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21. Computer Graphics through Key
22. The Definitive Guide to How Computers
23. Mathematics for Computer Algebra
24. The Limits of Mathematics: A Course
25. Discrete Mathematics in the Schools
26. Combinatorial Methods with Computer
27. Computer Image Processing and
28. Discrete Mathematics Using a Computer
29. Introduction to Combinatorial
30. Mathematical Structures for Computer
31. Computer Mathematics With Pascal
32. Applied Geometry for Computer
33. The Computer as Crucible: An Introduction
34. Turtle Geometry: The Computer
35. A Beginner's Guide to Discrete
36. Comprehensive Mathematics for
37. Elements of Discrete Mathematics
38. A First Course in Discrete Mathematics
39. Introductory Discrete Mathematics
40. Theoretical Computer Science:

21. Computer Graphics through Key Mathematics
by Huw Jones
Paperback: 357 Pages (2001-05-18)
list price: US$99.00 -- used & new: US$69.99
(price subject to change: see help)
Asin: 1852334223
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Editorial Review

Product Description
This book introduces readers to the mathematics that support computer graphics. The book is written in a clear, easy-to-understand way and is aimed at all those who have missed out on an extended mathematical education but who are studying or working in areas where computer graphics or 3D design plays an vital part. All those who have no formal training but who want to understand the foundations of computer graphics systems should read this book. ... Read more

22. The Definitive Guide to How Computers Do Math : Featuring the Virtual DIY Calculator
by Clive Maxfield, Alvin Brown
Paperback: 464 Pages (2005-09-27)
list price: US$41.95 -- used & new: US$22.00
(price subject to change: see help)
Asin: 0471732788
Average Customer Review: 5.0 out of 5 stars
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Editorial Review

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The Basics of Computer Arithmetic Made Enjoyable and Accessible-with a Special Program Included for Hands-on Learning

"The combination of this book and its associated virtual computer is fantastic! Experience over the last fifty years has shown me that there's only one way to truly understand how computers work; and that is to learn one computer and its instruction set-no matter how simple or primitive-from the ground up. Once you fully comprehend how that simple computer functions, you can easily extrapolate to more complex machines."
-Fred Hudson, retired engineer/scientist

"This book-along with the virtual DIY Calculator-is an incredibly useful teaching and learning tool. The interesting trivia nuggets keep you turning the pages to see what's next. Students will have so much fun reading the text and performing the labs that they won't even realize they are learning."
-Michael Haghighi, Chairperson of the Business and Computer Information Systems Division, Calhoun Community College, Alabama

"At last, a book that presents an innovative approach to the teaching of computer architecture. Written with authority and verve, witty, superbly illustrated, and enhanced with many laboratory exercises, this book is a must for students and teachers alike."
-Dr. Albert Koelmans, Lecturer in Computer Engineering, University of Newcastle upon Tyne, UK, and the 2003 recipient of the EASIT-Eng. Gold Award for Innovative Teaching in Computer Engineering

Packed with nuggets of information and tidbits of trivia, How Computers Do Math provides an incredibly fun and interesting introduction to the way in which computers perform their magic in general and math in particular. The accompanying CD-ROM contains a virtual computer/calculator called the DIY Calculator, and the book's step-by-step interactive laboratories guide you in the creation of a simple program to run on your DIY Calculator.

How Computers Do Math can be enjoyed by non-technical individuals; students of computer science, electronics engineering, and mathematics; and even practicing engineers. All of the illustrations and interactive laboratories featured in the book are provided on the CD-ROM for use by high school, college, and university educators as lecture notes and handouts.

For online resources and more information please visit the author's website at www.DIYCalculator.com.

  ... Read more

Customer Reviews (11)

5-0 out of 5 stars Amazing book
It is a pity that one can give only 5 stars! This book deserves more!
I have always been intrigued by the inner workings of a computer or calculator.
Even tried to study some assembly, but never succeeded to fully comprehend it.
The front cover may suggest it is going to be nothing than fun, like in some 'for dummies' books. (Although these books have there use.)
No, this is serious business here, but explained in a not overdone fun style, and explained in such a way even I can finally understand the subject.
It also contains many practical labs(with the DIY calculator) which enhance your knowledge in no time.
This is a great book to have!

5-0 out of 5 stars Disruptively good
I got this for my 13-year-old niece.She brought it to school and the other kids were fighting over who got to read it - while someone was giving a class presentation.I was pleased.

5-0 out of 5 stars Excellent View into How Computer Really Do Math
The Definitive Guide to How Computers Do Math : Featuring the Virtual DIY Calculator provides an excellent view into how computers _really_ perform math.While not a complete introduction to the subject (I would recommend learning a bit about Boolean logic and digital circuitry before starting here), it does offer a complete, thorough, and thoroughly fun journey to creating your own "working" computer.Along the way, you will learn the fun and fundamental details behind the mystery and magic of computers.

I've used the material (the book's CD-ROM includes bonus material) to teach computer architecture classes to students as young and middle-school.I've also used this book as a prize to up-and-coming computer science or electrical engineering students in the local elementary and middle-school science fair.

The author, Clive ("Max") Maxfield, has an engaging and entertaining style. You will likely enjoy his other books including Bebop to the Boolean Boogie, Third Edition: An Unconventional Guide to Electronics, which I also highly recommend.

