Mangano - Mathematica Cookbook

The Mathematica Cookbook is not necessarily meant to be read from start to finish like a conventional book (although you are certainly welcome to do so!). Having said that, the chapters are organized in a purposeful way. cover important techniques, extensions, and tools that make Mathematica unrivaled as a technical software development tool.

covers numerics. For the most part, Mathematica simply does the right thing when computing numeric results, as you would expect. In pure mathematics, numbers are formal objects that are well behaved, but when you represent numbers in a finite discrete device like a computer, often you will need to understand issues of precision and accuracy in order to get reasonable results on certain classes of problems. Further, numbers have different representations in Mathematica (Integers, Rationals, Complex, and some exotic types like Intervals). Then there is an issue of input and presentation: Mathematica supports different base representations and different display formats. This chapter has recipes that cover all these issues, and it is wise to have some familiarity with them before using any of the numeric algorithms.

Functional programming is a style of Mathematica development that most seasoned users prefer. dives deeply into functional programming, Mathematica style. Because Mathematica was designed to support multiple development paradigms, its functional programming abilities are not as pure as languages like Haskell. This is actually a big plus, because if you are using Mathematica chances are you are solving a problem, and its the solution rather than the aesthetics that is foremost in your mind. Mathematica programmers prefer the functional style because it leads to efficient programs. It also leads to elegant programs. In the context of programming, elegant means the combination of brevity, power, and clarity. There is an amazing sense of intellectual satisfaction that comes from finding a concise functional solution, and this feeling creates the positive feedback that will draw you into Mathematica. However, this style is often mysterious to people who come to Mathematica from other languages like Fortran, C, MATLAB, or Microsoft Excel. I think this chapter will help you discover the rewards of the functional style.

presents Mathematica data structures, which are largely built on the foundation of lists. From lists, Mathematica derives matrices and higher order tensors, sparse matrices, and more. Knowing how to manipulate these structures is essential for almost any application of Mathematica. This is obvious if you are doing linear algebra, but list processing is integral to almost every facet of use. This chapter also shows how to implement other types of data structures, such as a dictionary that leverages the fast associative look-up that is part of Mathematicas evaluation engine.

Pattern-based programming revolves around pattern matching and transformation. introduces Mathematicas rich pattern-based techniques. Patterns are not a feature of most mainstream languages, but they are tremendously powerful and essential if you hope to accomplish anything nontrivial in Mathematica. Of all the techniques at your disposal, pattern matching and replacement is the one most likely to yield the "wow" reaction you get when you see a seemingly simple looking piece of code do something not so simple. To whet your appetite, here is one of my favorites.