New news

Since February 11th, when I last posted, I have:

• been miserably sick for a week and a half with a sinus and upper-respiratory infection that caused me to lose my voice completely for two days (viral laryngitis -- it was like a miracle -- went away and then came back!)
• traveled to Philadelphia with the spouse, partly during my lost-voice days
• encouraged the spouse to engage in all the most button-pushing, inflammatory discussions possible while my voice was gone, so I would not be able to argue back (but he didn't have the heart! even though it might have been amusing!)
• had the best pretzel in my entire life at Reading Terminal Market and the best American Italian dinner of my life at Villa di Roma
• visited the ruins of George Washington's house on Presidents' Day (and lots of other historic sites too)
• thought about liberty and the American dream, and who is realizing that dream and who is not, and why
• written and graded the first midterm exam of Math 1110 here at the university
• slept a lot, then stayed up to grade, then relapsed into sickness, then slept some more
• and thought and written about polygon space, the space of n-sided polygons in 3-dimensional space up to rotation. This is a rather weird space to me so I've had to think a lot to understand even the basics.

A few other things have happened (for instance, I read Victor Kreiman's paper about using skew barred tableaux for Littlewood-Richardson computations, and then did some calculations that way!) but the highlights and lowlights really are the food of Philadelphia, illness, liberty, and the midterm. 

How's that for a crazy two weeks? Now it's time to catch up on my email...

More history facts

I subbed for a colleague's multivariable calculus class today, and looked up Taylor series on (gasp!) Wikipedia. Why would I do something so crass? Well, Wikipedia is actually pretty good for math -- I can evaluate what is true and what is false on a mathematical level, and the Wikipedia article has some history and links to other topics that I would not necessarily come up with on my own. In particular, some of the Wikipedia articles on math have some historical background included. The Taylor series article of course mentions Zeno, who comes up in my single-variable calculus class as well for his work on limits, and Taylor and Maclaurin, for whom Taylor and Maclaurin series are fairly or unfairly named. But I didn't know about Liu Hui's work on approximating pi (or work in applications of geometry), or Madhava of Sangamagrama's pioneering work on the infinite series for trigonometric functions. It sounds like Madhava in particular understood limits (and error terms and convergence of series) far before mathematicians in Europe, for instance. There's a rumor that Jesuit priests visiting India brought some of his ideas back to Europe.

In my historical explorations, I also found out that Cornell (my current institution) can boast of graduating the first black PhD mathematician in the world! Elbert Cox earned his PhD here in 1925, a year in which there were only 28 PhDs in mathematics given in the entire country. American mathematics was still very young. His advisor was William Lloyd Garrison Williams, a Quaker named after the abolitionist. Cox's thesis was on solutions to polynomial difference equations. Difference equations are a discrete analogue of differential equations, at least if the language then is the same as now. Difference equations are really cool, giving us maps like the logistic map. Chaos shows up pretty soon in this story...

A little bit more history: apparently the year that Elbert Cox was awarded the Scholarship of Mathematics at Cornell (the graduate fellowship of the time), the other awardee was Julia Dale, who had attended college in Missouri. Julia Dale also ended up in academia, in the end at Duke University. There she apparently headed the "women's division of mathematics" (!!). This contrasts with the career of Ida Metcalf, the second women in the US to get a PhD in mathematics (not necessarily coincidentally, also from Cornell) and the first American woman with a PhD in math to get recruited into finance, as a security analyst!

I am a real person, approved by the bureaucracy

I do have my NetID now, which makes me a real person!

I also bought really waterproof boots. This is good, as it has snowed and melted several more times here. No skiing.

Getting back into the teaching/research groove -- getting to know a new group of students. Different universities and colleges have distinctly different cultures around attendance, classroom behavior, office hours, enrollment changes, and all sorts of things. It's interesting to see what's true here. At St. Olaf I taught a very liberal-arts style math class, mentioning many applications to biology or economics and bringing up interconnections with art and history in small projects. At the U of MN I taught a very straightforwardly engineering-calc type of class a few times, and then worked with UMTYMP with students who are delighted by pondering the intricacies of infinity just for fun. Cornell is different than either -- it's a big school so I can't do the class projects and tweaking of the curriculum I did at St. Olaf, but I'm working with architecture students and hoteliers instead of engineers. I'm certainly still feeling out how to most effectively engage with the classical material of calculus. We're working on limits this week: a great philosophical achievement and abstract idea. What do limits mean to us today, though? Why do we study them, other than the fact that they're in the definition of the derivative?

Continuing my experiments with R in my contracting free time -- I learned a lot about murder in Baltimore and some about hospital quality as related to size and ownership from my Coursera course, which just wrapped up. I really enjoyed the experience! The concrete nature of statistics is a fun contrast to the abstraction of, say, torus actions on moduli spaces of stable maps.....