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| visits | member for | 1 year, 8 months |
| seen | Apr 24 at 10:58 | |
| stats | profile views | 121 |
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)
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Sep 15 |
awarded | Editor |
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Sep 15 |
revised |
Historical basis and mathematical significance of Riemann surfaces added 1 characters in body |
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Sep 15 |
asked | Historical basis and mathematical significance of Riemann surfaces |
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Sep 14 |
awarded | Supporter |
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Sep 14 |
awarded | Teacher |
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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.] |
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Sep 14 |
awarded | Commentator |
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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? ... |
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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? |
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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)... |
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Sep 14 |
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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.) |
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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?) |
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Sep 14 |
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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? |
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Sep 14 |
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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.) |
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Sep 14 |
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Primer on complex analysis and Riemann surfaces for undergraduate physics / theoretical physics majors (Plus, Weyl's book seems to be outdated for some reason.) |
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Sep 14 |
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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. |
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Sep 14 |
answered | Texts on Principal Bundles, Characteristic Classes, Intro to 4-manifolds / Gauge Theory |
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Sep 14 |
awarded | Student |
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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? |
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Sep 14 |
asked | Primer on complex analysis and Riemann surfaces for undergraduate physics / theoretical physics majors |
