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Street-Fighting Mathematics

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Street-Fighting Mathematics

An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. 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.

Applied MathematicsMathematics
Author
Sanjoy Mahajan
Publisher
Olin College of Engineering
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 38 sections
  1. 01: Dimensions
  2. 1.01: Economics- The power of multinational corporations
  3. 1.02: Newton mechanics- Free fall
  4. 1.03: Guessing Integrals
  5. 1.04: Summary and further problems
  6. 02: Easy Cases
  7. 2.01: Gaussian Integral Revisited
  8. 2.02: Plane Geometry - The Area of an Ellipse
  9. 2.03: Solid Geometry - The Volume of a Truncated Pyramid
  10. 2.04: Fluid mechanics- Drag
  11. 2.05: Summary and further problems
  12. 03: Lumping
  13. 3.01: Estimating populations - How many babies
  14. 3.02: Estimating Integrals
  15. 3.03: Estimating Derivatives
  16. 3.04: Analyzing differential equations- The spring-mass system
  17. 3.05: Predicting the Period of a Pendulum
  18. 3.06: Summary and Further Problems
  19. 04: Picture Proofs
  20. 4.01: Adding Odd Numbers
  21. 4.02: Arithmetic and Geometric Means
  22. 4.03: Approximating the logartihm
  23. 4.04: Bisecting a Triangle
  24. 4.05: Summing series
  25. 4.06: Summary and Further Problems
  26. 05: Taking out the big part
  27. 5.01: Multiplication using one and few
  28. 5.02: Fractional changes and low-enthropy expressions
  29. 5.03: Fractional changes with general exponents
  30. 5.04: Successive approximation- How deep is the well
  31. 5.05: Daunting Trigonometric Integral
  32. 5.06: Summary and further problems
  33. 06: Analogy
  34. 6.01: Spatial Trigonometry- The Bond Angle in Methane
  35. 6.02: Topology- How many regions
  36. 6.03: Operators - Euler-MacLaurin summation
  37. 6.04: Tangent roots- A daunting transcendental sum
  38. 6.05: Bon Voyage