About this course
Too much mathematical rigor teaches rigor mortis: the fear of making
an unjustified leap even when it lands on a correct result. Instead of
paralysis, have courage: Shoot first and ask questions later. Although
unwise as public policy, it is a valuable problem-solving philosophy
and the theme of this course: how to guess answers without a proof or
an exact calculation, in order to develop insight.
You will learn this skill by mastering six reasoning
tools---dimensional analysis, easy cases, lumping, pictorial
reasoning, taking out the big part, and analogy. The applications will
include mental calculation, estimating population growth rates,
understanding drag without differential equations, singing musical
intervals to estimate logarithms, approximating integrals, summing
infinite series, and turning differential equations into algebra.
Your learning will be supported by regular readings that you discuss
with other students, by short tablet videos, by quick problems to help
you check your understanding, by weekly homework problems, review and
and a final exam. You will work hard, and, by the end of the course,
have learned a rough-and-ready approach to using mathematics to
understand the world.
All required readings are available within the courseware, courtesy of
MIT Press. A print version of the course textbook,
Math, is also available for purchase.