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Results tagged with soft-question
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user 32389
Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.
3
votes
Uninteresting questions with interesting answers
Watson's integral. Seemingly uninteresting question: calculate
$$W_S=\frac{1}{\pi^3}\int\limits_0^\pi\int\limits_0^\pi\int\limits_0^\pi
\frac{dx\,dy\,dz}{3-\cos{x}-\cos{y}-\cos{z}},$$
produces truly a …
5
votes
Physicist trying to understand modern mathematics
On this website http://www.theorie.physik.uni-muenchen.de/activities/schools/archiv/2011_asc_school/index.html there are videos of the lectures given at the 2011 Arnold Sommerfeld PhD School ''Algebra …
- 16.5k
2
votes
Accepted
Reference for exercises with solutions for affine Lie algebras
You can find some exercises in the following lecture courses: http://www.maths.ed.ac.uk/~igordon/LA1.pdf (Infinite-dimensional Lie algebras, by Iain Gordon - no solutions are provided, though)
http:// …
- 16.5k
8
votes
Accepted
References for von Neumann Algebras
For a rapid introduction see http://www.math.berkeley.edu/~vfr/MATH20909/VonNeumann2009.pdf (Von Neumann Algebras, by Vaughan F.R. Jones -- "The purpose of these notes is to provide a rapid introducti …
- 16.5k
7
votes
Essays and thoughts on mathematics
The Psychology of Invention in the Mathematical Field (Jacques Hadamard's 1945 essay)
3
votes
Demystifying complex numbers
An interesting example of usage of complex numbers can be found in
http://arxiv.org/abs/math/0001097 (Michael Eastwood, Roger Penrose, Drawing with Complex Numbers).
19
votes
How does one justify funding for mathematics research?
A century old opinion: http://www.jstor.org/stable/2972761 (The Significance of Mathematics, by E. R. Hedrick)
Shall we not search our own house? Shall we not ask if our own collegiate and
gradu …
8
votes
Companion to theoretical physics for working mathematicians
If you are not interested too much in details, the following book can play the role of a comprehensive companion: http://www.amazon.com/Unified-Grand-Theoretical-Physics-Edition/dp/1439884463 (A Unif …
2
votes
Interesting Calculus Questions/Exercises
A very good calculus problem book is "Problems in Mathematical Analysis" by Boris Demidovich: http://www.mat.uniroma3.it/users/chierchia/VARIE/bdfc.pdf
1
vote
Accepted
Reference to complete derivation of Kossakowski–Lindblad equation and its steady solutions
It seems the following two articles http://arxiv.org/abs/1110.2122 (A simple derivation of the Lindblad equation, by Carlos Alexandre Brasil, Felipe Fernandes Fanchini, Reginaldo de Jesus Napolitano) …
- 16.5k
0
votes
Reference request for Stieltjes Transform
Maybe the following reference will be useful https://arxiv.org/abs/1105.0060 (Signal Processing in Large Systems: a New Paradigm, by R. Couillet, M. Debbah). See also chapter 3 in the book "Random Mat …
- 16.5k
4
votes
Book on symplectic geometry
A classic, physically inclined introduction is http://www.springer.com/us/book/9780817636951 (Structure of Dynamical Systems: A Symplectic View of Physics, by J.M. Souriau).
- 16.5k
1
vote
Accepted
Reference request: a guide through quantum probability
If you are interested in quantum probability from mathematical perspective, these two books will be helpful:
http://www.springer.com/mathematics/probability/book/978-3-540-60270-5 (Quantum Probabilit …
- 16.5k
1
vote
References on thin film equation: derivation and properties
Earlier references on derivation of this equation can be found in
https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/on-the-motion-of-a-small-viscous-droplet-that-wets-a-surfa …
- 16.5k
17
votes
Has Apéry's proof of the irrationality of $\zeta(3)$ ever been used to prove the irrationali...
As Frits Beukers writes in http://www.staff.science.uu.nl/~beuke106/caen.pdf "Ironically all generalisations tried so far did not give any new interesting results. Only through a combination of miracl …
- 16.5k