Saturday, October 27, 2012

A Mathematica Bibliography, Part 1: How to Use Mathematica and its Programming Language


Consider reading Steve McConnell's book, cited under Programming and Computer Science books, in parallel with these if you undertake any serious programming task or just for the enjoyment and edification of learning programming best practices. I am reminded of the beautiful remark I heard by Marvin Minsky in one of his AI classes: "Anyone who doesn't program is missing one of the more interesting cultural experiences of our time."

Abell, Martha L., Braselton, James P., and Rafter, John A., Statistics with Mathematica (San Diego: Academic Press, 1999). Good introduction even though now dated due to the huge inclusion of statistics functions in Mathematica 8.

Blachman, Nancy R., and Williams, Colin P., Mathematica, A Practical Approach (Upper Saddle River NJ; Prentice Hall PTR, 1999). Introduction for beginners. I started with this book.

Dick, Samuel, Riddle, Alfred, and Stein, Douglas, Mathematica in the Laboratory (Cambridge: Cambridge University Press, 1997). An overview of using Mathematica with laboratory data and instruments. But also has excellent practical guidance on importing and exporting files and data, and file operations, and a good introduction to fitting data although you should look at the new tutorials, such as tutorial/CurveFitting for the basics, and tutorial/StatisticalModelAnalysis for more advanced analysis.

Gray, John W., Mastering Mathematica, Programming Methods and Applications 2nd edition (San Diego: Academic Press, 1998). For beginners to experts.

Maeder, Roman E., Programming in Mathematica 3rd edition (Reading MA: Addison-Wesley, 1997). Maeder was the key player in designing the Mathematica programming language with Wolfram, which I consider a major scientific and linguistic synthesis. He then showed how to use the language in significant programming areas and wrote the Wolfram Education Group course on Programming in Mathematica. I have to say, leaving a comparison of importance to history, that this is like Halley or Newton's other followers showing how to use his synthesis, e.g. to calculate the orbit and time of return of a comet. Maeder's approach is elegantly concise, high-level, and to the point.

Mangano, Sal, Mathematica Cookbook (Sebastopol, CA, USA: O'Reilly, 2010). This is my current favorite book to sample for edification and pure enjoyment. I'd say most of it is for intermediate to advanced users.

Trott, Michael, The Mathematica GuideBook for Programming (New York: Springer, 2004).  For beginners to advanced users. I've read most of this book and Trott's style, like Wolfram's, has had a strong influence on my programming style. In particular, I follow Hoare and Trott toward the goal of writing code that can be read like prose, such as using long, descriptive variable names instead of abbreviations. This is one of four 1000-page tomes by the truly prolific Trott, who also compiled the astonishing 310,000-function Wolfram Functions site http://functions.wolfram.com. Until I saw a single individual walking down the hall at the 2007 WRI Technology Conference with a badge saying "Michael Trott," I really didn't think he could be one person. I thought he must be another Bourbaki, the legendary French mathematical collaborative that published under that name.

Wagner, David B., Power Programming with  Mathematica: The Kernel (New York: McGraw-Hill, 1996). Truly a classic to which I was introduced by MathGroup.

Wellin, Paul, Gaylord, Richard, and Kamin, Samuel, An Introduction to Programming with Mathematica (Cambridge: Cambridge University Press, 2005). For beginners to intermediate users. As clear as can be. Paul Wellin heads the Wolfram Education Group.

Wolfram, Stephen, A New Kind of Science (Champaign, IL: Wolfram Media, 2002). I include NKS (as it's known), even though it's an advanced tome, because the code that is downloadable from the book's website is as exemplary for good functional programming as can be found anywhere. For instance, the simple, elegant development of the code that led to what is now CellularAutomaton and TuringMachine at the start of Chapter 5 had a major influence toward simplifying my programming style and approach to programming as a series of "one liners" (q.v. http://blog.wolfram.com/2011/12/01/the-2011-mathematica-one-liner-competition/ by my WRI namesake, Chris Carlson).

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