Friday, May 28, 2010

RIP Martin Gardner: 1914-2010

Here are some tributes from some of our profession to one who arguably advanced our field more than most of us combined have. As Martin Gardner digested high level mathematics to a point easily attainable and entertaining to a lay audience, he exposed the art, the beauty and the fun of mathematical study to a whole generation of readers. He is one of the minds that inspired me. It is truly sad to hear of his passing.

From the pages of the Magazine that carried his articles for more than 25 years: Scientific American.

Friday, May 21, 2010

New Advice for Incoming Freshmen....

A new item under the category of Incoming Freshmen advice has been worked out, and an announcement here is worth the post. In short,
Who should be taking the honors versions of our mathematics courses?
A lot of questions have come up among individuals about the role of the honors versions of our service courses, and who is really qualified to take them. We have updated our advice page:
Before the change, the advice page recommended the honors version of multivariable calculus, 110.211 Honors Multivariable Calculus, to anyone with a score of 5 on the Advanced Placement BC-level exam. While this score certainly opens up access to the course, really the focus and intent of the course is different from that of the regular version 110.202 Calculus III.

The honors version, like all of our honors versions, is really a course in "mathematics taught the way mathematicians would really like to teach mathematics" (my quote). It is a highly theoretic versions of the standard curriculum, focusing to a large extent, on the underlying theory of a topic and focusing less on the applications and techniques. It is a great course for budding mathematics majors and those who aspire to learn mathematics in a more formal way. In fact, it is a great course to use as a bridge to higher level mathematics, and we encourage our mathematics majors to take the honors versions of all of the courses where we offer such a version.

On the other hand, the honors versions of our courses are not really for someone who simply wants to have the title "honors" on their transcript. Nor are they for students who are not interested in gaining a deep understanding of why topics like calculus are so foundational to higher level understanding of all mathematical modeling.

We have found that many students were jumping directly into this course (and the other honors courses) and having to reassess their choice after a couple of weeks into the semester. Many of these students found themselves switching "down" to the regular version of the course. Not a good way to start one's career here at Hopkins, no?

With this new advice page, we hope to better inform students of our intent, as well our offerings in courses. We always welcome any and ALL commentary of our curriculum, and strongly encourage questions about our programs.

And for ALL of the incoming freshmen out there, welcome to Hopkins. My door is always open!

Thursday, May 13, 2010

Why I teach....

There are many reasons why we do the things we do. The choice of one's career is typically not an actual choice more than an evolution of minor choices and mixed opportunities that lead one to where one winds up. I teach mathematics (among the many things I do here at Hopkins) because I really like it! It provides a sense of career fulfillment one usually has when one is markedly satisfied with their job choice. But why it brings this sense of fulfillment is a bit deeper. Just to try, I will throw an occasional post on this blog detailing why I love my job. Here is the first:

They say war is composed of seemingly endless hours of boredom and drudgery interspersed with occasional moments of pure and abject terror. A full appreciation as to why some people choose to fight wars (choose to reenlist during an active campaign and get back into the theater) can only come from an understanding of just what that adrenaline rush during the terror moments actually feels like.

When one is "doing" math research, one tends to struggle for long periods in an imagined world trying desperately to understand how the complicated parts of a seemingly beautiful structure work in a way that combines the imaginations of other mathematicians and the possibilities that are consistent with all other imagined structures. In this sense it is the purest of arts, as it only exists within the constructs of one's mind.

This usually leads to long periods of confusion and frustration interspersed with moments of total clarity. It is in these moments when something works out that one has a sense for something so much bigger than reality that the adrenaline rush hits and euphoria sets in. These moments and their constructions are filled with so much beauty to us, that we "know" exactly what Mozart or Monet must have felt. We live for these moments, and cannot wait to tell everyone else about them. (It is such a pity that these constructions are not so easily accessible outside of our small worlds!).

When I am teaching, I am describing, narrating, and constructing bits and pieces of an abstract (we say "formal") world that I see quite clearly to people who are trying to understand. I have many tools to help other people see more clearly. I use as many different perspectives as I can think of, look for visual clues in the looks of others to see if they are slowly comprehending, dig into details to find the keys to understanding. The act of teaching is just like the act of doing math research. How to give someone a fully see-able abstract object is not an easy task. But it is a puzzle that requires mathematics to solve (read: more abstract imaginative thinking).


every so often there is that moment; that single instant when after all of the description and frustration and time spent in trying to understand, the moment when full comprehension dawns. That moment when I have successfully handed over a fully developed complicated imagined object to someone else. There is that look the other person (a student, or a colleague) gets when they "see" it, when they get it, when they sense that they have grasped exactly what you are trying to hand to them. They see the beauty of it, and appreciate both the object itself as well as their accomplishment in being able to "see" it....

I teach for that moment. It does not matter how often it comes (although I strive for moments like that to come as often as possible), because when it does, nothing can top the sense of fulfillment it brings.

That sense of connection between student and teacher is totally 100% ethereal. And not only can it not be matched by ANY physical bond, it also leave a mark, which lingers in both parties for a long time.

This is why I teach....

Thursday, May 6, 2010

The 2010 J.J. Sylvester Awards!

I am proud to announce this year's winners of our J.J. Sylvester Award for Outstanding Performance by a graduating senior (we will fix this link problem shortly). This year's winners are:
  • Adam Saltz
  • Xinlu Huang
These two overachievers quite well-represent two of the three types of students we find here at Hopkins.

Adam is a math major intent on seeking a graduate degree in mathematics, although he will take an academic sabbatical this next year before attending graduate school. He will graduate with department honors with a perfect GPA in math, and receive a master's as well as a bachelor's degree in mathematics as part of our BA/MA program. He has also worked in the department as a Teaching Assistant, acting as a recitation instructor for our freshman classes. In this capacity, he is one of our best.

Xinlu, instead, is a combination Mathematics and Physics major who is also a student of the Peabody Institute. She averages about twice the normal number of credit hours per semester here (I am convinced that she owns a time-turner like the one Hermione uses at Hogwarts!), and carries an almost perfect GPA also. She will stay here at Hopkins for another year, however, to achieve her Master's at Peabody.

Congratulations to both of them. With credentials like these, many doors now stand open for each of them.

Incidentally, these two students represent the "I have always and only wanted to do math and view Hopkins as a stepping stone to graduate school" type and the "math is a great outlet for my creative side and I want the math degree to compliment my other interests and add a good credential to my resume/CV" type. The third type of student we see here at Hopkins is the Pre-Med, a wholly different yet equally as complex and interesting species. ;-)