implemented in practical applications such as circuits, signal processing, and more. A CD-ROM with the source code for the in-text computer programs includes calculation routines and simulations. ... Read more

Customer Reviews (1)

It's an excellent technical manual not to be missed.
College-level computer collections and specialty computer libraries will appreciate the technical detail and depth in Computer-Based Numerical & Statistical Techniques, a survey applicable not just to computer libraries but to libraries strong in industrial engineering, math, and science. This joins statistical analysis with computer-based numerical models and offers software-based examples and solutions, covering a range of math topics needed by the majority of university courses in calculus and ODEs. It's an excellent technical manual not to be missed. ... Read more

Product Description
Information usually comes in pieces, from different sources. It refers to different, but related questions. Therefore information needs to be aggregated and focused onto the relevant questions. Considering combination and focusing of information as the relevant operations leads to a generic algebraic structure for information. This book introduces and studies information from this algebraic point of view. Algebras of information provide the necessary abstract framework for generic inference procedures. They allow the application of these procedures to a large variety of different formalisms for representing information. At the same time they permit a generic study of conditional independence, a property considered as fundamental for knowledge presentation. Information algebras provide a natural framework to define and study uncertain information. Uncertain information is represented by random variables that naturally form information algebras. This theory also relates to probabilistic assumption-based reasoning in information systems and is the basis for the belief functions in the Dempster-Shafer theory of evidence. ... Read more

Product Description
A unique probability guide for computer science

While many computer science curricula include only an introductory course on general probability, there is a recognized need for further study of this mathematical discipline within the specific context of computer science. Probability and Statistics for Computer Science develops introductory topics in probability with this particular emphasis, providing computer science students with an invaluable resource in their continued studies and professional research.

James Johnson's text begins with the basic definitions of probability distributions and random variables and then elaborates their properties and applications. Probability and Statistics for Computer Science treats the most common discrete and continuous distributions, showing how they find use in decision and estimation problems, and constructs computer algorithms for generating observations from the various distributions. This one-of-a-kind resource also:

• Includes a thorough and rigorous development of all the necessary supporting mathematics

• Provides an opportunity to reconnect applications with the theoretical concepts of distributions introduced in prerequisite courses

• Gathers supporting topics in an appendix: set theory, limit processes, real number structure, Riemann-Stieltjes integrals, matrix transformation, and determinants

• Uses computer science examples such as client-server performance evaluation and image processing

The author also addresses a variety of supporting topics, such as estimation arguments with limits, properties of power series, and Markov processes. Johnson's text proves an ideal resource for computer science students and practitioners interested in a probability study specific to their field. ... Read more

Customer Reviews (2)

Excellent................
Undoubtedly, it is an excellent and remarkable well organized book. Every chapter contains all needed definitions and formulas, deep discussions of their meanings, proofs, and examples. I strongly recommend this book for every one who want to understand probability and statistics in depth.

Excellent
This text is not just for computer science majors; the applications are simply computer science applications.Instead of placing balls in urns and using dice to present basic examples, it uses very basic topics from computer science to exemplify the theory in such a way that any mathematically inclined reader could fully understand.All the mathematics are explained clearly and with full precision in the appendices and in supplementary modules, which is novel in my opinion.This book is truly rigorous at an introductory level, and completely bridges the gap between intuitive introductory texts and more rigorous graduate texts.However, even the intuition is there in this book; it really has everything.Bravo to this author for writing a truly fine book that is really needed in this area.If you really want to learn probability theory, then buy this book.The writing is of unusually high quality, and the technical presentation is very good and fresh in terms of what's on the market.You will understand the concepts, the theory, and how to prove everything from scratch by reading this book.Johson walks you through everything step by step in precise, clear detail. ... Read more

Product Description
Susanna Epp's Discrete Mathematics with Applications, Second Edition provides a clear introduction to discrete mathematics.Epp has always been recognized for her lucid, accessible prose that explains complex, abstract concepts with clarity and precision.This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought.The text is suitable for many course structures, including one-semester or full-year classes.Its emphasis on reasoning provides strong preparation for computer science or more advanced mathematics courses. ... Read more

Customer Reviews (37)

Discreet?
First I must say;I HATE DISCREET MATH, but with this book, I was able to muddle through even though the professor never even used one page from it after he recommended buying it.

a good introductory college level text book
I got this book to supplement the course book required for my class. This one has about as much text, but covers fewer things. It is very clear and precise, with lots of examples.

