"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
"a century ago this week. Mathematician Andrey A. Markov delivered a lecture that day to the Imperial Academy of Sciences in St. Petersburg on a computational technique now called the Markov chain.
Little noticed in its day, his idea for modeling probability is fundamental to all of present-day science, statistics, and scientific computing. Any attempt to simulate probable events based on vast amounts of data - the weather, a Google search, the behavior of liquids - relies on Markov's idea."
