http://friam.383.s1.nabble.com/Getting-Math-Chops-Back-Up-tp520638p520650.html
Frank is certainly right for us old timers, but things have changed a good
several applied mathematics tracks in the mathematical sciences. See
>
> I should just say, "What she (Cheryl) said..."
>
> I had sent the following to Owen "offline" but I was encouraged to send it
> to the list:
>
> "Owen,
>
> I have a lot to say about this. In particular, there is this difference
> between applied (or applicable) mathematics and "pure" mathematics.
> Mathematics departments tend to emphasize the latter. After my sophomore
> year at Berkeley the only thing we did in math courses was to learn to
> prove
> theorems. Our former classmates in Calculus 1-4 who were physics majors,
> for example, took "advanced calculus for science and engineering" while we
> math majors took "introductory real analysis". They learned differential
> equations and we learned the Heine-Borel theorem. They learned about
> matrices and linear transformations; we learned about groups, rings and
> fields. When we asked, "When are we going to learn about the stuff the
> physicists are learning?" we were told, "If you learn this stuff you can
> always learn that stuff."
>
> Maybe this was just characteristic of that time and place (Berkeley,
> 1960's)
> but I doubt it.
>
> Frank"
>
> In my graduate course in complex analysis we worked through Ahlfors in
> great
> detail. There were several problems the professor couldn't do (he was a
> specialist in the area).
>
>
> ---
> Frank C. Wimberly 140 Calle Ojo Feliz Santa Fe, NM 87505
> (505) 995-8715 or (505) 670-9918 (cell)
> wimberly3 at earthlink.net or wimberly at andrew.cmu.edu or
> wimberly at cal.berkeley.edu
>
>
>
>
> -----Original Message-----
> From: Friam-bounces at redfish.com [mailto:Friam-bounces at redfish.com] On
> Behalf
> Of Cheryl Fillekes
> Sent: Sunday, October 09, 2005 12:43 PM
> To: Friam at redfish.com
> Subject: Re: [FRIAM] Getting Math Chops Back Up
>
>
> Interesting story --
>
> For some of the mechanics of working problems in grad school, I
> still would often go back to my original notes from Richard
> Rand's classes at Cornell. He is now known as an absolutely
> legendary educator now, but back then he was just another professor
> -- whose lectures just happened to be gripping, fascinating...
> almost unforgettable. I eventually got rid of my record collection,
> but I sure hung on to those course notes, even after ditching the
> course textbooks.
>
> When I started graduate school at Chicago in Geophysics, I'd
> come out of a full 3 years of engineering math from Rand,
> including a graduate level courses that were weeding-out
> courses for physics grad students (I got a B) as an engineering
> undergraduate -- so in my first year at Chicago, I decided to
> sign up for what looked like the equivalent graduate level
> courses in differential equations...for review.
>
> My grad advisor in our "get to know your faculty advisor and
> choose your courses" meeting thought this was overly ambitious
> and suggested I take "at least a course in *calculus.*"
>
> I pointed out that I'd done that in uh, high school. He countered
> (definitively revealing that he'd not even read my transcript)
> "well that was a long time ago." When I pointed out that I'd
> taken half a dozen engineering mathematics and physics courses
> that required calculus as a prerequisite, and used calculus
> almost continually, he stiffened and answered that "Mathematics is
> Different Here at Chicago." (!!!) So I was like, "Oh what, you
> mean like 2+2=5 here?"
>
> He suggested a compromise whereby I'd sign up for sophomore-level
> complex analysis first quarter and ODE's second. I figured this
> one wasn't worth fighting, and besides I could use the easy "A"
> if I didn't get too bored in the mean time.
>
> In practice, I was pleasantly surprised. Whereas my
> engineering math courses had focussed primarily on technique,
> the mechanics of solving specific problems, and I could do
> Schwartz-Christoffel Transforms in my sleep already --these
> courses at Chicago focussed almost exclusively on proving a
> variety of properties of functions in the complex plane, i.e.