4-0 out of 5 stars Go Figure
This is an accurate, first-order of detail on how computers work. The CD is a nice bonus. I would recommend this text for high schoolers and above.

5-0 out of 5 stars Once again Cive does it!
I am a hobbyist and have found this book invaluable. I have a Computer Science background and so have no problems with the concepts. Even if you do have problems with the concepts, the Labs are a walk-through
and one can then kind of 'get it'.

Very satisfied and having fun! ... Read more

23. Mathematics for Computer Algebra
by Maurice Mignotte
 Hardcover: 346 Pages (1991-11-25)
list price: US$69.95 -- used & new: US$72.94
(price subject to change: see help)
Asin: 0387976752
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24. The Limits of Mathematics: A Course on Information Theory and the Limits of Formal Reasoning (Discrete Mathematics and Theoretical Computer Science)
by Gregory J. Chaitin
Hardcover: 168 Pages (2002-10-28)
list price: US$89.95 -- used & new: US$59.96
(price subject to change: see help)
Asin: 1852336684
Average Customer Review: 2.0 out of 5 stars
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Editorial Review

Product Description
This book is the final version of a course on algorithmic information theory and the epistemology of mathematics and physics. It discusses Einstein and Goedel's views on the nature of mathematics in the light of information theory, and sustains the thesis that mathematics is quasi-empirical. There is a foreword by Cris Calude of the University of Auckland, and supplementary material is available at the author's web site. The special feature of this book is that it presents a new "hands on" didatic approach using LISP and Mathematica software. The reader will be able to derive an understanding of the close relationship between mathematics and physics. "The Limits of Mathematics is a very personal and idiosyncratic account of Greg Chaitin's entire career in developing algorithmic information theory. The combination of the edited transcripts of his three introductory lectures maintains all the energy and content of the oral presentations, while the material on AIT itself gives a full explanation of how to implement Greg's ideas on real computers for those who want to try their hand at furthering the theory." ... Read more

Customer Reviews (1)

2-0 out of 5 stars A subjective estimation
I wish that I could give this book a higher rating than I have, for the subject matter is one that I find of enormous intrinsic interest. Moreover, Dr. Chaitin is one of the most important contributors to this field of the last 30+ years.

My reasons for being disappointed in this book may well be the reasons others enthusiastically endorse it. Dr. Chaitin himself, in his preface, places this volume as the one thing he would most wish to save were a disaster to wipe out the rest of his oeuvre.

The sub-title of the book is "A Course on Information Theory and the Limits of Formal Reasoning." This sub-heading I find to be quite misleading. The book is not a "course" on any thing -- rather, it is a collection of a very small number of informal papers that Dr. Chaitin has given in recent years, and a very large number of pages devoted to LISP programs that can be used to demonstrate aspects of his extensions to the results of Turing and Goedel. The collection of articles seem largely redundant to me; any one of the articles by itself would be sufficient to summarize the rest of the book's contents. As for the programming, that should either have been provided in the form of a CD-ROM (as only someone of a genuinely "special" nature would actually sit down and manually type in all those instructions) or a functioning URL (such URL's as do appear in the book do not seem to be working as of this writing, Mar. 2007).

I was hoping to get something more comprehenive, and that could function as a stand-alone text. This book seems to be neither. The technical details are all to be found elsewhere, and the functional aspects that might translate into an actual course of study are simply not to be found at all. Dr. Chaitin notes that the original technical work of his, published in the 60's, had a formal error that has since been corrected. Quite frankly, I would rather have that work plus a footnote regarding the later developments, than this volume which (sadly) I find of no real help. (I have since ordered and received a used, 1987 imprint of his "Algorithmic Information Theory" as printed by Cambridge.)

Alternatively, and perhaps more importantly, I would very much liked to have seen this "course" developed as a *COURSE*, rather than as three more or less popular, and largely independent, lectures. These lectures seem, at best, only to minimally build upon one another. A more integrated and coherent work that developed its subject in a step-wise manner, rather than repeating itself with only slightly different glosses, is something that I would have liked much more.

My background in logic and computer science, while not trivial, remains that of a studious and committed autodidact. It is possible that someone with less of a background in topics of formal reasoning than myself would find this book of enormous value. For me, however, it lacked both the technical details to make it a worthy struggle, and the pedagogical depth to make it of significant value. ... Read more

25. Discrete Mathematics in the Schools (Series in Discrete Mathematics & Theoretical Computer Science)
by Joseph G. Rosenstein, Deborah S. Franzblau, and Fred S. Roberts
Paperback: 452 Pages (2000-01-31)
list price: US$36.00 -- used & new: US$35.95
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Asin: 0821811371
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Editorial Review

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This volume is a collection of articles written by experienced primary, secondary, and collegiate educators. The book explains why discrete mathematics should be taught in K--12 classrooms and offers practical guidance on how to do so.

In this book, teachers at all levels will find a great deal of valuable material to help them introduce discrete mathematics in their classrooms. One main article provides a comprehensive and detailed view of discrete mathematics for K--12. Another surveys the resources that are available for teachers. School and district curriculum leaders will find material that addresses how discrete mathematics can be introduced into their curricula. College faculty members will find ideas and topics that can be incorporated into a variety of courses.


Classroom activities and an annotated list of resources.

Authors who are directors of innovative programs and who are well known for their work.

