A list of books for discovering mathematics using computer software

I'm searching for books that allow one to discover/experiment with mathematics by using computer environments such as Mathematica/Magma/Magma/Pari-GP, etc.

Until now, I discovered these:


Solution 1:

If you want to learn about graph theory, there is a book called Algorithmic Graph Theory that uses Sage: "Theory and algorithms are illustrated using the Sage open source mathematics software." This book is free. There's also a link on that site to Explorations in Algebraic Graph Theory with Sage by Beezer and Godsil, which is also free.

Solution 2:

If you're interested in number theory, William Stein wrote a book called Algebraic Number Theory, a Computational Approach, which uses Sage quite a bit throughout to illustrate points. And he also wrote Modular Forms, A Computational Approach which uses Sage quite a bit throughout. These are both free. The second one you can download here.

Solution 3:

Here's a couple of links. I am not sure that those fulfill your request, though.

This is a course in Maple by H. Boas. It is primarily aimed at learning the basics of Maple. Nevertheless, the chapter "Slicing bread with Maple" is intended as a computer-aided lecture on higher-dimensional geometry and I find it both amusing and interesting.

'Experiments with MATLAB' by Cleve Moler. The title is pretty much self-explanatory: it is a book in which MATLAB is employed to work out some college-level mathematical facts. This book is a spinoff of the classic Numerical Computing with MATLAB by the same author.

Solution 4:

As these questions appear to be acceptable around these parts, I'll add:

  • SciPy and NumPy
  • A second for Mathematica Cookbook
  • R in a Nutshell and R Cookbook
  • Exploring Everyday Things with R and Ruby which covers "learning how to assemble, process, simulate, and analyze the available data"

  • Excel Scientific and Engineering Cookbook