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visits member for 3 years, 3 months
seen Apr 24 '13 at 10:58

Undergraduate theoretical physics student.

Interests:

Physics: all areas of fundamental physics.

Math: all areas related to the above.

(specifically, the interface of theoretical physics and mathematics)


Sep
15
answered Texts on Principal Bundles, Characteristic Classes, Intro to 4-manifolds / Gauge Theory
Sep
15
awarded  Editor
Sep
15
revised Historical basis and mathematical significance of Riemann surfaces
added 1 characters in body
Sep
15
asked Historical basis and mathematical significance of Riemann surfaces
Sep
14
awarded  Supporter
Sep
14
awarded  Teacher
Sep
14
comment Primer on complex analysis and Riemann surfaces for undergraduate physics / theoretical physics majors
Many popular books on history of maths refer to Riemann as a "towering" figure of mathematics. But I don't understand what makes a "towering" figure in maths: all mathematicians do math. They're all doing the same thing. So what made him so 'towering' from the rest of his contemporaries? [I know what I wrote above comes of a bit pretentious, but I'm not trying to be pretentious - just trying to understand what made him so important vs. other mathematicians of his time.]
Sep
14
awarded  Commentator
Sep
14
comment Primer on complex analysis and Riemann surfaces for undergraduate physics / theoretical physics majors
ie. was Riemann the first synthesizer of these streams, and the one who brought forth their essential unity via his use of the "Riemann" surface ideas? ...
Sep
14
comment Primer on complex analysis and Riemann surfaces for undergraduate physics / theoretical physics majors
... which led finally to the mathematical ideas that are now referred to as 'modern' maths?
Sep
14
comment Primer on complex analysis and Riemann surfaces for undergraduate physics / theoretical physics majors
Okay. Thanks for the note. But I'm still a bit curious (mystified) regarding the supposedly 'classical' vs. 'modern' maths: was it in the course of the gradual development of the various subject-areas: i.e. the emergence of non-Euclidean geometry via the 5th axiom of Euclid being overturned [Geometry]; the steady progress of algebra (from insolubility of quintic equation onwards, to using complex analytic ideas for the proof of the Fundamental Theorem of Algebra [Algebra]); and the development of complex analysis as a progression from calculus / real analysis [Analysis]... (cont'd)...
Sep
14
comment Primer on complex analysis and Riemann surfaces for undergraduate physics / theoretical physics majors
(Incidentally, Penrose's book sort of delves cursorily into this: so was curious where the 'classical'-'modern' transition lies - in terms of historical period and mathematical content, and what / how Riemann surfaces have to do with it.)
Sep
14
comment Primer on complex analysis and Riemann surfaces for undergraduate physics / theoretical physics majors
(i.e. was 'classical' maths mostly geometry, algebra, and mostly real analysis, while complex analysis - and the introduction of Riemann surfaces - the "transition" stage to 'modern' mathematics?)
Sep
14
comment Primer on complex analysis and Riemann surfaces for undergraduate physics / theoretical physics majors
(While we're on this specific topic: was wondering what made Jost's "Compact Riemann surfaces" such a good 'introduction' to modern mathematics? .. I've been - and kind of still am - under the impression that there's general divisions in pure maths - and within each there is a body of well developed theory (with, no doubt, connections with others): but why specifically is "Compact Riemann surfaces" unique the way the book seems to suggest?
Sep
14
comment Primer on complex analysis and Riemann surfaces for undergraduate physics / theoretical physics majors
"... without the hassles of pure mathematics" - a book which provides a good 'feel' / intuition for the subject-content, ie. isn't too focused on being rigorous and [math] theory-oriented. (Plus, it's a definite plus if it included many examples from physics, but it's not absolutely required.)
Sep
14
comment Primer on complex analysis and Riemann surfaces for undergraduate physics / theoretical physics majors
(Plus, Weyl's book seems to be outdated for some reason.)
Sep
14
comment Primer on complex analysis and Riemann surfaces for undergraduate physics / theoretical physics majors
I've cursorily glanced through Weyl's "The Concept of a Riemann Surface". But not sure it might be the right fit for my needs- I'm searching for a work to allow me to learn about Riemann surfaces as hassle-free as possible [from a physics / theoretical physics point of view] - without the complications of pure mathematics; and possibly with substantial example questions-and-solutions and problems sets at ends of chapters.
Sep
14
answered Texts on Principal Bundles, Characteristic Classes, Intro to 4-manifolds / Gauge Theory
Sep
14
awarded  Student
Sep
14
comment Primer on complex analysis and Riemann surfaces for undergraduate physics / theoretical physics majors
I have his text. Penrose especially recommends it, but for Riemann surfaces I'm still searching for a good starter. ... Any suggestions there?