A Professor's Interrupted Research Hours

[mathwonk]

TA's can certainly teach elementary calc AT leAST IN THE WAY THEY leARNED IT, BUT a prof can teach it anyway he/she wants to.

there are many many ways to explain a subject you really understand, and have spent years thinking about.

i can teach calc with insights from archimedes, or newton, or fermat, or euler, riemann, or errett bishop, john tate, or any of the many other masters i have come to know, either personally or through their writings.

i may be wrong, but i think i understand calculus better than most textbook authors, [not the ones i recommend here, but many of the ones we often use], and I try to incorporate my understanding in every class.

how many elementary calc profs will show you how to compute the volume of a 4 dimensional sphere by the same technique used for a three dimensional one?

see if you can read the treatment in a standard book and see how to extend it. many of them give it in a way that is not clearly extendable. why?

how many know that newton already proved "riemann integrability" of monotone functions? (see michael comenetz's calc book). or that riemann himself already proved that a riemann integrable fucntion is equivalent to one whose discon tinuities have "lebesgue measure" zero. (see riemanns works, paper on trigonometric functions). or that fermats algebraic method already computes the derivative of every function in elementary calc, without limits, except sin and exp.

of course many profesors know these things, but not all, and probably not most TA's. I have even seen [and reviewed] calc books, good ones too, whose authors were clearly unAWARE OF these points, since they contradicted them.

how many TA's know the connection between differential forms AND DERHAM COHOMOLOGY? IT IS HARD TO GIVE insights into more advanced material unlessone knows it oneself. when i taught advanced calc the first time, i used stokes theorem to rpove the non existence of vector fields on an (even dimensional) sphere, and the brouwer fixed point theorem. and this was in 1971.

 

[mathwonk]

here is a simple question a bright student might conceivably ask: why do we assume continuity in the FTC? I.e. there are many integrable fucntions that are not continuous. how do we recognize their indefinite integrals?


i.e. any integrable function has an indefinite integral, which is also a function of its upper limit.

what properties does this function have that characterizes it, so we can recognize it and use it to evaluate the integral? Or is the method of antiderivatives available only for continous functions?

people who have done research are likely to ask such questions, whereas people who only learn from books uncuriously, do not, they just repeat everythig the same way it occurred in theior book.

 

[quasar987]

Besides that, if TAs taught all of my courses, I would have missed some great stories, like the one about the time my E&M professor met Paul Dirac (story available upon request).

Let's hear it! :tongue2:

 

[arunma]

Let's hear it! :tongue2:

My pleasure!

My professor was once at a physics conference in Trieste. During the lunch break he visited a restaurant to sample the local cuisine. At a nearby table, he happened to notice an old man eating with his wife. Now this man was different from everyone else. He wasn't engaged in any conversation, he had a dispassionate frown on his face, and he slowly ate his meal as if he were having prison gruel. That afternoon my professor attended a talk by Paul Dirac, and it turned out it was the guy from the restaurant!

OK...it sounded funnier when I heard it in person.

 

[Gokul43201]

TA's can teach university courses adequately (I've had TA's substitute for my professors for extended periods of time). A professor's talents should be left enitrely for research IMHO (and, in terms of helping out the next generation, advising PhD students--the professor's expertise is needed for that).

But considering that most creative and significant advances in math and science have happened through people in their 20s and 30s, I could argue that students, postdocs and junior faculty should never have to teach - that job should be given entirely to professors.

 

[mathwonk]

but why change the system that has worked so well? how do you know it wasnt having to teach that made the young faculty so productive?

 

[George Jones]

My pleasure!

My professor was once at a physics conference in Trieste. During the lunch break he visited a restaurant to sample the local cuisine. At a nearby table, he happened to notice an old man eating with his wife. Now this man was different from everyone else. He wasn't engaged in any conversation, he had a dispassionate frown on his face, and he slowly ate his meal as if he were having prison gruel. That afternoon my professor attended a talk by Paul Dirac, and it turned out it was the guy from the restaurant!

OK...it sounded funnier when I heard it in person.

What was the expression on the face of Wigner's sister?

 

[mathwonk]

wow! i recall trieste from my stay there as having some of the best restaurant food in the world.

 

[quasar987]

My pleasure!

My professor was once at a physics conference in Trieste. During the lunch break he visited a restaurant to sample the local cuisine. At a nearby table, he happened to notice an old man eating with his wife. Now this man was different from everyone else. He wasn't engaged in any conversation, he had a dispassionate frown on his face, and he slowly ate his meal as if he were having prison gruel. That afternoon my professor attended a talk by Paul Dirac, and it turned out it was the guy from the restaurant!

OK...it sounded funnier when I heard it in person.

I still had a laugh out of it.

Dirac is my favorite character from physics along with Landau.

 

[Gokul43201]

but why change the system that has worked so well? how do you know it wasnt having to teach that made the young faculty so productive?

You've misunderstood the context of that rebuttal - it was a devil's advocate argument to that posed by the OP.

