I attended Shahriar Shahriari’s MAA Minicourse Beyond Formulas and Algorithms: Teaching a Conceptual/thematics Single Variable Calculus Course at the 2008 Joint Mathematics Meeting. He talked about having his calculus students derive the prime number theorem. Recall that the prime number theorem states that if is the number of primes less than or equal to ,…
Tag: Math
Jenga mathematics
I like this: on his blog The Endeavor, John D. Cook draws an analogy between strengthening a theorem and the game Jenga. Jenga is a game where you start with a tower of wooden pegs and take turns removing pegs until someone makes the tower collapse… I use the phrase “Jenga mathematics” to refer to generalizing…
Do you give partial credit? How to grade Venn diagrams
Suppose that on an exam you asked your class to shade the region corresponding to in the figure below. The problem is worth 5 points. The correct answer is: When you received their solutions, some students had regions shaded that shouldn’t be shaded and left regions unshaded when they should be shaded. My question is:…
Four shuffles suffice
It takes a while to shuffle a deck of cards seven times, but it is well known that that is how many riffle shuffles it takes to fully randomize a deck of 52 standard playing cards. This was shown in 1992 by Bayer and Diaconis. As it turns out, however, for some games fewer than…
Judges, sonar, and innumeracy
Good Math, Bad Math has an interesting blog post about the recent Supreme Court case over the Navy’s use of sonar near marine wildlife. In the blog (and in the readers’ comments that follow), they talk about Chief Justice John Roberts use (misuse) of mathematics in his written decision.
Honda Civic plays the William Tell Overture
American Honda paid for a viral marketing campaign in Lancaster, CA for the Honda Civic. They cut grooves in the road so that when a car drives over the road at 55 mph (in a Honda Civic, presumably), it will play Rossini’s William Tell Overture (yes, that’s the Lone Ranger theme song). The “debut” of…
Folding a golden rectangle
Recently I wrote about the mathematics of cutting and folding paper and about the golden ratio, . Here’s a video that brings these two ideas together. We see how to create a golden rectangle (a rectangle for which the ratio of the sides is ) by folding a piece of paper. [via Anthony Brand’s maths…
Job opening: Lucasian Chair of Mathematics
There is going to be a new faculty member in the Lucasian Chair of Mathematics at Cambridge University. The current Lucasian Chair, Stephen Hawking, is turning 67 on January 8, 2009, and will reach the manditory retirement age. The chair was founded in 1663. Past holders of the chair are: 1664 Isaac Barrow 1669 Sir…
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 Richeson: Division by Zero 