Recently I’ve had a number of people ask for more information about how I teach topology. I’ve taught it five times using a “modified Moore method” or “inquiry-based learning” approach. I’ve modified it each time, trying to work out the bugs. I think it is pretty successful now. Context. At our college all math majors…
Category: Teaching
How do you place incoming mathematics students?
Our department is looking for a better method of placing incoming students in mathematics courses. Currently we have a placement exam that determines whether a student should begin in a calculus I course or in a calculus/precalculus hybrid course (our lowest-level math class). The exam consists of 25 precalculus questions. It does a pretty good…
Mathematics departments at liberal arts colleges
I’m often curious about how other mathematics departments do things—how they structure their curriculum, run the Putnam Exam, handle research projects, etc. This invariably leads to a lot of web searching. So I decided to put together a collection of links to mathematics departments at schools like mine (a small liberal arts college). Because I…
Parametric curve project for multivariable calculus
I’m teaching two sections of Multivariable Calculus this semester. Each class has 3 hours of lecture and a 1 hour 20 minute lab each week. Last week the students were learning about parametric equations. So in lab I wanted to give them some hands-on experience with 2-dimensional parametric curves. Their assignment was to create a…
Advice for new college students
I’m teaching a first year seminar this semester. This isn’t a math course. (The title of my course is “Science or Nonsense?” We will look at a wide range of topics including the paranormal, evolution, climate change, the vaccine/autism controversy, alternative medicines, etc.) We are required to focus on academic writing, library research, oral communication,…
A quick guide to LaTeX
This semester I’ll be teaching real analysis. I am going to have the students type their homework in LaTeX. To make this as easy for them as possible, I will give them a template that is all ready for them to enter their solutions. They shouldn’t have to worry about headers, packages, font sizes, margins,…
Volumes of n-dimensional balls
We all know that the area of a circle is and the volume of a sphere is , but what about the volumes (or hypervolumes) of balls of higher dimension? For a fun exercise I had my multivariable calculus class compute the volumes of various balls using multiple integrals. The surprising results inspired this post….
Movie day in topology class: the Poincaré conjecture
Today was the last day of the topology class I’ve been teaching. I decided to devote the day to the Poincaré conjecture. I started by telling the students a little about the history of the problem. Then I showed them three videos. The first video was an excellent 50-minute lecture by Fields medalist Curt McMullen…
Interview on Strongly Connected Components
I had the pleasure of chatting with Samuel Hansen on the telephone a little while ago. Our conversation is now online as Episode 16 of his Strongly Connected Components podcast series. Check it out! While you’re at it, check out his other interviews as well as his other podcast series, Combinations and Permutation (he discussed my book…
Making a hyperboloid out of skewers and rubber bands
George Hart, of the Museum of Mathematics, writes a weekly column at Make Magazine called “Math Monday.” A few weeks ago he showed how to make a hyperboloid of one sheet out of 32 shish kabob skewers and 176 hair rubber bands. (Here is a direct link to the instructions.) We just finished talking about…
David Richeson: Division by Zero 