What good is Mathematica ?

Wolfram Research doesn't hold back in charging for it, except in academic environments. The School of Mines has a Mathematica site license, meaning that it should be readily available on campus. Relatively inexpensive student versions are also available.

Depending on the instructor, upper-division physics courses may rely heavily on moderate familiarity with Mathematica . The uses of Mathematica include:

• Analytic and numerical solutions of a large number of algebraic equations, sophisticated factorizations, number theory, Fourier and Laplace transforms, evaluation of limits, combinatorics and a wide variety of probability and statistics functions, matrix arithmetic and eigenproblems, solutions of ordinary differential equations, analytic integration of an immense class of functions, vector calculus, series expansions, substitutions, calculus, and a myriad of special functions. Calculations that took hours to do by hand can take less than a second, although Mathematica can be obtuse about simplifications.

• Convenience: It also includes handy tabulated data available via function calls, including up to date physical constants, world maps, geodesy, and the Periodic Table.

• Graphics: A rich variety of tools for generating all sorts of graphics, including publication quality graphics, provided its weaknesses in labeling are circumvented.

• Teaching/learning: The Mathematica `Notebook' is a platform-independent file which encapsulates in a clean, hierarchical document formatting labels interspersed with Mathematica input and output, graphics, and pedagogical remarks. The graphics generated in Linux-platform Notebooks are conventional arbitrary-resolution Encapsulated PostScript, and can saved for import into vector-based drawing files.

• Programming: As a functional programming language, for the prototyping of algorithms, etc.

• Special-purpose packages: A Mathematica `package', an object related to a Notebook, makes Mathematica very extensible. A specialized package can be designed to be readily imported into a Notebook session to provide special expertise; examples occur later.

• Wolfram has missed no opportunity to market fancy add-on suites for digital image processing, neural network applications, finance, etc., and there is a plethora of third-party tools.