A description of discrete mathematics providing the opportunity for a fresh start for students who have been previously unsuccessful in mathematics.

Discussion on discrete mathematics as it is used to achieve the goals of the current effort to improve mathematics education.

Guidance on topics, resources and teaching; a valuable guide for both pre-service and in-service professional development. ... Read more

26. Combinatorial Methods with Computer Applications (Discrete Mathematics and Its Applications)
by Jonathan L. Gross
Hardcover: 664 Pages (2007-11-16)
list price: US$99.95 -- used & new: US$59.00
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Asin: 1584887435
Average Customer Review: 4.5 out of 5 stars
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Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinatorial methods course or in a combined graph theory and combinatorics course.

After an introduction to combinatorics, the book explores six systematic approaches within a comprehensive framework: sequences, solving recurrences, evaluating summation expressions, binomial coefficients, partitions and permutations, and integer methods. The author then focuses on graph theory, covering topics such as trees, isomorphism, automorphism, planarity, coloring, and network flows. The final chapters discuss automorphism groups in algebraic counting methods and describe combinatorial designs, including Latin squares, block designs, projective planes, and affine planes. In addition, the appendix supplies background material on relations, functions, algebraic systems, finite fields, and vector spaces.

Paving the way for students to understand and perform combinatorial calculations, this accessible text presents the discrete methods necessary for applications to algorithmic analysis, performance evaluation, and statistics as well as for the solution of combinatorial problems in engineering and the social sciences. ... Read more

Customer Reviews (2)

4-0 out of 5 stars generally good book on discrete mathematics
This is, on the whole, a generally good book on discrete mathematics- strong on graphs (the author's specialty) and networks, not so comprehensive on combinatorics. The eclectic mix of topics covered - permutations, recurrences, generating functions, graphs, networks, finite geometries, etc - tend to make the book disjointed and unfocused at times. The reader will be better served by studying the topics individually in greater depth. A possible reading list would be: Combinatorial Problems and Exercises by Lovasz, generatingfunctionology by Wilf and, yes, Gross's very own Graph Theory and Its Applications.

5-0 out of 5 stars Combinatorics
Good book overall. Easy to read and informative. Good at teaching you how to solve problems. Example problems are sometimes only the easiest problems, and extending the method to harder problems is not always trivially apparent. Also sometimes skips somewhat important steps in solving example problems. ... Read more

27. Computer Image Processing and Recognition (Computer Science and Applied Mathematics)
by Ernest L. Hall
 Hardcover: 601 Pages (1980-09)
list price: US$59.95 -- used & new: US$15.00
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Asin: 0123188504
Average Customer Review: 4.0 out of 5 stars
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Customer Reviews (1)

4-0 out of 5 stars Good overview of image processing and recognition.
I thought that this book was very readable and a good introduction to the field of Image Processing and Recognition.I am hoping that this authorcontinues to publish in the future! For those currently in this field, thisbook is an excellent way to discover the roots of this kind of technology. ... Read more

28. Discrete Mathematics Using a Computer
by John O'Donnell, Cordelia Hall, Rex Page
Paperback: 441 Pages (2006-07-10)
list price: US$64.95 -- used & new: US$43.65
(price subject to change: see help)
Asin: 1846282411
Average Customer Review: 3.0 out of 5 stars
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Editorial Review

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Discrete Mathematics Using a Computer offers a new, "hands-on" approach to teaching Discrete Mathematics. Using software that is freely available on Mac, PC and Unix platforms, the functional language Haskell allows students to experiment with mathematical notations and concepts -- a practical approach that provides students with instant feedback and allows lecturers to monitor progress easily.

This second edition of the successful textbook contains significant additional material on the applications of formal methods to practical programming problems. There are more examples of induction proofs on small programs, as well as a new chapter showing how a mathematical approach can be used to motivate AVL trees, an important and complex data structure.

Designed for 1st and 2nd year undergraduate students, the book is also well suited for self-study. No prior knowledge of functional programming is required; everything the student needs is either provided or can be picked up easily as they go along.

Key features include:

  • Numerous exercises and examples
  • A web page with software tools and additional practice problems, solutions, and explanations, as well as course slides
  • Suggestions for further reading

Complete with an accompanying instructor's guide, available via the web, this volume is intended as the primary teaching text for Discrete Mathematics courses, but will also provide useful reading for Conversion Masters and Formal Methods courses.

Visit the book’s Web page at: http://www.dcs.gla.ac.uk/~jtod/discrete-mathematics/

... Read more

Customer Reviews (2)

5-0 out of 5 stars From maths to software: elegant and clever
Discrete Mathematics Using a Computer is the best book I have seen so far when studying how to use the elegance of discrete mathematics (for example: list comprehension, recursion, sets, relations, trees) in programming. The book is exceptional in showing how you can transform mathematical thoughts into the functional programming language HASKELL without loosing the expressiveness of the mathematical formulation. The book shows how to write two- ore three-liners of compact, readable code that implements algorithms (like tree traversal) that usually takes at least a page or two of ugly "for-if-loop-code" in languages like C++ or Java. There are chapters on important applications of the proposed concepts for the design of digital circuits and for
AVL Trees. The text clearly shows the strengths of functional programming compared to imperative programming (Java, C, ...) for many programming tasks and it helps the programmer to better choose his tools.
Finally, the book contains clever and helpfull exercises with many answers. The book has a website providing dedicated code (HASKELL) for theexamples.

