Teaching, Training, and Advising for the Harvard Mathematics Department. Oh, and some computer stuff.
I have left Harvard as of July 1, 2008 to take a position at
NYU.
This website has been cached and left static. Feel free to browse
my new website,
aka "What the heck is a Clinical Associate Professor?"
This workshop will focus concretely on courses, programs and materials that aim to increase teachers’ mathematical knowledge for teaching. Both courses and programs that lead to initial certification and professional development of current teachers will be examined at the workshop. In addition, the workshop will examine efforts by colleges, universities, school districts, professional organizations and funding agencies to support people who teach these courses or lead these workshops.
I work with the Harvard Extension School’s Master of Liberal Arts in Mathematics for Teaching program, which aims to acquaint schoolteachers with higher mathematics. The goal is not so much to give them material that will be directly applicable to the classroom, but to stretch their minds mathematically so they will be able to stretch their students’ minds.
This past semester I’ve taught a probability course in this program using the Moore method. It’s been a real challenge for my students and me because I’ve never done that before. But I found it enjoyable and the students seem to have received it well, too. My colleague Bret Benesh and I will be presenting at this conference on our experiences with Inquiry-based courses in the ALM program.
I am a child of the 80s (Atari, not Nintendo), so I’m very interested in the upcoming CGI Transformers movie. True, I’m married with two little ones, which means I go to the movies about once a year, twice if you count the annual Pixar product. Still, graphics are cool, and so I was pretty excited to see these shots of what the new transformers look like.
I just started looking at Slideshare, a flickr/photobucket-style sharing application for presentations. You upload your presentations (looks like you can use PowerPoint, OpenOffice, or a PDF) and you get a little flash app to embed on your blog as well as hosting of the presentation and all its slides.
Here’s an example, using the talk I gave at UC Irvine last month:
I have disk space available to upload my own stuff here at work, but the flash interface is pretty cool.
In this problem, we will use calculus to investigate the classic James Bond filmGoldfinger (1964). The film concerns James Bond’s attempts to foil the nefarious plot of the evil billionaire Auric Goldfinger. As his name would suggest, Goldfinger has an insatiable love for gold. He plans to destroy the US gold reserves. Doing so will plunge the US economy into chaos and increase the value of his own gold by at least ten-fold. The US gold reserve is stored at Fort Knox. Goldfinger’s plan is to spray the fort with Delta 9 nerve gas to disable the guards. Goldfinger’s henchmen will then detonate an atomic bomb inside the fort vault. Bond has infiltrated the vault and is trying to disarm the bomb before it goes off. However, he has only a very limited amount of time as nerve gas is being pumped into the vault while he works. Your job is to determine whether James Bond has enough time to disarm the bomb.
The size of the vault is 1000 cubic meters. Nerve gas is being pumped into the room at a rate of 9.846 cubic meters per minute. Nerve agent is present in the nerve gas at a concentration of .001 milligrams per cubic meter. Inside the vault are fans that mix the air in the room and blow air out at a rate of 9.846 cubic mters per minute (the same rate at which gas is being pumped in). Delta 9 nerve agent is fatal at a concentration of .0001 milligrams per cubic meter. Bond needs 10 minutes to disarm Goldfinger’s bomb and escape from the vault.
Let f (t) equal the milligrams of nerve agent in the vault after t minutes have elapsed. Using the information given in the previous paragraph, find a differential equation that f satisfies. What is the initial condition that is satisfied by f ?
Solve the differential equation that you derived in the previous question. Does Bond have enough time to disarm the bomb?
After Bond disarms the bomb, how long does it take for the amount of nerve agent in the vault to reach fatal levels? Give your answer to 3 decimal places.
Recently a certain 128-bit integer that was part of the key to decrypting high definition DVDs got out onto the web. The company developing the technology demanded that web sites publishing the number delete it because it consisted of a “circumvention technology” under the Digital Millennium Copyright Act (DCMA). Unfortunately, that toothpaste won’t go back into the tube.
The legal argument is that the company holding the technology copyrights also owns the number. If that holds up, then You Can Own an Integer Too.
I’ll let the lawyers wrangle the case. But here’s mine:
This is another really small package with invaluable flexibility. When typesetting URLs in LaTeX documents we usually want:
the URL typeset in a “computer-looking” (i.e., monospace) font
the ability to use characters which are special to LaTeX but often appear in URLs, like ~, &, #, %
clickability
The url.sty package does this all for you. There are some caveats: if you put a % in a URL it’s now fragile and you can’t use that as an argument to another macro. But in general
\url{http://www.example.com/}
will typeset to a nice-looking URL, which if you use PDFLaTeX with the hyperref package, will be clickable.
I just found PhpMathPublisher on the web and it looks kind of interesting. The name pretty much describes it: a PHP package that parses a kind of math input and produces image-based output.
Most packages (such as LaTeXRender) along these lines serve as a front end to TeX or LaTeX, then serve up a generated image file. There are some drawbacks to this:
TeX and LaTeX are complicated programs with huge distributions, and may not be available to all web programmers
because these programs can include files, there’s a potential security leak in allowing all web users to effectively execute TeX code on the server.
PhpMathPublisher has a tex-like syntax but seems to parse the input on its own and use GD to assemble a formula. Here’s the markup:
Dunking Donuts: Culinary Calculations of the Euler Characteristic (Alexander P. Ellis, ‘07)
Dirichlet’s Prime Number Theorem: Algebraic and Analytic Aspects (Igor Rapinchuk, ‘07)
Quivers (Virigina Fisher ‘08 et al)
A Fitness-Based Model for Complex Networks (Zhou Fan ‘10)
Does Every Polynomial Root have a Simple Approximation? (Bryan Gin-Ge Chen ‘07
Plut there’s an article about the ABC conjecture by Prof. Noam Elkies, a list of problems, and a nice little anecdote about teacher preparation by Dennis Gaitsgory.
And since I’m talking a lot of TeX these days, I’ll say that there are some very nice graphics done in METAPOST by Zachary Abel, ‘10.
Tom Dukich has some very cool geeky math pun art, but he also does music. Listen to some of his math sonification songs, like π on the piano (1000 digits of π, each digit with its own note) or “e on the cuica.”
A colleague of mine once tried assigning a lot of writing in his introductory calculus class. He got results that might be expected by somebody who has tried this before: resistance from many of the students. He told me a student complained on his evaluations:
This is a MATH class. I shouldn’t have to write anything.
Why do some students perceive math and writing as opposites? Here’s a sample scan from one of my favorite mathematics papers: “The moment map and equivariant cohomology,” by Sir Michael Atiyah and the late Raoul Bott, published in the journal Topology (Vol. 23, No. 1, pp. 1-28, 1984).
I would guess there are about 800 words and 11 equations on this pair of pages. These two mathematicians are absolute titans of the 20th century, and are considered brilliant lecturers as well as excellent writers (I took a number of classes from Bott as a graduate student. I eulogized him on this blog last year.) I think the case that can be made that they are good at conveying the mathematics because they are able to say so much without resorting to notation. And being able to talk about mathematics probably was a part of their being able to create such beautiful mathematics.
conference at the Mathematical Sciences Research Institute coming up at the end of the month.
