6.055J/2.038J (Spring 2010)
Art of approximation in science and engineering

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
Schedule
L39 May 12 (W) Summary. Your questions!
L38 May 10 (M) Unit 9: Springs 4.
L37 May 07 (F) Unit 9: Springs 3.
L36 May 05 (W) Unit 9: Springs 2. reading memo |  with your annotations
L35 May 03 (M) Unit 9: Springs 1. reading memo |  with your annotations
L34 Apr 30 (F) Unit 8: Probabilistic reasoning 4. reading memo |  with your annotations
L33 Apr 28 (W) Unit 8: Probabilistic reasoning 3. reading memo |  with your annotations
L32 Apr 26 (M) Unit 8: Probabilistic reasoning 2. reading memo |  with your annotations
L31 Apr 23 (F) Unit 8: Probabilistic reasoning 1. reading memo |  with your annotations
L30 Apr 21 (W) Unit 7: Lumping 4. reading memo |  with your annotations
L29 Apr 16 (F) Unit 7: Lumping 3. (no new reading)
L28 Apr 14 (W) Unit 7: Lumping 2. reading memo |  with your annotations
L27 Apr 12 (M) Unit 7: Lumping 1. reading memo |  with your annotations
L26 Apr 09 (F) Unit 6: Easy cases 4. (no new reading)
L25 Apr 07 (W) Unit 6: Easy cases 3. reading memo |  with your annotations
L24 Apr 05 (M) Unit 6: Easy cases 2. reading memo |  with your annotations
L23 Apr 02 (F) Unit 6: Easy cases 1. reading memo |  with your annotations
L22 Mar 31 (W) Unit 5: Dimensional analysis 4. reading memo |  with your annotations
L21 Mar 29 (M) Unit 5: Dimensional analysis 3. reading memo |  with your annotations
L20 Mar 19 (F) Unit 5: Dimensional analysis 2. reading memo |  with your annotations
L19 Mar 17 (W) Unit 5: Dimensional analysis 1. reading memo |  with your annotations
L18 Mar 15 (M) Unit 4: Proportional reasoning 4. reading memo |  with your annotations
L17 Mar 12 (F) Unit 4: Proportional reasoning 3. reading memo |  with your annotations
L16 Mar 10 (W) Unit 4: Proportional reasoning 2. reading memo |  with your annotations
L15 Mar 08 (M) Unit 4: Proportional reasoning 1. reading memo |  with your annotations
L14 Mar 05 (F) Unit 3: Symmetry and conservation 4. reading memo |  with your annotations
L13 Mar 03 (W) Unit 3: Symmetry and conservation 3. reading memo |  with your annotations
L12 Mar 01 (M) Unit 3: Symmetry and conservation 2. reading memo |  with your annotations
L11 Feb 26 (F) Unit 3: Symmetry and conservation 1. reading memo |  with your annotations
L10 Feb 24 (W) Unit 2: Abstraction 4. reading memo |  with your annotations
L09 Feb 22 (M) Unit 2: Abstraction 3. reading memo |  with your annotations
L08 Feb 19 (F) Unit 2: Abstraction 2. reading memo |  with your annotations
L07 Feb 17 (W) Unit 2: Abstraction 1. reading memo |  with your annotations
L06 Feb 16 (T) Unit 1: Divide and conquer 5. reading memo |  with your annotations
L05 Feb 12 (F) Unit 1: Divide and conquer 4. reading memo |  with your annotations
L04 Feb 10 (W) Unit 1: Divide and conquer 3. reading memo |  with your annotations
L03 Feb 08 (M) Unit 1: Divide and conquer 2. reading memo |  with your annotations
L02 Feb 05 (F) Unit 1: Divide and conquer 1. reading memo |  with your annotations
L01 Feb 03 (W) Course overview and grading philosophy.
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)
Interesting books 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

Sanjoy Mahajan  (email).    Materials created with free software: GNU Emacs, GNU Make, Python, and ConTeXt (based on TeX).