Monday, June 15, 2009

Math in the Media: Math and the City?!?

Drawing a crowd in close enough to hear what you have to say is what a headline is all about. A guest columnist for the New York Times' The Wild Side, Steven Strogatz, filling in for Olivia Judson, pulled me in easily with his headline in the column on May 19th:

Math and the City

Though not quite similar to Sarah Jessica Parker ('s work, it is a good title.

Here, instead, Mr. Strogatz discusses a couple examples of the mathematics of life that mathematicians tend to see everywhere via their training; patterns, proportions and logical structure that show up again and again in disparate contexts. In this case, Zipf's Law on the frequency of word usage in a language, patterns in economies of scale, similarities in the energy needs of a city based on its size to the energy needs of mammals based on their size all share a remarkable one-ness in their structure. "Spooky" is Steven's word fo it.

Its a good read....

One personal note, though (said with tongue firmly planted in cheek): Steven leads the article with
"One of the pleasures of looking at the world through mathematical eyes is that you can see certain patterns that would otherwise be hidden."
Right, he is. Sometimes is seems kinda like what Neo sees at the end of The Matrix (although in our case there is no trace of any sort of messianic behavior, no doubt).

And it is quite a pleasure. That is, when it isn't a curse.

Wednesday, June 10, 2009

Sleeping; a good study tip?

Want to do better on your next math exam? Try sleeping well the night before. Easy right?

Apparently, cramming may not be the right approach to optimizing performance. This article in the Daily Telegraph today by Science Corrrespondent Richard Alleyne,

announces the results of a University of Pittsburgh study that says
a night of "high quality sleep" helps schoolchildren get better exam results - especially in maths.
Arguably, the study is small (56 students) and the article quotes another article from the Daily Telegraph who quotes the study. But the results make sense, at least from my perspective.

One caveat: The type of sleep most effective is not long in time, but restful in nature, with few if any awakenings or disturbances. However, knowing one has an exam the next day may be cause enough to make the sleep not so restful, no?

Still.... There is good advice in these results.

Mathematics Study Tips - Scrimmaging

Here is a thought experiment: Choose a competitive team sport that requires special skills and one that you have not really played on a regular basis. Then imagine yourself watching 40 hours of instructional videos (about the semester-length of the lecture portion of a standard Hopkins math class) while seated on the couch. Or, if you like, imagine going into the back yard or to a court and practicing a set of drills designed to skill-up your ability to play.

Now imagine jumping into the middle of a real game filled with people who really know how to play. How will you do in that first game? Not so hot, huh?

Building a skill set in a way in which one can play effectively in a sport such as soccer, tennis, basketball, etc. requires many techniques. But one of the absolutely necessary ones is to scrimmage; practice playing in mock games to get a feel for the competition, put drill skills into practice, adapt technique, and learn to think amidst all the action.

Duh, right?

So how come almost no students study for an exam by actually trying to do never-before-seen problems out of the context of which section they are in and in a timed environment? SCRIMMAGE FOR AN EXAM!?!? Well, why the heck not?

Examinations can be extremely stressful and frustrating. "I know this stuff! I've done problems just like these hundreds of times! But with only an hour to do 6-7-9 problems, I just blank! I must be a terrible test-taker."

I doubt it. Most of us can easily pass a walking test, I believe. But then again, we have been practicing that for a while now, right?

Try this next time: After each section is covered and HW problems done, grab a set of problems from that section which are of the same type as those in the HW assignment. Bank them (write them down without reference to the section they came from). As an exam approaches, take some out and under a specific time limit (10 minutes per problem in a calculus course, maybe?) do the problems without regard to notes, book, or any other source (be smart: do this in a place without ANY distractions).

If you can easily do the problems, then those types of problems are yours to jam on in the exam.

If you cannot, then you know what to study a bit more. In this case, study, wait some time, and then try again on a couple more.

Give it a shot. It's better than re-doing HW problems, or re-reading chapters five times over.

In bocca al lupo!

Tuesday, June 9, 2009

More Virtual Math!

Here is a current update of an earlier post here:

For the last few years, the Mathematics Department have been running online versions some of our freshman and sophomore level service courses (110.108-9 Calculus I-II, 110.201 Linear Algebra, 110.202 Calculus III and 110.302 Differential Equations). Designed and implemented inhouse, these course run for seven weeks in the summer, co-instructed by two of our graduate students each, and are identical in every other way to the in-class versions we run during the regular semesters. This year's version start this next week, on June 15th.

The design philosophies of these courses center around two fundamental principles:
  1. The courses sacrifice nothing, both in content and in implementation, from the standard in-class, lecture-based version of the course (which ran concurrently in the summer).

  2. The courses feature live, online lecturing, as well as live recitation sessions, as a core part of the instruction (currently we are the only implementation of online education using fully interactive and live lecturing, I believe; Tell me if I am mistaken. It's hard to keep up).

The implementation of this endeavor is facilitated by a software package called Elluminate Live! (ELive!), a virtual classroom environment that features (screen shot at right):

  • an online virtual whiteboard which acts like a chalkboard.

  • streaming audio,

  • Powerpoint-style slides that can be superimposed on the whiteboard and written over,

  • Classroom attendance moderation,

  • full student interaction including notification of a "raised hand", side chatroom (fully monitored by the instructor, voice and/or whiteboard enabling for each students or students,

  • full recording of live sessions for asynchronous reviewing later, with time stamps for accompanying notes.

Course document management is handled via the WebCT course management software. Homework is done the old fashioned way, but submitted via fax and/or email and graded electronically, and exams are proctored locally. For more details, see the Math Department's webpage.

Past results have been excellent, and this summer we are offering four of our courses in this format (all of the above with the exception of 110.108 Calculus I). I can provide tons more information is anyone is interested.

Thought I would throw this out there again. Cheers....

Tuesday, June 2, 2009

Something from the "who'dda thunkit?" category:

Apparently, "mathematician is the best career in America right now", with a median income of over 90K. But really, don't take the word of a monk about how great the monastery is. Take it from the Karl Fendelander. In an article on Yahoo! hotjobs entitled

"The Hottest $40-an-Hour Careers"

Mathematician rates up there with Art Director, Geoscientist, Computer Software Engineer and Pharmacist. Go figure!!

Here is the relevant entry:


This career has numbers on its side. In their sweeping study of jobs in America, CareerCast [a job search portal] found that mathematicians are at the very top -- that's right, mathematician is the best career in America right now. Mathematicians are extremely satisfied with their jobs, happy with their lives, and, of course, don't mind that $40+ an hour.

A bachelor's degree get you started, but getting any further usually requires a post-graduate degree. From finance to physics, mathematicians find careers in any industry that deals with numbers.

Median Hourly Wage for Mathematicians in 2007: $43.72 ($90,930 yearly)

From an insider, to be honest, the career can cause awkward silences at cocktail parties ;-) .

But its an excellent lifestyle, rated as one of the lowest in stress, and we are in demand.