"Street-Fighting Mathematics:
The Art of Educated Guessing and Opportunistic Problem Solving" by
Sanjoy Mahajan, published in 2010. "Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool-the general principle-from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest." Available as a free download (Creative Commons License), .pdf): http://mitpress.mit.edu/books/full_pdfs/Street-Fighting_Mathematics.pdf
"This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathematics."
Interactive Mathematics uses LiveMath, Flash and Scientific Notebook to enhance mathematics lessons.
Topics range from grade 8 algebra to college-level Laplace Transformations.
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