6.055J/2.038J (Spring 2009)
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.

Newest items have a light yellow background.

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
L01 Feb 04 Course intro |  Intro to divide and conquer: CDROM example |  Your questions
L02 Feb 06 Multiple methods/tree representations |  Your questions
L03 Feb 09 Oil imports |  Your questions
L04 Feb 11
L05 Feb 13 Estimating accuracy
L06 Feb 17 Gold or bills?
L07 Feb 18 Unix
L08 Feb 20 Deliberate practice
L09 Feb 23
L10 Feb 25 Word frequencies |  Text of Decline and Fall, vol. 1 (for word frequencies)
L11 Feb 27 Abstraction: Operators
-- Mar 02 Class cancelled due to snowstorm
L12 Mar 04 Abstraction: Recursion
L13 Mar 06 Intro to lossless compression |  Symmetry
L14 Mar 09 Cube solitaire
-- Mar 11 No class: I am giving a seminar at Cornell
L15 Mar 13 Cone experiment: Drag from conservation of energy
L16 Mar 16 Cycling |  Flying index card
L17 Mar 18 Flight
L18 Mar 20 Mountain heights
L19 Mar 30 Animal jump heights
L20 Apr 01 Dimensional analysis: Exxon, Nigeria
L21 Apr 03 Pyramid volume, dimensionless groups
-- Apr 06 No class: I am in Boulder giving seminars
-- Apr 08 No class: I am in Boulder giving seminars
-- Apr 10 No class: I am in Boulder giving seminars
L22 Apr 13 Size of hydrogen |  Bending of light (not done in lecture)
L23 Apr 15 Connections for long-lasting learning
L24 Apr 17 Bond energy everywhere
L25 Apr 22 Easy cases 1: Atwood machine
L26 Apr 24 Easy cases 2: Volume of a truncated pyramid
L27 Apr 27 Easy cases 3: Drag
L28 Apr 29 Lumping 1: Diaper usage; integration
L29 May 01 Lumping 2: Pendulum period
L30 May 04 Lumping 3: Random walks, heat flow
L31 May 06 Springs 1: Speed of sound
L32 May 08 Springs 2: Wood blocks
L33 May 11 Springs 3: Xylophones
L34 May 13 Summary. Your questions!
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"
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)
Interesting links Dangers of the resistive grid (comic)