1-0 out of 5 stars Pitiful excuse for a textbook
This book purports to be a college text for discrete math.It is terrible.There aren't nearly enough examples in the book.Explanations are woefully brief, giving one sentence to the definition of a set intersection, for example.Many new concepts sneak up on you without ever being discussed.In one instance it started using a point by point proof method without ever introducing that method.The rules given in some proofs are not defined earlier, leaving the reader to wonder what the authors are doing in their proof.The use of Haskel is another downside.There is no way to check your proofs aside from the proof checker software included which will drive a person to complete insanity.The software is so terribly picky in its syntax, you take more time verifying your proof than actually coming up with it.When there are errors with your syntax, it doesn't give a meaningful message.This is more the fault of Haskel, however.Nevertheless, it is the fault of the authors to choose this terrible method for teaching.Garbage. ... Read more

29. Introduction to Combinatorial Mathematics (Computer Science Series)
by Chung L. Liu
 Hardcover: 393 Pages (1968-06)
list price: US$108.65 -- used & new: US$188.08
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Asin: 0070381240
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30. Mathematical Structures for Computer Science
by Judith L. Gersting
Hardcover: 784 Pages (2006-07-07)
-- used & new: US$49.99
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Asin: 071676864X
Average Customer Review: 3.0 out of 5 stars
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Editorial Review

Product Description

Computing Curricula 2001 (CC2001), a joint undertaking of the Institute for Electrical and Electronic Engineers/Computer Society (IEEE/CS) and the Association for Computing Machinery (ACM), identifies the essential material for an undergraduate degree in computer science.

This Sixth Edition of Mathematical Structures for Computer Science covers all the topics in the CC2001 suggested curriculum for a one-semester intensive discrete structures course, and virtually everything suggested for a two-semester version of a discrete structures course. Gersting's text binds together what otherwise appears to be a collection of disjointed topics by emphasizing the following themes:
• Importance of logical thinking
• Power of mathematical notation
• Usefulness of abstractions
... Read more

Customer Reviews (24)

5-0 out of 5 stars Good for the class I took
Used this book mostly for homework. The class I had it for was pretty easy, so I didn't need it much for reference. However, when the occasional confusion surfaced in class, I could immediately gostraight to the book and sort out what was going on. Explains things very clearly with good examples.

1-0 out of 5 stars Horrible
I suffered through the first few weeks of my Discrete Mathematics course, and got my first C on an assignment EVER.This immediately sent up red flags.I was struggling to understand the concepts as presented in this book, despite that I have had no problem understanding Algebra, Trgonometry and Calculus.On a hunch that the book might be bad, I checked Amazon, and now you are seeing what I saw: low ratings!

I ordered Susanna Epp's book, and for the remainder of the course I read her coverage of a topic, and used this book only for the class-assigned homework problems.My grades are back to A's.So, it wasn't just me.It was this horrible book.The author just doesn't communicate the topics in a way that can be understood by those new to the subject.There are many cases of terms used without being defined, and concepts being refered to that have not yet been introduced (in other words, out-of-order presentation of topics).Worse than this, the step-by-step examples tend to use only the simplest cases, yet more difficult cases appear in the chapter exercises.In most of the text, the concept is explained, and then the student is asked to apply it (as an exercise) without an example, and expected to flip to the back of the book if they need to see the solution.

If you are stuck with this as I required textbook, I pity you.Get Susanna Epp's book (Or Rosen's) if you'd like to actually learn the topic.

3-0 out of 5 stars OK but not great
I used this book for an undergraduate course in Discrete Mathematics. I'd say that the book tended to confuse more than clarify, at least in its initial explanation of things. Working through the example problems often helped correct that, though. My professor thought the author was pretty ambitious to be aimed at undergrads and ended up skipping most of the material on Turing machines; he also skipped the material on Probability because our computer science students must take a Prob & Stats course; otherwise, he stuck very closely to the book.

I felt the book was structured well in that new chapters often built upon previous ones. The chapters on Formal Logic and Proof Techniques were long and detailed, but have since helped with my programming assignments. The chapters on Sets, Relations, Graphs, Trees, and Algorithms were the most valuable since they directly relate to my courses in Databases and Analysis of Algorithms.

The book helped but I feel that my professor is what really made it work for me. The book isn't bad, but it's not great either; if anything, it's "alright."

5-0 out of 5 stars Fast Delivery As Described
Although Amazon's shipment estimator gave me a 3-week estimate, the product arrived at my house within five days of payment.The book was in the condition described; no marks inside, binding intact & firm, and ready to be sold again after I finish using it.It was a good decision to buy this book from the seller rather than paying 3x the price to buy it used at my University's bookstore!

3-0 out of 5 stars Needs better explanations
This book definitely needs a teacher who thoroughly understands the material.Should not be used as a self teaching tool.Instead of every other exercise question having an answer in the back of the book, only a few starred ones are available in each section.Also, each lesson and practice problems don't cover all the areas in the exercises.There will be some exercises for which there are no examples in the book, including symbology not explained in the book. ... Read more

31. Computer Mathematics With Pascal Programming
by Donald D. Spencer
 Paperback: 336 Pages (1996-03)
list price: US$24.95
Isbn: 0892182512
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32. Applied Geometry for Computer Graphics and CAD (Springer Undergraduate Mathematics Series)
by Duncan Marsh
Paperback: 352 Pages (2004-11-05)
list price: US$39.95 -- used & new: US$23.56
(price subject to change: see help)
Asin: 1852338016
Average Customer Review: 4.0 out of 5 stars
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Focussing on the manipulation and representation of geometrical objects, this book explores the application of geometry to computer graphics and computer-aided design (CAD).