Feynman wrote about how he rejected an offer from IAS (Princeton) that allowed him to do research unencumbered by teaching responsibilities. Why? He found that he was a better researcher when he had to mix in teaching.

http://www.cs.umbc.edu/www/graduate/feynman-teaching.shtml [Broken]

 

[andytoh]

Interesting article, but I would never have turned down the position of heavenly, uninterrupted research offered to Feynman. Ok, so perhaps there will be dry spells due to lack of ideas. In that case, how about just read something new. Ideas may come along then (for example mathwonk's stumble upon the heat equation during his perusals), while at the same time you are expanding your knowledge, and thus indirectly improving your research skills. This, in my opionion, is far more productive for your research than to teach elementary topics you've mastered many years ago.

By the way, in the same article Feynman said "In any thinking process there are moments when everything is going good and you've got wonderful ideas. Teaching is an interruption, and so it's the greatest pain in the neck in the world."

 

[arunma]

Interesting article, but I would never have turned down the position of heavenly, uninterrupted research offered to Feynman. Ok, so perhaps there will be dry spells due to lack of ideas. In that case, how about just read something new. Ideas may come along then (for example mathwonk's stumble upon the heat equation during his perusals), while at the same time you are expanding your knowledge, and thus indirectly improving your research skills. This, in my opionion, is far more productive for your research than to teach elementary topics you've mastered many years ago.

By the way, in the same article Feynman said "In any thinking process there are moments when everything is going good and you've got wonderful ideas. Teaching is an interruption, and so it's the greatest pain in the neck in the world."

It's probably just personal preference here, but I don't think I'd ever want a position that was all research and no teaching. In fact when I sent out my grad school applications, I specifically asked to be considered for TAs over RAs (which doesn't seem so hard, since everyone else wants an RA). Teaching new students about physics has a certain appeal. Besides this, I imagine that presenting elementary material would never get old. From what little teaching experience I've had, I find that when teaching elementary physics topics, I almost always learn something new.

 

[J77]

Is there nothing like this available to lecturers in the US?

http://www.epsrc.ac.uk/ResearchFunding/Opportunities/Fellowships/ARF/default.htm [Broken]

 

[Dr Transport]

Is there nothing like this available to lecturers in the US?

http://www.epsrc.ac.uk/ResearchFunding/Opportunities/Fellowships/ARF/default.htm [Broken]

Yes, they do, It is called The Institute of Advanced Study and is a private entity. If you want something different try the national labs. Faculty members in the US are expected to teach unless they are a research faculty member, then they are expected to research and cover their salaries with contract money.

 

[mathwonk]

I have heard people say that stuff about teaching being an aid to research but in my experience it is not true.

I was on a full time research appointment at harvard for 2 years, and it was the most productive period of ym life. The key is being around people who are stimulating and knowledgable, and being able to talk to them.

We had research and learning seminars that were attended by workers from all over the state. You might call it teaching, but I was able to choose my own topic and give lectures from my own choice of sources, and the audience was extremely high level.

Mumford gave me his personal notes on theta functions, not yet published as the Tata lectures on Theta, and I lectured on them to a large audience. When I finished the elementary part, Freitag took over and pushed the level up to his current research.

All the while I was working on research problems of my own choice and talking to people about them. The flow of information to Harvard included updates on the most recent work of researchers throughout the world, and kept me far ahead of people elsewhere.

Profesors there including Fields medalists would explain their work to me, or ask me questions about fine points they failed to understand in the reserach of other specialists and I would happily research them for them and report back. Sometimes I discovered things this way that were presented at International conferences as new results over a year later.

There was never any lapse of activity or downtime. There were too many experts, too much to learn, to much to do. Teaching in comparison is like walking in plowed ground, trying t get one foot in front of the other, and longing for the time one will reach the other side.

I have also been to the IAS in Princeton, admittedly only on a vist, and compared to that time in Harvard, it was relatively unproductive. I.e. even the Institute was less stimulating to me eprsonally than the department at Harvard. Maybe the Institute is too isolated to be exciting. Maybe that isolated atmosphere where each person sits in his own office and thinks is what makes it potentially stifling.

My friends who have had semesters or years at the Institute however loved it. It is considered by many the ideal place to get a research program moving. Perhaps I am someone who functions better when able to talk to people rather than just sit and reflect.

And maybe teaching at Princeton or Harvard is a nice break from research because you get to teach something interesting, or teaching graduate subjects and research students, but teaching beginning courses for the 40th time, or even the third time, takes a real effort to make interesting again to oneself and to the class. Of course those of us who do it strive for that again and again. The summer break helps.

But the opinions expresed here are precisely backwards from my experience. I.e. research is much more necessary to good teaching than teaching is to good research. It is easy to do nothing but research and love it and do it well. Routine unrelated teaching does not help at all. But teaching really well without doing research is almost impossible. Research illuminates and motivates and enlivens teaching in an essential way.

I know people who love undergraduate teaching, and who have continued to love it and do it well for years, but some of them teach mainly honors and advanced courses, and primarily to majors. And they also keep in touch with research and advanced graduate teaching.

Those yeomen who teach the precalc and other staples of many programs over and over, without ever a break of graduate teaching or research time off, do a saintly service to school and students alike, with essentially no hope of ever resuscitating their research activities.