Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session


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.


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!


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.

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



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