User kostya - MathOverflow

Answer by Kostya for Your favorite surprising connections in Mathematics

2011-03-14T11:38:42Z

Being a physicist I'm still puzzled by the connection between:

Wick theorem -- which is combinatorics (for me).
Multivariate Gaussian integrals -- which is calculus (for me).
Determinants and eigensystems -- which is linear algebra (for me).

Answer by Kostya for Tools for long-distance collaboration

2010-12-15T17:42:55Z

I once had experience of writing "collaborative" text in LaTeX by using subversion -- a software versioning and a revision control system for program-developers. That was really cool! Everytime you have the most up to date version. All the "collisions" are dealt with automatically e.t.c.

The problem is -- all your collaborators has to be familiar with this software and the concepts. That's why I had such experience only once.

But I still use it for my own projects -- I setted up repository on my usb dongle, so I do not depend on the computer I use...

Answer by Kostya for homology and cohomology of a quotient manifold

2010-12-09T10:33:31Z

I think that you have to investigate in the direction of fibrations. And then, maybe, spectral sequences.

edit: Concernig your comment -- I am interested in that as well.

Right now my investigation got me there -- check the book "Modern Geometry - Methods and Applications: Part 3: Introduction to Homology Theory" by: B.A. Dubrovin, A.T. Fomenko, S.P. Novikov.

Chapter 20.

It is quite difficult for me to read the book (Yeah, you got me, I'm a physicist.) so I cannot give you anything but the direction.

Any CAS that deals with the word problem

2010-12-06T15:29:32Z

I'm new to the combinatorial group theory, so maybe my question is a bit naiive.

I know that the word problem is generally "unsolvable". On the other hand there are specific cases, when the problem can be solved.

It seems that some computer algebra tool, that implements all the progress in that direction would be of use. Do you know any such tool? Or how to use existing CAS'es for this purpose?

Answer by Kostya for Should I not cite an arxiv.org paper?

2010-10-05T14:29:28Z

Why not? I saw citations that looked like: "[42] J.Smith. Private discussions."

These are definitely not peer-reviewed...

Answer by Kostya for What programming languages do mathematicians use?

2010-01-30T18:51:07Z

No one mentioned OCAML here, so I think It is my "duty" to add this language.

OCAML slightly less "extravagant" than Haskell. It allows you write partially imperative programs in a way that most "non-functional people" would understand. So it is easier to learn and after you did it -- Haskell will be a breeze for you.

OCAML also is VERY strictly typed. If you know exactly what you want then it will be nearly impossible to make a mistake. The language is very fast and has a lot of tools distributed with it. Many people consider the language as alternative for C. Last but not least -- there is a F# language -- .NET version of OCAML supported by Microsoft.

So if I need to quickly check some idea -- I use Mathematica or Haskell. But if I need to write something that should be reliable and stable, so I can share the program with others -- then I use OCAML.