> analytic functions vs piecewise continuous functions, contour
> integration and so forth. In other words, it was complex *analysis*
> based on Ahlfors' text, not Complex Functions based on, say,
> Church. What had previously seemed to be a chore with some
> incomprehensible beauty behind it, was now was something truly
> beautiful I was getting the tools to actually take apart and
> put back together, lectures from people with some real insight
> and understanding.
>
> ODEs and PDEs were even better in that regard, the ODEs course
> being based on Birkhoff and Gian-Carlo Rota's text, which is
> so beautifully written, it reads more like an exciting novel
> in places, *particularly* the proofs. I'd been through Green's
> functions at least 3 times in different courses, for example,
> and again, could blow through the problem sets -- but it was
> just symbol manipulation. It never even occured to me to even
> ask *why* Green's functions gave you the particular solution.
> It was just the technique you applied when you had a forcing
> function, and it worked.
>
> So one night, I'm studying for the midterm, and get sidetracked
> reading Gian-Carlo's one-page proof on Green's functions. He
> actually drew me in to the story, when I "should have been
> studying" in the only way I knew how back then: working problems
> (in this case correcting some of the mistakes in Birkhoff and Rota).
> I thought for sure I was going to blow the exam, but this proof was
> cool and so interesting and so clearly written -- that I was
> able to reproduce the proof on the exam the next day...and I
> was the only one in the class able to do that. So what I thought
> was "being sidetracked" -- actually taking an interest in the
> material for its own sake rather than chugging through that
> odious chore called math homework -- turned out to be a more
> effective study technique as well as a whole lot more fun.
>
> I had amost the same experience with a proof of the uniqueness
> and completeness of Fourier Series in PDEs, which Chicago taught
> from Weinberger's text.
>
> That first year at Chicago, math went from being a Beautiful BFJ
> to something even more beautiful and engaging -- like great art.
>
> When I was working through Guckenheimer and Holmes on my own
> (there wasn't a course at Chicago that used it) I used Hirsch and
> Smale as my ODEs reference rather than Birkhoff and Rota, because
> Hirsch and Smale uses the same notation and way of expressing
> things (Guckenheimer was Smale's student, after all).
>
> The nice thing about these classics is that you can go back to them and
> re-read them like a good novel. They're incredibly enjoyable as well
> as merely useful.
>
> Some of these are really expensive these days, but I think most of
> them are on the bookshelf at SFI:
>
> Complex Analysis:
> Ahlfors
>
>
http://www.amazon.com/exec/obidos/tg/detail/-/0070006571/qid=1128869678/sr=8> -1/ref=pd_bbs_1/102-6245318-2684139?v=glance&s=books&n=507846
>
> ODEs:
> Birkhoff and Rota
>
>
http://www.amazon.com/exec/obidos/tg/detail/-/0471860034/qid=1128869773/sr=1> -1/ref=sr_1_1/102-6245318-2684139?v=glance&s=books
>
> Hirsch and Smale
>
>
http://www.amazon.com/exec/obidos/tg/detail/-/0123495504/qid=1128871551/sr=1> -3/ref=sr_1_3/102-6245318-2684139?v=glance&s=books
>
> PDEs:
> Weinberger
>
>
http://www.amazon.com/exec/obidos/tg/detail/-/048668640X/qid=1128869893/sr=1> -1/ref=sr_1_1/102-6245318-2684139?v=glance&s=books
>
> Nonlinear Dynamics:
> Guckenheimer and Holmes
>
>
http://www.amazon.com/exec/obidos/tg/detail/-/0387908196/qid=1128869955/sr=2> -1/ref=pd_bbs_b_2_1/102-6245318-2684139?v=glance&s=books
>
> Note that none of these really drag you into Courant and Hilbert
> territory.
>
> Cheryl
>
>
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> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9:30a-11:30 at ad hoc locations
> Lecture schedule, archives, unsubscribe, etc.:
>
http://www.friam.org>
George T. Duncan