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…

# Category: Teaching

## 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…

## Readers’ response: Euler’s greatest hits

My friend Gene Chase is teaching a history of mathematics class at Messiah College this semester. He asked me if I was interested in giving a visiting lecture in his class in a few weeks. The topic: Leonhard Euler. He said that I could talk about whatever I wanted. Wow, the possibilities! So I was…

## Using wikis in mathematics classes

Wikipedia describes a wiki as a website that allows the easy creation and editing of any number of interlinked web pages… [Wikis] are often used to create collaborative websites, to power community websites, for personal note taking, in corporate intranets, and in knowledge management systems. I have used wikis in three of my classes: two…

## What is the cardinality of the Euclidean topology?

I’m teaching topology this semester. The students are looking at different topologies on the real number line. For homework I asked them to think about which topologies are “the same” (if any) and which are “different,” and why they thought that was the case. We haven’t yet talked about continuous maps or homeomorphisms, so I…

## Three applets illustrating parametric curves

In my multivariable calculus we’re talking about parametric curves. I’m using this applet for displaying parametric curves. You can use predefined curves or enter your own. Although the applet is on my web page, it was created by Marc Renault, a friend who teaches down the road at Shippensburg University. I only tweaked it slightly when…

## Why do mirrors reverse right and left but not up and down?

[I apologize to those of you who have been reading my blog for more than a year. I’m reposting something I wrote last year at this time. I was then, and am now, teaching Calculus III, and we just finished discussing the cross product. I ended the conversation by telling my classes how the cross…

## Three applets for linear algebra or multivariable calculus

This semester I’m teaching two sections of Calculus III (multivariable calculus) and I happen to be teaching the first four weeks of Linear Algebra. The first couple weeks of both courses cover properties of vectors in Rn. (Of course, just to confuse the instructor and the students who happen to be in both classes, the…

## Division by Zero listed as one of 50 Best Blogs for Education Leaders

This morning I was pleased to discover that my blog appears on OnlineUniversities.com‘s blog in their list of the 50 Best Blogs for Education Leaders; it was one of the five blogs listed in the Subject Specific category. What a nice surprise. I’m very honored for the recognition! This is the first I’d read their…

## Steven Strogatz writes about the elements of mathematics in the NY Times

Yesterday the mathematician Steven Stragatz wrote the first article in a mulit-part series for the NY Times. In this first article, called From Fish to Infinity, he describes his intent. Crazy as it sounds, over the next several weeks… I’ll be writing about the elements of mathematics, from pre-school to grad school, for anyone out…

## How to email all the students in your class with only two clicks of your mouse

[Update: thanks to one of the comments below, I could rename this post “How to email all the students in your class with only one click of your mouse.”] This post has no math in it. But it may be helpful to teachers (and others who regularly email a group of people). I often have…