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 The MIT Press. A print version of the course textbook, Street-Fighting Math, is also available for purchase. The MIT Press is offering enrolled students a special 30% discount on books ordered directly through the publisher’s website. To take advantage of this offer, please use promotion code SFM30 at The MIT Press.
Do I need to buy a textbook?
Back in 2010, MIT Press agreed to publish the textbook, Street-Fighting Mathematics, under a free license (in print and online).
Thus, the book is legally available all over the internet, including on this course platform.
As a registered student in this course, you can also purchase a printed book from MIT Press at a discount.
Do you often get into street fights?
The last time was in high school, when I was attacked for being “different” and suspended for fighting back.
However, in my problem-solving fights (and now that I’m older!), I regularly use reasoning tools and we’ll do the same in this course.
This course deals with an important topic that is neglected in the traditional mathematics curriculum: how to guess and estimate the answers to math problems. You will learn, for example, how to estimate the size of the diaper market in the United States,...
This course deals with an important topic that is neglected in the traditional mathematics curriculum: how to guess and estimate the answers to math problems. You will learn, for example, how to estimate the size of the diaper market in the United States, how to estimate the surface temperature of planets in the solar system, and how to estimate many definite integrals.
This course requires a knowledge of calculus. If you are familiar with Taylor series, you know enough to take this course.
To find out if you want to take this course, download the textbook of the same name, which the instructor graciously makes available for free. If you enjoy the textbook, you will enjoy the course. One advantage of the course is that it provides insightful solutions for many of the problems in the textbook.
The course materials consist of excerpts from the textbook, short video lectures, and problems with solutions that are revealed after you submit your answers. The instructor interacts with students by responding to some of the questions and comments posted in the discussion forum.
The course materials are comprehensive enough that you can take the course without reading the textbook. The instructor does not require or even encourage you to read the textbook, but I found it quite valuable.
The material is difficult, but it is easy to get a certificate, because grading is very lenient.
I do not know if or when this course will be offered again.
Okayama Brett completed this course, spending 4 hours a week on it and found the course difficulty to be medium.
You'll learn some techniques for approximating solutions to mathematical problems. I'd never seen those techniques before, and they give insight into how a mathematical mind can attack difficult problems. The course is based on the professor's book.
Some of the problems posed were hard and relied on some intuition, and at times I felt the professor assumed we knew some math tricks which would make some of the problems straightforward, but I didn't know them so I was struggling.
Overall though I'd recommend the course, even as an archived course. It's worth seeing the techniques so you can apply them in the future in other courses.
Anonymous completed this course.
I have mixed feelings about this course. Some of the topics seemed so basic as to be almost common sense. Others were quite challenging and presented in a way that didn't always make them understandable.