18.098 | January IAP 2008 | Undergraduate

Street-Fighting Mathematics

Pages

Collaboration is fine and encouraged. Write up your own problem set; acknowledge significant help, whether from animate or inanimate sources just as you would in a scientific paper.

ASSIGNMENTS SOLUTIONS
Problem set 1 (PDF) (PDF)
Problem set 2 (PDF) (PDF)
Problem set 3 (PDF) (PDF)

The readings for each session are designed to be read after attending that session. For a listing of the topics discussed in each session, see here: (PDF)

Published Textbook

Buy at MIT Press Mahajan, Sanjoy. Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving. Cambridge, MA: MIT Press, 2010. ISBN: 9780262514293.

The book is available as a free download (PDF) from MIT Press.

Textbook (Earlier Edition)

An earlier version of the textbook as one file may be found here: (PDF - 1.3 MB)

Title page and table of contents (PDF)

References (PDF)

SES # TOPICS READINGS
1 Dimensions

Chapter 1 - Dimensions, pp. 3-12 (PDF)

Questions from lecture 1 (PDF)

2 Extreme cases

Chapter 2 - Extreme cases, pp. 13-26 (PDF)

Questions and answers from lecture 2 (PDF)

3 Application: drag

Chapter 2 - Extreme cases, pp. 26-30 (PDF)

Questions from lecture 3 (PDF)

4 More on drag  
5 Discretization Chapter 3 - Discretization, pp. 31-40 (PDF)
6 Application: pendulum period Chapter 3 - Discretization, pp. 41-44 (PDF)
7 Picture proofs Chapter 4 - Picture proofs, pp. 45-56 (PDF)
8 Taking out the big part Chapter 5 - Taking out the big part, pp. 57-79 (PDF)
9 Analogy Chapter 6 - Analogy, pp. 80-85 (PDF)
10 Application: operators Chapter 7 - Operators, pp. 86-90 (PDF)
11 Application: singing logarithms Handout - approximating logarithms using musical intervals (PDF)

These books present calculus, fluid motion, and problem solving in accessible ways.

Cipra, Barry. Misteaks [sic] and How to Find Them Before the Teacher Does. 3rd ed. Wellesley, MA: A. K. Peters, Ltd., 2000. ISBN: 9781568811222.

Pólya, George. Mathematics and Plausible Reasoning. 2 vols. Princeton, NJ: Princeton University Press, 1990. ISBN: 9780691025094 (v. 1) and 9780691025100 (v. 2).

———. Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving. Combined ed. New York, NY: Wiley, 1981. ISBN: 9780471089759.

Schey, H. M. Div, Grad, Curl, and All That: An Informal Text on Vector Calculus. 4th ed. New York, NY: W.W. Norton, 2005. ISBN: 9780393925166.

Van Dyke, Milton. An Album of Fluid Motion. Stanford, CA: Parabolic Press, 1982. ISBN: 9780915760022.

Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session

Description

This course teaches the art of guessing results and solving problems without doing a proof or an exact calculation. Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis. Applications include mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations. (No epsilons or deltas are harmed by taking this course.)

This course is designed to teach you a flexible attitude toward problem solving. I’ve divided the attitude into six skills or tools. There are others, and more detail on each, but life is short and these six make a decent toolkit.

Logistics

In lecture, I will introduce you to each skill or tool through a series of examples, often posed as questions. Afterwards, you can read more in the corresponding book chapter (see readings). At the end of each session, you will have the opportunity to submit any questions you may have and give ongoing feedback about the course content. The feedback form is given here: (PDF).

Problem Sets

There will be three problem sets, each covering one week (two tools). Collaboration is fine and encouraged. Write up your own problem set; acknowledge significant help, whether from animate or inanimate sources just as you would in an academic paper.

I’ll provide solutions after the lecture where the problem set is turned in. Problem sets will be graded using this scale:

  • P: A decent effort.
  • D: Not a decent effort.
  • F: Did not turn in, or did not make even an indecent effort!

Grading

The course is graded P/D/F based on problem sets and class participation. I expect and hope to pass everyone, so learn, enjoy, and don’t stress.

ACTIVITIES PERCENTAGES
Three problem sets (30% each) 90%
Class participation 10%

Calendar

SES # TOPICS KEY DATES
1 Dimensions  
2 Extreme cases Problem set 1 out
3 Application: drag  
4 More on drag Problem set 1 due and problem set 2 out
5 Discretization  
6 Application: pendulum period  
7 Picture proofs Problem set 2 due and problem set 3 out
8 Taking out the big part  
9 Analogy Problem set 3 due
10 Application: operators  
11 Application: singing logarithms  

Course Info

Instructor
As Taught In
January IAP 2008
Learning Resource Types
Problem Sets with Solutions
Online Textbook