Utterly Pointless
This book doesnt seem to have any head or tail. Half the time I wonder what exactly Im supposed to do, and WHY I should be doing it. The author does not properly impress upon the reader the reasons why each subtopic might be important, so you come away with the idea that "well, we're doing it this way because some mathematician did it this way in the past".

Unfortunately, I suspect this is the case with most, if not all books dealing with discrete math.

(Note: This is from a Computer Science Major, maybe math majors have a different view).

This is when I fell in love with Math.
This book is well written, it contains good examples, and excellent exposition. This was my introduction to mathematical proofs, and after studying it well, I was able to approach more advanced courses, such as advanced calculus and modern algebra with a clear view of how to approach problems where a mathematical proof is needed. I highly recommend this book to undergraduate math majors.

Nice and Clear
I honestly can't see how you'd make a book explaining such topics as prime numbers and set theory any clearer than this one.I consider this to be a high quality book.It's easy to understand and reference.Its one drawback is that it covers only a limited number of topics, and none of them are heavy duty.If I found a book that explained graduate level math as well as this one explains undergraduate math, I'd consider it to be gold. ... Read more

Product Description
Designed for those people who want to gain a practical knowledge of modern techniques, this book contains all the material necessary for a course on the numerical solution of differential equations. Written by two of the field's leading authorities, it provides a unified presentation of initial value and boundary value problems in ODEs as well as differential-algebraic equations. The approach is aimed at a thorough understanding of the issues and methods for practical computation while avoiding an extensive theorem-proof type of exposition. It also addresses reasons why existing software succeeds or fails. This is a practical and mathematically well informed introduction that emphasizes basic methods and theory, issues in the use and development of mathematical software, and examples from scientific engineering applications. Topics requiring an extensive amount of mathematical development are introduced, motivated, and included in the exercises, but a complete and rigorous mathematical presentation is referenced rather than included. ... Read more

Customer Reviews (1)

Its a handbook for numerical solutions of ODE & DAE.
This book is excellent.The concepts about stiff, initial value problems, boundary value problems and differential-Algebraic equations (DAE) is treated with relative deep.

The numerical methods for many cases is covered.

The bad is that don't show the code.The code is in a web (NETLIB) and is writed in Fortran Language.

Is very expensive! ... Read more

Product Description

Visualisation and Processing of Tensor Fields provides researchers an inspirational look at how to process and visualize complicated 2D and 3D images known as tensor fields. Tensor fields are the natural representation for many physical quantities; they can describe how water moves around in the brain, how gravity varies around the earth, or how materials are stressed and deformed. With its numerous color figures, this book helps the reader understand both the underlying mathematics and the applications of tensor fields. The reader also will learn about the most recent research topics and open research questions.

Product Description
Image processing problems are often not well defined because real images are contaminated with noise and other uncertain factors. In Mathematics of Shape Description, the authors take a mathematical approach to address these problems using the morphological and set-theoretic approach to image processing and computer graphics by presenting a simple shape model using two basic shape operators called Minkowski addition and decomposition.

This book is ideal for professional researchers and engineers in Information Processing, Image Measurement, Shape Description, Shape Representation and Computer Graphics. Post-graduate and advanced undergraduate students in pure and applied mathematics, computer sciences, robotics and engineering will also benefit from this book.

 Key Features

• Explains the fundamental and advanced relationships between algebraic system and shape description through the set-theoretic approach
• Promotes interaction of image processing geochronology and mathematics in the field of algebraic geometry
• Provides a shape description scheme that is a notational system for the shape of objects
• Offers a thorough and detailed discussion on the mathematical characteristics and significance of the Minkowski operators

... Read more