New features in this revised and updated edition include: the application of quaternions to computer graphics animation and orientation; discussions of the main geometric CAD surface operations and constructions: extruded, rotated and swept surfaces; offset surfaces; thickening and shelling; and skin and loft surfaces; an introduction to rendering methods in computer graphics and CAD: colour, illumination models, shading algorithms, silhouettes and shadows.

Over 300 exercises are included, many of which encourage the reader to implement the techniques and algorithms discussed through the use of a computer package with graphing and computer algebra capabilities. A dedicated website also offers further resources and links to other useful websites.

... Read more

Customer Reviews (1)

4-0 out of 5 stars Good computer graphics text
This text has a novel approach to entry level computer graphics using homogeneous coordinates entirely.I struggled a bit with the use of these representations in perspective transformations.However once I got it I found the derivations and formulas to be easy to get and easy to use. The book has an extensive set of exercises with complete answers.I deducted one star because the theoretical aspects of homogeneous transformations could use expansion and simplification. ... Read more

33. The Computer as Crucible: An Introduction to Experimental Mathematics
by Jonathan Borwein, Keith Devlin
Paperback: 200 Pages (2008-11-24)
list price: US$29.95 -- used & new: US$23.79
(price subject to change: see help)
Asin: 1568813430
Average Customer Review: 5.0 out of 5 stars
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Keith Devlin and Jonathan Borwein, two well-known mathematicians with expertise in different mathematical specialties but with a common interest in experimentation in mathematics, have joined forces to create this introduction to experimental mathematics. They cover a variety of topics and examples to give the reader a good sense of the current state of play in the rapidly growing new field of experimental mathematics. The writing is clear and the explanations are enhanced by relevant historical facts and stories of mathematicians and their encounters with the field over time. ... Read more

Customer Reviews (1)

5-0 out of 5 stars A lovely little book which builds a strong case for experimental mathematics
Jonathan Borwein and Keith Devlin are well-known mathematicians who have a strong appreciation of, and expertise in, experimental mathematics. In this book they provide us with a concise, inviting introduction to the field.

The first chapter tries to succinctly explain what experimental mathematics is and why it's a fundamental tool for the modern mathematician. The following is their definition:

"Experimental mathematics is the use of a computer to run computations--sometimes no more than trial-and-error tests--to look for patterns, to identify particular numbers and sequences, to gather evidence in support of specific mathematical assertions that may themselves arise by computational means, including search. Like contemporary chemists--and before them the alchemists of old--who mix various substances together in a crucible and heat them to a high temperature to see what happens, today's experimental mathematician puts a hopefully potent mix of numbers, formulas, and algorithms into a computer in the hope that something of interest emerges."

They immediately address some of the possible objections and illustrate how an approach that doesn't focus on formal proof, but rather on exploration and experimentation, ultimately leads to hypotheses which can then be, in many cases, proved analytically. The authors argue that in this sense, thanks to the aid of advanced computers, mathematics is becoming more and more similar to other natural sciences.

They also make a case for how great mathematicians like Euler, Gauss, and Reimann were doing experimental mathematics well before calculators where available. Their calculations on paper were far more limited than what computers afford us these days, yet they served them well when it came to sharpening and verifying their intuitions.

The rest of the book is a continuous series of examples that show the advantages of this approach in practice. The examples are highly interesting (some of them stunning) and tend to focus on calculus, analysis and analytical number theory. Each chapter is accompanied by a section called "Explorations". I found this section to be particularly valuable. Within it you'll find exercises, and further examples and considerations. The answers/solutions to the actual problems are provided in the second to last chapter, just before the brief epilogue.

Chapter 2 discusses how to calculate an arbitrary digit for irrational numbers like pi, in certain bases. They illustrate how the so called BBP Formula (Bailey-Borwein-Plouffe formula, co-discovered by Jonathan Borwein's brother) came to be. The use of a program which implements the PSQL integer relation algorithm in high-precision, floating-point arithmetic was key to its discovery. The BBP Formula in turn allowed the calculation of the quadrillionth binary digit of pi back in 2000.

Chapter 3 focuses on identifying numbers, digits patterns, and sequences once you obtain a numeric result through your calculations and experimentation. They introduce the subject with relatively obvious values like the approximations of e - 2 or pi + e/2, but the chapter quickly escalates to an example where a closed form for a seemingly random sequence needs to be found.

Chapter 4 analyzes the Reimann Zeta function from the eyes of an experimental mathematician, and shows us what kind of insight we can gain from this unique perspective.

In chapter 5 we learn how by numerically evaluating definite integrals, it is sometimes possible to identify the resulting value which will help us to analytically resolve those particular integrals. The examples presented in this chapter originate for the most part from physics and are very challenging if attempted without the aid of experimental methods. The explorations section provides a few more interesting integrals, including some for which a closed form is not known. The authors even include an integral that intentionally stumps Mathematica 6 and Maple 11.

