The Art of Approximation in Science and Engineering
Course facts
- Payment: Free, no certificate
- Credits: Non Credit
- Learning style: Self-paced, start anytime
- Resources: Problem Set Solutions; Problem Sets
MIT OpenCourseWare details
- As taught in: Spring 2008
- Department: Electrical Engineering and Computer Science, Mechanical Engineering
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Simple reasoning for complex problems: divide and conquer, dimensional analysis and special cases, with examples from physics and biology.
An approximate model can be better than an exact one, if it keeps only what matters. This class teaches simple reasoning for complex phenomena through three groups of techniques: divide and conquer, symmetry and invariance, and what it calls lying, or discarding complexity. Applications come from the natural and manmade worlds, such as using falling coffee filters to reason about airplane fuel efficiency.
What You Will Achieve
- Break hard estimates into smaller parts
- Use proportional reasoning and box models
- Apply dimensional analysis to physical problems
- Build useful models using special cases and spring models
Program Overview
Managing Complexity
The first sessions organize a problem into manageable parts.
- Divide and conquer
- Heterogeneous hierarchies
Removing Spurious Complexity
The longest section removes what a problem does not need.
- Proportional reasoning
- Conservation/box models
- Dimensions
Discarding Actual Complexity
The last sessions make deliberate simplifications.
- Special cases
- Discretization
- Spring models
Course Completion
Job Outlook
Estimation and modeling skills help scientists and engineers in many fields reason about problems without an exact solution.
Good for: Science and engineering students who know basic mechanics and calculus and want to reason quickly about hard problems.
Keep in mind: Only homework with solutions and a topic list are published, with no notes or videos listed here. Physics and calculus background is expected, and the last set has no solution.
Bottom line: A way to learn estimation, with problem sets that reward curiosity.
Frequently Asked Questions
What examples does the class use?
They include turbulent drag, xylophone acoustics, the design of compact discs, how stars twinkle, the bending of starlight, and how high an animal jumps as a function of its size.
What does the class mean by lying?
It is the name for techniques that discard complexity, namely special cases, spring models and discretization. The syllabus compares them to lossy compression.
How should you use the problem sets?
An open universe policy encourages collaboration and other sources, but says to avoid looking up answers until you solve the problem or have tried hard.
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