The Mathematica GuideBook for Programming

About the GuideBooks. The Mathematica GuideBooks by Michael Trott form a four-volume set that has been in development for over a decade. The GuideBooks provide an exploration of the various facets of Mathematica as a tool for solving scientific problems. Each Mathematica GuideBook is available separately and covers one of the key features of Mathematica: programming, visualization, numerics, and symbolics. While there is some overlap and the four books build on one another, each one is self-contained and for the most part each book stands on its own. The four-volume set is over 5000 pages printed in a small font. The author of the GuideBooks, Michael Trott, is a member of the R&D division of Wolfram Research, the makers of Mathematica. Readers who use The Wolfram Functions Site [7] will be familiar with Trott’s work. Leafing through the GuideBooks page by page, it is clear that Trott’s mammoth work goes far beyond “The Mathematica Book” [13]. The author uses Mathematica’s mathematical and scientific capabilities to explore, solve, and visualize a variety of problems. The GuideBooks cover applications of Mathematica to classic and current problems in mathematics, computer science (mainly graphics and visualization), and some theoretical physics. Trott’s approach is as follows: First, discuss the unique features of a Mathematica function, including its arguments, attributes, and options. Then, give small and large examples of applications with detailed references. At the end of each chapter, Trott encourages the readers to practice what they have learned through an extensive set of exercises with solutions. Each accompanying DVD contains the full text and executable Mathematica code of all four volumes. In addition, the DVD that accompanies a specific volume also contains the Mathematica output, graphics, and animations covered in that volume. Each DVD has a hyper-linked table of contents and hyper-linked index to help readers quickly find items in the entire series. The DVDs have well-designed navigation palettes, some utility notebooks and extra files. The website for the books [6] offers additional materials and updates. Paraphrasing Trott slightly, the author hopes to accomplish the following goals: (i) Give the reader a solid working knowledge of Mathematica; (ii) Provide a detailed knowledge of the key aspects of Mathematica needed to create the “best”, fastest, shortest, and most elegant solution to problems from the natural sciences; (iii) Convince the reader that working with Mathematica can be fruitful, enlightening, and joyful. The GuideBooks provide a delightful tour through the world of mathematics and other scientific disciplines. No prior knowledge of Mathematica is needed to read the GuideBooks. In my opinion, their length and level of detail make the GuideBooks unsuitable as textbooks for courses (e.g. Modeling with Mathematica). Nonetheless, they are an indispensable resource for teachers, researchers, and artists alike.