Chapter 6 is dedicated to serendipitous discoveries ("proof by serendipity") with a few interesting examples of how "luck" met preparation, ultimately enriching the body of mathematical knowledge almost by chance.

In chapter 7 the authors go back to talk about pi, this time in base 10, to calculate its digits with efficient, fast converging formulas and methods. The chapter wraps up with a discussion about the normality of pi, which hasn't been proven of course, but appears to be empirically supported by the statistical analysis of the first trillion digits. In the explorations section there is a nice discussion about the implementation of fast arithmetic through the Karatsuba multiplication, and the subject of Montecarlo simulations (a very inefficient method of calculating pi, but a great way to show the idea behind Montecarlo simulations).

Chapter 8 has a bold title, "The computer knows more math than you do". This provocative title is quickly diminished to put it in context though. The authors start by approaching a tough problem posed by Donald Knuth (of TeX and Art of Computer Programming fame) to the readers of the American Mathematical Monthly. In an attempt to solve this the authors invite us to go on a journey involving the Lambert W function, the Pochhammer function, and Abel's limit theorem. The rest of the chapter illustrates another difficult problem whose solution obtained through the aid of Maple has important implications not only for mathematics, but also for quantum field theory and statistical mechanics.

In chapter 9 a few infinite series are calculated in order to show how CAS systems and experimental methodology can still be useful when dealing with problems that involve infinite sequences, series, and products.

Chapter 10 is dedicated to the limits and the dangers of this approach. Several examples showcase how one can be misled into making assumptions, and how to avoid this from happening.

In chapter 11, conscious of the selective focus on analysis and analytical number theory throughout the book, Borwein and Devlin introduce other examples such as a topology problem whose proof was reached thanks to a deeper insight gained through computer visualization of a surface, a knot theory problem, the Four Color Theorem, the Robbins Conjecture, the computation of E_8, and so on. In truth, I feel that such a thin book could have used more examples like the ones in chapter 11, in order to make a stronger case for the applicability of experimental mathematics to areas outside of analysis.

The book is well written and the tone is never heavy, despite the advanced mathematical examples within it. The authors include historical background and anecdotes which makes for a more interesting read and provides a human perspective behind the formulas presented. The (at times) funny illustrations and occasional jokes are definitely a pleasant addition.

This book is relatively tool agnostic; Maple and Mathematica are referenced throughout, and so are a few online tools to identify number sequences and known numeric values. Overall though, the emphasis in on the methodology rather than a particular CAS (Computer Algebra System) or programming language. In fact, with the exception of a snippet of Maple code in one of the explorations in the first chapter, the book describe the examples from a mathematical and algorithmic standpoint. You won't find source code for the examples illustrated.

The ideal target audience for The Computer as Crucible is graduate students and researchers. A bright, motivated high-school student will get the gist of this book, but a more mature mathematical audience will actually be able to follow the steps within the examples and fully appreciate the insight on how an experimental approach can aid their research.

Despite the numerous examples employed to make their case, the authors start the book by explaining that it is not intended to be comprehensive. It's meant to be thought provoking and to whet your appetite as to what is now possible in mathematical research thanks to computers.

As a computer programmer who's passionate about mathematics, experimental mathematics fascinates me greatly. As such, I hope to work my way through the actual textbooks that are generally suggested as a follow up to this book. Namely, I've already started reading Mathematics by Experiment, which is co-authored by Jonathan Borwein himself. Other textbooks referenced in this introduction are Experimental Mathematics in Action and Experimentation in Mathematics: Computational Paths to Discovery.

In conclusion, The Computer as Crucible is a lovely little book which builds a strong case for experimental mathematics. Any practicing mathematician or serious amateur should consider checking out this introduction to a topic that will no doubt transform mathematics.

Full disclosure: I received a complimentary copy of this book for review. ... Read more

34. Turtle Geometry: The Computer as a Medium for Exploring Mathematics (Artificial Intelligence)
by Harold Abelson, Andrea diSessa
Paperback: 497 Pages (1986-07-09)
list price: US$45.00 -- used & new: US$24.98
(price subject to change: see help)
Asin: 0262510375
Average Customer Review: 5.0 out of 5 stars
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Turtle Geometry presents an innovative program of mathematical discovery that demonstrates how the effective use of personal computers can profoundly change the nature of a student's contact with mathematics. Using this book and a few simple computer programs, students can explore the properties of space by following an imaginary turtle across the screen.

The concept of turtle geometry grew out of the Logo Group at MIT. Directed by Seymour Papert, author of Mindstorms, this group has done extensive work with preschool children, high school students and university undergraduates. ... Read more

Customer Reviews (5)

5-0 out of 5 stars Amazing book
Just an all around great book; interesting way to explore geometry, in a format that's easily understandable for both beginning & advanced students.

4-0 out of 5 stars Good enough
Not as new as I expected. Doesn't have original cover, though I can settle with the enforced hard cover.

5-0 out of 5 stars forward thinking book about using the computer for mathematics education
Turtle Geometry teaches mathematics and physics via the computer and the Logo programming language. The mathematics covered is pretty advanced, including topology, and general relativity. Yet, through the use of turtle geometry this advanced math and physics becomes accessible to the layperson. Although all of the examples are in the Logo programming language there are listings of Basic routines in the back of the book. With the help of the Basic routines I was able to easily translate the Logo/Basic code to the Python programming language which I choose to use for reading this book. The reviewers of this book mention it as the beginnning of a revolution in mathematics education. It seems though, that this revolution did not come about as computers are still not used very effectively in the classroom. I think this is very sad as the teaching approach used in Turtle Geometry could be very successful in the classroom.

