How to Avoid Algebraic Paralysis
Being a bibliophile, I am attracted to books with unusual titles, such as Sanjoy Mahajan's StreetFighting Mathematics. I had to buy a copy to see what this was all about.
Mahajan quickly explains that "streetfighting 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 worksdon'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 streetfighting tools specific to mathematics:
 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
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."
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 StreetFighting 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:
