Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving

Street-Fighting Mathematics is a practical guide to solving partly-defined mathematical problems through educated guessing, without requiring formal proof or exact calculation. The book argues that traditional mathematics education emphasizes solving precisely stated problems exactly, while real-world situations often present incomplete problems that need only moderately accurate solutions. Mahajan presents six tools for opportunistic problem solving: Dimensional Analysis, Easy Cases, Lumping, Picture Proofs, Successive Approximation, and Reasoning by Analogy. Each tool is illustrated with numerous examples, with the general principle separated from specific applications so readers can apply the techniques to problems of their own interest. The book grew from a short course taught at MIT for students ranging from first-year undergraduates to graduate students preparing for careers in physics, mathematics, management, electrical engineering, computer science, and biology. The course demonstrated how an approach avoiding mathematical rigor could teach students to use mathematics to solve real problems.