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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Previous versions of the course: Spring 2008 website | OCW site (based on Spring 2008 course)
Please fill out the online (HKN) course evaluation.
|Time/place||MWF 11-12, Room 4-265|
|Instructor||Sanjoy Mahajan (primary), Rohan Abeyaratne|
|Handouts||Grading philosophy | Useful constants | Tree of techniques|
|Homework||HW 1 | HW 2 | HW 3 | HW 4 | HW 5|
|Solutions||Sol 1 | Sol 2 | Sol 3 | Sol 4 | Sol 5|
|Programs||Combining range estimates | Using the program|
|Email lists||Announcement list | Discussion list|
|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"|
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)
|Interesting links||Dangers of the resistive grid (comic)|