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The Mathematica GuideBook for Numerics 1st ed. 2006 Edition

4.5 out of 5 stars 4 customer reviews
ISBN-13: 978-0387950112
ISBN-10: 0387950117
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Editorial Reviews

Review

From the reviews:

"The numerics volume has two chapters. … offer a treasure trove of identities and formulas. … take the reader on a thrilling tour of the features of Mathematica. I am impressed with the breadth and depth of Trott’s coverage and his profound understanding of the strengths and limitations of Mathematica. … includes a multiplatform DVD-ROM which allows the reader to experiment with code and view graphics in color. … an invaluable resource and classic reference for scientists who use Mathematica in teaching or research." (Willy Hereman, SIAM Review, Vol. 49 (1), 2007)

About the Author

Trott is a symbolic computation and computer graphics expert. He holds a Ph.D. in theoretical physics and joined the R&D team at Wolfram Research in 1994.
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Product Details

  • Hardcover: 1208 pages
  • Publisher: Springer; 1st ed. 2006 edition (June 21, 2007)
  • Language: English
  • ISBN-10: 0387950117
  • ISBN-13: 978-0387950112
  • Product Dimensions: 7.3 x 2.4 x 9.5 inches
  • Shipping Weight: 4.8 pounds (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Best Sellers Rank: #1,755,597 in Books (See Top 100 in Books)

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By Andreas Lauschke on March 31, 2006
Format: Hardcover
Michael Trott's GuideBooks are an invaluable reference for the serious Mathematica programmer. The unsurpassed symbolic computation engine, superior programming paradigms, lightning-fast numerics, and state-of-the-art visualization can justly be considered four of the main pillars of the Mathematica system, and Michael Trott, himself a well-established and renowed expert programmer at Wolfram Research, provides the most in-depth coverage available in these areas. Unlike the contents normally to be found in a numerics book, this numerics GuideBook includes several methods and principles from other fields of mathematics and programming. This GuideBook is truly astonishing in terms of its breadth. The material is highly relevant for the ambitious numerics programmer, and the writing style is very readable, fluent, and consistent. The structure of the material is logical and break-free, and the examples are very well-chosen.

Several elucidating examples also further the knowledge about the mathematical or physical subject matter itself. Just to mention a few, I was amazed to discover that magnetic field lines of stationary flows are NOT closed in general, and some examples of modern mathematics and physics literature are used in contrast to classical physics, such as the continuous time random walk on a graph or quantum carpets in a solution, which provides an interesting classical vs. quantum variant. And next to textbook examples the reader will find many "real life" examples interspersed throughout the book as well, which makes the results quite "tangible".
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While this book is getting long in the tooth (it was built around version 5.1 whereas today's version is 9.0.1), it is still a very good reference for hard core Mathematica users. I have used Mathematica since 1988 (Version 1) and still am awed by the complexity and the usefulness of the system. The trouble with Mathematica is that is so complex that really good references don't exist. This book for an advanced user explains many of the numerical computational limitations and phenomena that one experiences while using Mathematica. However, it is not for the novice. (For the novice, try to find The Mathematica Book by Stephen Wolfram, version 4. I prefer this version over later versions for its completeness.) While it is dated, it is still a valid reference although some of the examples are obsolete. (Example: Page 106: Developer'SystemOptions has been replaced with SystemOptions. )

To get the best use of the this long book, one should skim it and actually run the test code that might be of interest in Mathematica. Later, in the future, where one has a pertinent problem in writing Mathematica code, this book will be useful. In addition, one should go tot he Springer website and download the available materials. This will include the examples from the book which can be either copied into Mathematica or run native. Since some of the examples are quite complex, this is very useful to avoid mistakes although I tend to learn from the mistakes.

I would also recommend for the serious user the three other Guidebooks (Programming, Symbolics and Graphics) for a complete set.
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Trott is one of the most gifted programmers and teachers you'll ever encounter, and one of the few mathematicians left who knows CAS at a PhD level and DOESN'T work for TI or HP with all kinds of "I won't tell" agreements! The four guidebooks in the Mathematica series represent over 5,000 pages detailing all aspects of numerics, symbolics, graphics, and most importantly, programming. No mathematician, engineer, researcher (including "R" biostats folks), computer scientist or physicist using mathematica can pass on this series.

Even if you use a "free" version of GNU-CAS or the home version of Mathematica (Wolfram Mathematica 9 Home Edition (Windows/Mac/Linux)), this series gives a peek into CAS levels that have long been unpatented trade secrets of TI and HP and very tough to decode. NO other good recent books cover the behind the curtain aspects of CAS as well as these volumes. If you're a math programmer, even if you love Maple, you'll find this series way helpful, at all kinds of levels.

Mathematica is a layered object language, and has multiple compile levels (with an overriding interpreter), which are essentially functions in what, as a programmer, you'd call arrays or hashes (or in Mathematica-speak, lists, functions, rules and patterns). You MUST read the programming book to "get" the rest of the series, otherwise you'll be stuck in what seems like a no-man's land of not being able to define your own classes yet not being able to use typical CAS-like functions in assembly-- when in fact both, and much more, are supported once you get it. We still use the graphics volume at our shader joes sub, and it is as relevant in 2013 as it was 5 years ago.
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