Simple reasoning techniques for complex phenomena: divide and conquer, dimensional analysis, extreme cases, continuity, scaling, successive approximation, balancing, cheap calculus, and symmetry. Applications from physical and biological sciences, mathematics, and engineering. Examples include bird and machine flight, neuron biophysics, weather, prime numbers, and animal locomotion. Emphasis on low-cost experiments to test ideas and on fostering curiosity about phenomena in the world.
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Please fill out the course evaluation. It is linked here.
Previous versions of the course: Spring 2009 website | Spring 2008 website | OCW site (based on Spring 2008 course)
|Time/place||MWF 11-12, Room 4-163|
|Instructor||Sanjoy Mahajan (primary), Rohan Abeyaratne|
|Handouts||Rough grading philosophy | How to do reading memos | Assignment schedule | Revised grading policy | (comments on the revised policy) | (comments on the draft policy) | Bibliography for the readings | Numbers for the backs of envelopes | Singing logarithms | Trignometric integral|
|Data/Programs||Text of Decline and Fall, vol. 1 (for HW 02) | coin-game.py|
|Desert-island pretest||pretest (enter answers by Monday 2/15 @11pm here)|
|Readings||All readings in one file | All annotated readings in one file|
|Homework||HW 9 (optional: not due) | HW 8 (with your annotations) | HW 7 (with your annotations) | HW 6 (with your annotations) | HW 5 (with your annotations) | HW 4 (with your annotations) | HW 3 (with your annotations) | HW 2 (with your annotations) | HW 1 (with your annotations)|
|Solutions||All solution sets | All annotated solution sets | Sol 9(optional: not due) | Sol 8 (with your annotations) | Sol 7 (with your annotations) | Sol 6 (with your annotations) | Sol 5 (with your annotations) | Sol 4 (with your annotations) | Sol 3 (with your annotations) | Sol 2 (with your annotations) | Sol 1 (with your annotations)|
|Web forms||Homework submission | Reading/solution memo grades|
|Interesting papers||Review article on deliberate practice | G. B. West et. al., "A General Model for the Origin of Allometric Scaling Laws in Biology | G. B. West et. al., "The Fourth Dimension of Life: Fractal Geometry and Allometric Scaling of Organisms" | Drag and physics textbooks (Mahajan/Hogg)|
Arthur Engel, Problem-solving Strategies (Springer, 1998)|
Knut Schmid-Nielsen, Scaling: Why Animal Size is So Important (CUP, 1984)
Steven Vogel, Life in Moving Fluids (Princeton, 1996)
George Polya, Induction and Analogy in Mathematics (Princeton, 1954)
Sanjoy Mahajan, Street-Fighting Mathematics (MIT Press, 2010)
Raymond, The Art of Unix Programming
|Interesting links||Dangers of the resistive grid (comic) | Python | MetaPost | Asymptote (a better MetaPost) | UNIX shell programming|
|Promises||Calculate 1/17 to 6 digits in one's head | Falling cones | Singing logarithms|