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Getting Math Chops Back Up

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Cheryl Fillekes

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

Bruce Sawhill

Getting Math Chops Back Up

Hey Cheryl;

How's life in NZ?

Our company is doing well, we now have a "real" name and are publicly
known:

www.dayjet.com

We start flying next June, alas no plans to fly to NZ or even across
the US, though.

Cheers,

Bruce

P.S> Very entertaining digression on the beauty of math.

On Oct 9, 2005, at 9:43 AM, Cheryl Fillekes wrote:

>
> 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
>
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9:30a-11:30 at ad hoc locations
> Lecture schedule, archives, unsubscribe, etc.:
> http://www.friam.org
>

Frank Wimberly

Getting Math Chops Back Up

In reply to this post by Cheryl Fillekes

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: [hidden email] [mailto:[hidden email]] 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

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9:30a-11:30 at ad hoc locations
Lecture schedule, archives, unsubscribe, etc.:
http://www.friam.org

Russell Standish

Getting Math Chops Back Up

Seems to be fairly typical of maths departments everywhere. I was one
of those too impatient to learn theorem proofs (as in memorising
them), but exposure to theorem proving technique is still useful for
the odd occasion one has to do it oneself.

Cheers

On Sun, Oct 09, 2005 at 02:11:59PM -0400, Frank Wimberly wrote:

> 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
>
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9:30a-11:30 at ad hoc locations
> Lecture schedule, archives, unsubscribe, etc.:
> http://www.friam.org
>
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9:30a-11:30 at ad hoc locations
> Lecture schedule, archives, unsubscribe, etc.:
> http://www.friam.org

--
*PS: A number of people ask me about the attachment to my email, which
is of type "application/pgp-signature". Don't worry, it is not a
virus. It is an electronic signature, that may be used to verify this
email came from me if you have PGP or GPG installed. Otherwise, you
may safely ignore this attachment.

----------------------------------------------------------------------------
A/Prof Russell Standish Phone 8308 3119 (mobile)
Mathematics 0425 253119 (")
UNSW SYDNEY 2052 R.Standish at unsw.edu.au
Australia http://parallel.hpc.unsw.edu.au/rks
International prefix +612, Interstate prefix 02
----------------------------------------------------------------------------

Martin C. Martin

Getting Math Chops Back Up

In reply to this post by Frank Wimberly

Frank Wimberly wrote:

It was my experience at the University of Toronto in the 1990. I took
the math route, and learned real analysis and Heine-Borel, while my
physics friends learned ODEs and linear algebra.

If you're interested in freshman real analysis, a great book is Calculus
by Michael Spivak. It even gets 4 1/2 stars at amazon:

http://www.amazon.com/gp/product/0914098896

No table of derivatives; lots of epsilon-delta.

- Martin

Mikhail Gorelkin

Getting Math Chops Back Up

In reply to this post by Cheryl Fillekes

> "Oh what, you mean like 2+2=5 here?"

Beauty of math is sometimes 2 + 2 = 5 (or something else like in real life!
Maybe even "everything else" like singularities in complex analysis) -
Lobachevsky, Puankare / Lyapunov (bifurcation theory), Lebegue (integral
Lebegue), and many others. Otherwise it would be boring :-)

- Mikhail

----- Original Message -----
From: "Cheryl Fillekes" <[hidden email]>
To: <Friam at redfish.com>
Sent: Sunday, October 09, 2005 12:43 PM
Subject: Re: [FRIAM] Getting Math Chops Back Up

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
>
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9:30a-11:30 at ad hoc locations
> Lecture schedule, archives, unsubscribe, etc.:
> http://www.friam.org
>

Mikhail Gorelkin

Getting Math Chops Back Up

P.S. It seems Godel doesn't prohibit it :-)

----- Original Message -----
From: "Mikhail Gorelkin" <[hidden email]>
To: "The Friday Morning Applied Complexity Coffee Group" <Friam at redfish.com>
Sent: Sunday, October 09, 2005 9:37 PM
Subject: Re: [FRIAM] Getting Math Chops Back Up

> > "Oh what, you mean like 2+2=5 here?"
>
> Beauty of math is sometimes 2 + 2 = 5 (or something else like in real
life!

> Maybe even "everything else" like singularities in complex analysis) -
> Lobachevsky, Puankare / Lyapunov (bifurcation theory), Lebegue (integral
> Lebegue), and many others. Otherwise it would be boring :-)
>
>
>
> - Mikhail
>
> ----- Original Message -----
> From: "Cheryl Fillekes" <cfillekes at mail.utexas.edu>
> To: <Friam at redfish.com>
> Sent: Sunday, October 09, 2005 12:43 PM
> 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
> >
> >
> > ============================================================
> > FRIAM Applied Complexity Group listserv
> > Meets Fridays 9:30a-11:30 at ad hoc locations
> > Lecture schedule, archives, unsubscribe, etc.:
> > http://www.friam.org
> >
>
> ============================================================
> 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 Duncan-2

Getting Math Chops Back Up

In reply to this post by Frank Wimberly

Frank is certainly right for us old timers, but things have changed a good
bit,
at least in some universities.

At mine, Carnegie Mellon, most all undergrad "math" majors now pursue one of
several applied mathematics tracks in the mathematical sciences. See
http://www.math.cmu.edu/ug/degree.html

It was interesting that when these options were first opened up (even with
fewer
of them) virtually all traditional mathematics majors moved to one of these
applied options.

George

On 10/9/05, Frank Wimberly <wimberly3 at earthlink.net> wrote:

>
> 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
>
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9:30a-11:30 at ad hoc locations
> Lecture schedule, archives, unsubscribe, etc.:
> http://www.friam.org
>
>
> ============================================================
> 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
Professor of Statistics
Heinz School of Public Policy and Management
Carnegie Mellon University
Pittsburgh, PA 15213
(412) 268-2172
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