Physics Books for a Math Ph.D. Student
November 18th, 2008 by WaltSlashdot has a thread discussing physics books recommendations for a math Ph.D. student who would like more physical intution into partial differential equations. There are some good suggestions, and many comments that come dangerously close to “You’re a math Ph.D. student and you don’t know what a PDE is?”
November 18th, 2008 at 11:33 pm
This is why I stopped reading Slashdot ten years ago. The same old “all math is analysis” trope dragged out by people who think they know what math is ’cause they’re engineers.
November 18th, 2008 at 11:40 pm
I’m with John. I got sick of “all math is analysis” back when I was asked “Oh, are you a calculus major then?” as an undergrad, and then got the “Oh, but that’s easy!” when I said that I’m studying algebra. Most of the suggestions on the part of the thread I bothered to look at were of the “PDE? But I took that as an undergrad!” variety, interspersed with the set of books needed for ugrad + first year physics.
November 19th, 2008 at 8:19 am
Gee.. I’m a phd math student, doing abstract algebra and combinatorics, and I’m no afraid to sa.. I do’t know PDE.
Why would I need to learn such sillyness? Nobody is however saying: “you don’t know category theory? what kind of math phd student you are?”
Such smug posters probably know less “real math” than the one asking.
November 19th, 2008 at 10:22 am
Indeed, Drini. category theory:analysis::mathematics:reading
November 19th, 2008 at 12:07 pm
People say that PDE can be very beautiful. But I’m just as happy staying in my own p-adic neighborhood.
November 20th, 2008 at 1:34 am
Indeed, Drini. category theory:analysis::mathematics:reading
While I sympathise with whatever seems to be so awful about the teaching of analysis, or the proselytising of its acolytes, in the Land of the Free, is there really any need for this kind of cliquey joke?
As a nominal analyst, I am surprised as to how much various commenters here must have been browbeaten by it. My own mathematical education, such as it was, seemed to consist of feeling inferior for not understanding algebraic or differential geometry, and struggling with algebraic topology. (PDE didn’t really exist in my curriculum, at least not to the extent that you all seem to have experienced.)
November 20th, 2008 at 7:47 am
Yemon, I think you miss my point. In American society, mathematics is something people are bizarrely proud of not knowing, while illiteracy is a shameful secret. Similarly, among mathematicians analysis is generally seen as essential and fundamental, while category theory is dismissed as “abstract nonsense”.
And yes, I know that the term was coined as a self-effacing, ironic joke, but it ends up being interpreted literally, and used to dismiss the entire field of study.
As for proselytizing, you’ve missed something there too. Analysts in a mathematics department generally aren’t that bad. What we’re talking about is the commenters at Slashdot, whose mathematical knowledge is pretty much restricted to engineering at best. They take this warped, analysis-heavy view of mathematics and take it to the extreme that they believe analysis is all of mathematics. PDEs are good at modeling real-world phenomena, so they’re familiar with PDEs, and so they project that knowledge back and take it to be the whole of mathematics.
November 20th, 2008 at 9:05 am
You can check out an excellent book right here:
http://www.nyupress.org/books/Godels_Proof-products_id-7913.html
November 20th, 2008 at 2:38 pm
here is the story of the time
i learned that “algebra” \not= “high-school stuff”
(a comment in another blog earlier this year).
November 20th, 2008 at 5:26 pm
John Armstrong - among mathematicians analysis is generally seen as essential and fundamental, while category theory is dismissed as “abstract nonsense”.
Is that really the case? I had generally gotten the opposite impression. Among mathematicians, category theory is seen as essential and fundamental, while analysis (or at least, PDE) is seen as tedious and uninteresting. Perhaps this is different at different departments though - I get the sense that at “prestigious” places, more abstract algebraic and category-theoretic stuff is more valued, while at other places there may be more emphasis on applied math and relatives.
November 20th, 2008 at 6:16 pm
Kenny: I’d say it’s more accurately put that at more prestigious places it is more likely to find a self-sustaining category-oriented community.
And all that sociology is as maybe if category theory is still looked sideways at in less rarified air. If you’re committed to the categorical viewpoint, you’re in for some chilly receptions on the job market.
November 20th, 2008 at 9:18 pm
*raises eyebrow*
Many Americans just do not have the breadth of introduction nor a breadth of interest as some others may be ‘lucky’ to have. They tend to be more focused and it serves them well for the most part. Like the individual that posted seeking guidance on reading material they seek out knowledge where they wish and/or need to know more.
The posters on slashdot are not a good statistical representation of anything - to use them as a sample is applying bad methodology lol
Seems to me like a lot of PhD’d quants the world over along with greedy individuals have screwed billions worldwide - why not pick apart a typical quant’s curriculum or MBAs for that matter too lol
Each and every individual is responsible for his or her own ignorance. So I wouldn’t presume to be as arrogant as some (on slashdot and here) and try to make lump trash-talk statements on the topic of ‘ignorance’ on national nor ethnic nor regional nor academic degree bases.
C++ya,
xkey
November 21st, 2008 at 5:08 am
Thomas, I’m not using Slashdot as any sort of sample. I’m using those posters as an example.
Although I do now have to consider whether my analogy is apt. Maybe reading isn’t as universal a skill as I’d thought.
November 21st, 2008 at 10:58 am
I’m surprised to hear category theory still described as “abstract nonsense”. You are aware that a lot of Haskell programmers use in it their day-to-day activities? For example, monads are used for a whole variety of applications.
November 21st, 2008 at 12:43 pm
Of course I’m aware. But is your average analyst? Are even all Haskell programmers aware of the theoretical underpinnings of their language?
November 21st, 2008 at 2:12 pm
I guess this is as good a place as any for this question. Do you guys know of good books to study physics from a mathematical point of view? I’m very interested in the relations between physics and algebraic/symplectic geometry and representation theory, but my knowledge of physics is not good enough.
November 21st, 2008 at 4:24 pm
Grétar: try Nakahara’s Geometry, Topology, and Physics. It’s part of the IoP’s “Graduate Student Series in Physics”.
November 21st, 2008 at 7:30 pm
Thanks very much, I’m going to take a look at it.
November 22nd, 2008 at 2:59 am
Regarding books on geometry and physics:
In addition to Nakahara’s book, try (for symplectic geometry) “Symplectic Techniques in Physics” by Guillemin and Sternberg. I also like Choquet-Bruhat & DeWitt-Morette’s “Analysis Manifolds and Physics” Vol 1 and 2. And I would recommend at least some parts of “Quantum Fields and Strings: A Course For Mathematicians” by Deligne et al.
November 23rd, 2008 at 2:12 am
Regarding books on geometry and physics:
I’m reading Semi-Riemannian Geometry With Applications to Relativity by Barrett O’Neill at the moment. Maybe that fits your requirement of physics from a mathematical point of view.
November 26th, 2008 at 1:35 pm
Martin’s Manifold Theory: An Introduction for Mathematical Physicists provides a very clear bridge between two communities … especially good for complex manifolds.
November 30th, 2008 at 12:23 am
Every mathematician should be an expert on PDE. Every mathematician should also be an expert on number theory, topology, differential geometry, algebraic geometry, complex analysis, functional analysis, category theory, probability theory, mathematical logic, group theory, and much more. Every mathematician should live to 1000.
December 16th, 2008 at 5:31 am
Why dont all those quarrelers use their time to learn/do whatever math they like/think important instead of sparring with all that blablabla; I guess they would really get more pleasure out of politics/rethorics than math after all……