5-0 out of 5 stars My favorite geometry textbook
I discovered this little gem of a book while exploring the stacks in the library when I was attending a local junior college back in the 80's.The author uses Logo's turtle graphics as a way of exploring the properties ofgeometric space.From very simple beginnings drawing regular polygons andother simple shapes, the book gradually works its way to more and morecomplicated scenarios.After exploring the properties of ordinary turtlegraphics, turtle graphics are tried on the surfaces of spheres and cubes,then on more complicated surfaces.Little by little, concepts ofnon-Euclidean geometry are introduced, until the final chapters in whichthe turtle is used to demonstrate the geometric nature of gravity inEinstein's general theory of relativity.

I strongly recommend this bookto anyone with interests in computer programming, geometry and physics. The unusual approach this book takes to the understanding of curved spaceis deceptively simple and surprisingly powerful.

5-0 out of 5 stars Very good book to show how to use logo as a tool for math
Anyone interested in logo from beginners to advanced users will benefit from reading this book.It has very easy and simple to understand examples, along with a review, and questions at the end of every chapter.Some solutions are provided at the end of the book, (and their even correct, as opposed to many other text books I've read).The pace of the book gets gradually more difficulst, yet more interesting as you reach the climax at the end.A must read for anyone interested in Mathematics. ... Read more

35. A Beginner's Guide to Discrete Mathematics
by W.D. Wallis
Paperback: 388 Pages (2002-11-08)
list price: US$49.95 -- used & new: US$35.17
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Asin: 0817642692
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This introduction to discrete mathematics is aimed primarily at undergraduates in mathematics and computer science at the freshmen and sophomore levels. The text has a distinctly applied orientation and begins with a survey of number systems and elementary set theory. Included are discussions of scientific notation and the representation of numbers in computers. Lists are presented as an example of data structures. An introduction to counting includes the Binomial Theorem and mathematical induction, which serves as a starting point for a brief study of recursion. The basics of probability theory are then covered.

Graph study is discussed, including Euler and Hamilton cycles and trees. This is a vehicle for some easy proofs, as well as serving as another example of a data structure. Matrices and vectors are then defined. The book concludes with an introduction to cryptography, including the RSA cryptosystem, together with the necessary elementary number theory, e.g., Euclidean algorithm, Fermat's Little Theorem.

Good examples occur throughout. At the end of every section there are two problem sets of equal difficulty. However, solutions are only given to the first set. References and index conclude the work.

A math course at the college level is required to handle this text. College algebra would be the most helpful. ... Read more

36. Comprehensive Mathematics for Computer Scientists 2: Calculus and ODEs, Splines, Probability, Fourier and Wavelet Theory, Fractals and Neural Networks, ... and Lambda Calculus (Universitext) (v. 2)
by Guerino B. Mazzola, Gérard Milmeister, Jody Weissmann
Paperback: 355 Pages (2004-11-23)
list price: US$59.95 -- used & new: US$36.43
(price subject to change: see help)
Asin: 3540208615
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This two-volume textbook Comprehensive Mathematics for the Working Computer Scientist 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. This text is complemented by an online university course which covers the same theoretical content, however, in a totally different presentation. The student or working scientist who once gets involved in this text may at any time consult the online interface which comprises applets and other interactive tools.

... Read more

37. Elements of Discrete Mathematics (Mcgraw Hill Computer Science Series)
by Chung Laung Liu
 Hardcover: 433 Pages (1985-03-01)
list price: US$119.30 -- used & new: US$38.95
(price subject to change: see help)
Asin: 007038133X
Average Customer Review: 4.5 out of 5 stars
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Customer Reviews (2)

4-0 out of 5 stars Solutions
I wanted to know whether there is any officially published solution book for the above book?As its certainly not possible to solve each n every problem which one(actually each n everyone) would find time consuming. So let me know about it.That's the only reason i rated the book 4 stars.Its worth 5 starsotherwise.

5-0 out of 5 stars I need detail solution book for its exercise!
Can u tell me if this text book has a detail answer book to its exercis ?? I need to know... Please mail me about my question... Thank you so much ... Read more

38. A First Course in Discrete Mathematics (Springer Undergraduate Mathematics Series) (Volume 0)
by Ian Anderson
Paperback: 200 Pages (2000-12-12)
list price: US$49.95 -- used & new: US$35.95
(price subject to change: see help)
Asin: 1852332360
Average Customer Review: 4.0 out of 5 stars
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Textbook providing an accessible introduction to discrete mathematics and related topics, for undergraduate and graduate mathematics students. Topics covered include finite projective planes, the inclusion-exclusion principle, latin squares, the menage problem, and magic squares. Softcover. DLC: Mathematics. ... Read more

Customer Reviews (1)

4-0 out of 5 stars Concise and non-trivial
Discrete maths underpins most of modern cryptography and information theory. Quite different from continuum maths like calculus that a student might already be familiar with. Here, Anderson provides us with a concise introduction to the subject, that assumes no prior coursework in this field.

