Being a bibliophile, I am attracted to books with unusual titles, such as Sanjoy Mahajan's Street-Fighting Mathematics. I had to buy a copy to see what this was all about.
Mahajan quickly explains that "street-fighting mathematics" is the "art of educated guessing and opportunistic problem solving." I find that a big leap...
The opening blurb on the back cover was great: "In problem solving, as in street fighting, rules are for fools: do whatever works--don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions...."
As the author, Mahajan has a Ph.D. in theoretical physics from CIT, but presently helps direct MIT's Teaching and Learning Laboratory. The book itself is an outgrowth of an interim course he taught at MIT.
In the book, Mahajan discusses and illustrates the power of six street-fighting tools specific to mathematics:
Throughout the book, Mahajan's mantra is: "Too much mathematical rigor teaches rigor mortis," which he claims is equivalent to "Failure to make timely approximations leads to algebraic paralysis."
- Dimensional analysis
- Build of knowledge of easy cases
- Simplifying by lumping
- Pictorial proofs or reasoning
- Analyze the big part first and use successive approximations
- Reason by analogy
The book is an enjoyable excursion, and includes suggestions worthy to pass on to students. Be forewarned that the level of mathematics is primarily calculus and beyond, with a strong applied aroma. But, this is expected in a course that involves MIT students interested in physics, mathematics, management, electrical engineering, computer science, and biology.
Finally, if you cannot find the book, you should peruse the course Street-Fighting Mathematics, available as part of MIT's OpenCourseWare. In addition to providing guided assignments, the course includes links to the original readings that led to the text. A sample problem: