User humberto rafeiro - MathOverflow

Answer by Humberto Rafeiro for Do good math jokes exist?

2009-10-30T13:25:53Z

The continuous functions are having a ball. At the dance floor, cosine and sine are jumping up and down, and the polynomials are forming a ring. But the exponential function is standing separately the whole evening. Due to sympathy for it, the identity joins it and suggest: "Come one, just integrate yourself!" – "I've tried that already", answers the exponential function, "but it didn't change a bit!"

another one

Why the mathematician named his dog "Cauchy"? Because he leaves a residue at every pole

Answer by Humberto Rafeiro for Free, high quality mathematical writing online?

2009-10-28T15:20:26Z

IF you want to see free academic video courses from leading universities, just go to

http://www.academicearth.org/

Answer by Humberto Rafeiro for Tools for collaborative paper-writing

2009-10-28T15:08:45Z

There is a tool that is very promising, it is called ScribTeX, The free collaborative LaTeX editor. Its description is giving

Welcome to ScribTeX, the online collaborative LaTeX editor. ScribTeX allows you to work on LaTeX documents from anywhere with internet access and share them with your friends and colleagues easily. You can:
* Create and edit LaTeX documents and automatically render them to PDFs;
* View a complete revision history of all your files;
* Keep your documents private, allow people of your choosing to view or edit them, or publish them to world;
* Use BibTeX to keep track of your references and include them in LaTeX documents;
* Upload images and include them in your LaTeX documents;
* Create custom style files and use them in your LaTeX documents.

Hope this can help many of us doing better collaborative work.

Answer by Humberto Rafeiro for Undergraduate Level Math Books

2009-10-28T12:41:55Z

I didn't see any suggested books from the great Russian school of mathematics, here is a brief list of superb, well written, example oriented books:

Elements of the Theory of Functions and Functional Analysis by A. N. Kolmogorov and S. V. Fomin
Theory of Functions of a Real Variable by I. P. Natanson (this I think, it's hard to find)
Theory of Functions of a Complex Variable, Second Edition (3 vol. set)
Elements of Functional Analysis by L.A. Lusternik and V.J. Sobolev
Problems in Mathematical Analysis by B. Demidovich
Calcul intégral et differentiel (2 vol. set) by N. Piskounov. In English should be something like Differential and Integral Calculus
A Course of Mathematical Analysis (2 vol. set ) S. Nikols'skii
Differentialrechnung und Integralrechnung (3 vol. set), by Gregor M. Fichtenholz. Unfortunately, there is no English translation of this book, only the German translation that it's mentioned. I think this was THE calculus book on Russia. THIS BOOK SHOULD BE TRANSLATED INTO ENGLISH, and I suspect that there is no copyright, it appears around 1959 I think.
Mathematical Analysis (2 vol. set) by Vladimir A. Zorich. This is a very recent book from a great mathematician which is in Moscow university. The book is based upon is lecture.

I have also found a Spanish translation of a book written by S. Banach about "Differential and integral calculus". It is very good as an undergraduate book. The spanish translation (for those who want to search) is Calculo diferencial e integral

Books that undergraduate should not touch (in my humble opinion) are books written in bourbaki's style.