He manages in a short text to cover a wide range of reasonably advanced issues, like the finite projective planes and magic squares. In keeping with many of the Springer maths texts, the level of analysis is not trivial. (Not a Dummy's book!) Still, with careful attention, a competent student should be able to assimilate these ideas. ... Read more

39. Introductory Discrete Mathematics (Dover Books on Mathematics)
by V. K . Balakrishnan
Paperback: 248 Pages (2010-10-18)
list price: US$12.95 -- used & new: US$10.77
(price subject to change: see help)
Asin: 0486691152
Average Customer Review: 2.5 out of 5 stars
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Concise, undergraduate-level text focuses on combinatorics, graph theory with applications to some standard network optimization problems, and algorithms to solve these problems. Applications are emphasized and more than 200 exercises help students test their grasp of the material. Appendix. Bibliography. Answers to Selected Exercises.
... Read more

Customer Reviews (6)

1-0 out of 5 stars Avoid this book, droogs
I've taken a first semester Discrete Math course, and am currently taking the second semester of it. I bought this book on a whim, hoping it might supplement my text, or at least clarify a few points. It fails at both of those things. Here's why:

1) Abundant errors: I read the first 15 pages and found at least one *serious* typo per page (i.e. a typo that could impede learning). Plus, the grammar ranges from illegal to ambiguous. Thankfully, I was familiar with all of the material that I was reading -- were I not, severe confusion and discouragement would have been the result.

2) Poor examples: They're too abstract or too simple -- and there aren't even very many of them. Oftentimes, he contradicts what he's trying to illustrate due to a small oversight or typo. It's truly bad.

3) Gratuitous brevity (yes I know that may sound paradoxical): The author uses compound sentences in his definitions; sometimes going as far as to define two or three concepts IN THE SAME SENTENCE! It's infuriating.

4) Chapter Zero: This deserves its own rant section. Chapter zero contains nearly all of the material from the first four chapters of my current textbook: Logic, Set theory, Induction, Relations, etc. Somehow the author crams all of it into about 24 pages (plus 4 or 5 pages of exercises). He fails at clarity or lucidity. It's an ambomination -- it reads like lecture notes (you know, the ones only the professor looks at).

OK -- I WANTED to like this book. It's kind of cute, I'll admit it. And the price is sweet. But friends, you get what you pay for. Even after I came across the first 5 or so serious typos I was willing to forgive. Eventually, the sheer amount of contradictory examples and ambiguous sentences riled me up so much that I considered tearing the book in half. Really. I doubt I'll ever open the thing again.

5-0 out of 5 stars Excellent Text
As with any Dover text, it is important to remember that this text is designed to teach the material, not to coddle the reader.This text provides broad and deep coverage of the various topics that fall under discrete mathematics (set theory, boolean logic, graph theory, etc.) with clarity and simplicity.This book is not designed to help you pass a test, but is instead designed to help you grasp and understand the topic, which it does very well.Easily the best book I own on this topic (I often joke that the author covered my first semester course on discrete math in the first chapter!).

2-0 out of 5 stars Too succinct for the discrete novice
I learned much more from the Schaum's Outline (ISBN: 0070380457 -Schaum'sOutline of Theory and Problems of Discrete Mathematics (Schaum's OutlineSeries) by Seymour Lipschutz, Marc Lipson (Contributor), Seymour Lipschultz).

That book overcomes the two shortcomings of this one: for aself-proclaimed introductory work on discrete mathematics, this textcontains too few worked out in-chapter examples, and too many omitted stepsin the reasoning.On this latter point, there were many times my readingbrought me to the phrase "It follows from the definition that..."or "obviously..." when, for me, it didn't follow, or it wasn'tobvious. Contrary to another reviewer's assessment, I found quite a lot oftypos, but none too serious.To its credit, the book does contain a lot ofend-of-chapter problems with solutions, and it is inexpensive.

The authorof the text I review here wrote another in this field, the Schaum's outlineseries offering with ISBN 007003575X, which is not the Schaum's text Irecommend above.I express no opinion on this other work of his.

1-0 out of 5 stars Near-Useless Garbage
This is an unreadable, low quality text. The theorems and proofs are explained in a ridiculously formal and boring style. I challenge you to read and understand a full page of this book on your first try. Avoid atall costs, and if your professor is using this text, avoid the course atall costs, and try talking some sense into your professor.

1-0 out of 5 stars Near-Useless Garbage
This is an unreadable, low quality text. The theorems and proofs are explained in a ridiculously formal and boring style. I challenge you to read and understand a full page of this book on your first try. Avoid atall costs, and if your professor is using this text, avoid the course atall costs, and try talking some sense into your professor. ... Read more

40. Theoretical Computer Science: Introduction to Automata, Computability, Complexity, Algorithmics, Randomization, Communication, and Cryptography (Texts in Theoretical Computer Science. An EATCS Series)
by Juraj Hromkovic
Paperback: 313 Pages (2010-11-02)
list price: US$89.95 -- used & new: US$71.97
(price subject to change: see help)
Asin: 3642057292
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Juraj Hromkovic takes the reader on an elegant route through the theoretical fundamentals of computer science. The author shows that theoretical computer science is a fascinating discipline, full of spectacular contributions and miracles. The book also presents the development of the computer scientist's way of thinking as well as fundamental concepts such as approximation and randomization in algorithmics, and the basic ideas of cryptography and interconnection network design.

... Read more

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