I was shocked yesterday afternoon. I turned on the television to see what was on for my kids (PBS, of course) only to see, not Bob the Builder or Word World, but the Cantor set being constructed right before my eyes. It turned out that it was a new NOVA special called Hunting the Hidden…
Category: Teaching
Calculus in politics
In his October 1996 editorial in the Notices of the American Mathematical Society, “Mathematics Is an Edifice, Not a Toolbox,” Hugo Rossi wrote: In the fall of 1972 President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used the third derivative to advance his…
Advice for the budding mathematician of any age
Fields Medal winner Terry Tao put together a page on his blog titled Career Advice. He writes: Here is my collection of various pieces of advice on academic career issues in mathematics, roughly arranged by the stage of career at which the advice is most pertinent (though of course some of the advice pertains to…
E-Z Pass, speeding tickets, and the mean value theorem
On Monday I gave a lecture on the mean value theorem in my Calculus I class. The mean value theorem says that if is a differentiable function and , then there exists a value such that . That is, the average rate of change of the function over must be achieved (as an instantaneous rate…
David Foster Wallace’s commencement address
Here is a commencement address given by the late David Foster Wallace at Kenyon College in 2005. It was recently reprinted in the Wall Street Journal. It is both inspirational and melancholy, especially after David Foster Wallace’s apparent death by suicide. He says: Twenty years after my own graduation, I have come gradually to understand…
The US does not produce enough mathematical stars
The New York Times has an article today, “Math Skills Suffer in U.S., Study Finds“, which announces an upcoming article in the Notices of the AMS by Janet Mertz, Jonathan Kane, Joseph Gallian, and Titu Andreescu. The Times writes: The United States is failing to develop the math skills of both girls and boys, especially…
Flash cards are a good idea
I recently came across an article by the mathematician Ethan Akin, whose work in topology and dynamical systems I admire greatly, called “In Defense of ‘Mindless Rote’“. In the article he defends the traditional education model of having students memorize mathematical facts and techniques. He begins with the following quote from Alfred North Whitehead’s Introduction to Mathematics….
What is the difference between a theorem, a lemma, and a corollary?
I prepared the following handout for my Discrete Mathematics class (here’s a pdf version). Definition — a precise and unambiguous description of the meaning of a mathematical term. It characterizes the meaning of a word by giving all the properties and only those properties that must be true. Theorem — a mathematical statement that is proved using rigorous mathematical reasoning. In…
The nuts and bolts of writing mathematics
This was a handout that I made for my Discrete Mathematics class. At our college this course is the gateway to the mathematics major and is the students’ introduction to writing mathematical arguments. Here is a pdf of the handout. The nuts and bolts of writing mathematics You know that I write slowly. This is chiefly…
Doodle replaces sign-up sheet on the door
Suppose you have to schedule meetings with all of your first-year advisees. The old-school way to do this is to tape a piece of paper to your door with all of your free times listed. The students come by and sign up for their desired slot. This works pretty well, but the downside is that…
David Richeson: Division by Zero 