- Wolfram Alpha: Ask it just about anything and you'll get an answer. Don't forget to ask some non-math related questions, too.
- SageMath: Open source replacement for Mathematica, Maple, and Matlab. Based on Python. Can be installed on Mac or Linux machines, or run in the cloud on any machine connected to the internet.
- Maxima: Open source computer algebra system that can be installed on any machine.
- Scilab: Open source replacement for Matlab that can be installed on any machine.
- R: Open source software for statistics and graphics.
Free Books and Articles
The pages below contain collections of books on most undergraduate math topics:
- Flatland: A Romance of Many Dimensions, by A Square (Edwin A. Abbott)
- Second Revised Edition, 1884
- A short, satirical story about a two dimensional world visited by a three dimensional sphere. Very entertaining, and it may help you to understand the concept of higher dimensions.
- A Mathematician's Apology, by G. H. Hardy
- Cambridge University Press, 1940
- Hardy's justification for devoting his life to mathematics.
- The Unreasonable Effectiveness of Mathematics in the Natural Sciences, by Eugene Wigner
- Communications in Pure and Applied Mathematics, vol. 13, No. I, February 1960
- A brief and interesting essay about the role of mathematics in the natural sciences, particularly physics.
- Harvard Mathematics Review: There's only six issues, but each is filled with articles written by and for undergraduates.
- Rose Hulman Undergraduate Math Journal
- Involve: A math journal that publishes papers with at least one undergraduate author. These may be a little higher level, but a good summary of an article would be a great talk.
- arXiv.org: Open e-print archive with over 100000 articles in physics, 10000 in mathematics, and 1000 in computer science.