18.098 / 6.099 Street-Fighting Mathematics

As taught in: January IAP 2008

Two cones of the same geometry but different dimension fall. Which one falls faster?

When you drop two paper cones of different size but the same shape, which one falls faster? See Section 2.7 in readings for an explanation. (Image by MIT OpenCourseWare.)

Level:

Undergraduate

Instructors:

Dr. Sanjoy Mahajan

Course Features

Course Highlights

This course features in readings an electronic textbook developed specifically for the course. The chapters are accessible to anyone with a knowledge of algebra, trigonometry, and some single variable calculus. Dr. Mahajan writes with a clear, conversational style.

Course Description

This course teaches the art of guessing results and solving problems without doing a proof or an exact calculation. Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis. Applications include mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations. (No epsilons or deltas are harmed by taking this course.) This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.