Poincaré inequality

from The Encyclopedia of Mathematics

in a ball (case $1\leqslant p < n$)

Let $f\in W^1_p(\mathbb R^n)$, $1\leqslant p < n$ and $p^* = \frac{np}{n-p}$ then the following inequality holds

\begin{equation}
\Bigl(\int\limits_{B}|f(x)-f_B|^{p^*}\,dx\Bigr)^{\frac{1}{p^*}} \leqslant C\Bigl(\int\limits_{B}|\nabla f(x)|^{p}\,dx\Bigr)^{\frac{1}{p}}
\end{equation}

for any balls $B \subset \mathbb R^n$, and constant $C$ depends only on $n$ and $p$. Here $f_B = \frac{1}{|B|}\int\limits_{B}f\,dx$.

Generalized derivative

from Encyclopedia of Mathematics.

An extension of the idea of a derivative to some classes of non-differentiable functions. The first definition is due to S.L. Sobolev, who arrived at a definition of a generalized derivative from the point of view of his concept of a generalized function.

The story of staff

http://www.storyofstuff.org/

Internet Resources For TOEFL Preparation

No doubt, the Internet provides wide opportunity to entertain, to communicate and to study. If you are going to prepare yourself for the TOEFl, you might use internet resourses to do your studing more confortable and successful. The test consist of four sections: a reading, a listening, a speaking and a writing, fome free resources and materials for preparation are described below. For the reading section you should practice reading  and expand vocabulary. For the listening section you should listen to lections and conversations in English. Do not afraid and start writing essay to prepare for the writing section. You should study to speak English well, so it is good idea to find english-speaking friends and talk with them through the Skype.


First of all, it is necessarily to be familiar with a structure of the test. You can purchase some official sample tests ets.org/toefl. Or there is free samples
http://www.stuff.co.uk/toefl.htm.


Your vocabulary is very important. Use wordstep.com to build your vocabulary.
Read news and articles interesting for you in English.

 Voice of America ( http://www.voanews.com/learningenglish) is a  very useful resource where you can listen to news and interesting programs, and  you can read the same text. Grammar video lessons (engvid.com) would be helpful  for you if you feel lack of enough confidence in English grammar, but also it would be useful for the listening section.


Finally, If you will read a lot, attentively listen to English speech,  speak with someone in English, write and show you attemps of essay writing you will have not only high score on the TOEFL but also be able to use English in your life.

Department of Mechanics and Mathematics

Department of Mechanics and Mathematics is one the largests department in Novosibirsk State University. Pure mathematics is mostly studied on the department and even applied mathematics is studied from theoretical side of views. Lots of graduates don't stay in research institutes nor in University. Usually, they do something that isn't directly connected to mathematics.

Words and Their Stories: Number Phrases (Part 2)

Words and Their Stories: Number Phrases (Part 2)

Math Forum: Rene Descartes (Chameleon Graphing: Plane History)

Math Forum: Rene Descartes (Chameleon Graphing: Plane History):

Про то, как Декарт не использовал отрицательные числа. 

How to Write a Letter

How to Write a CV (Curriculum Vitae)

How to Write a Curriculum Vitae

How to Write a Good Resume or CV

LaTeX CV Template

Game Theory — Open Yale Courses

Game Theory — Open Yale Courses

Fundamentals of Physics with Ramamurti Shankar

YouTube - Broadcast Yourself.

http://oyc.yale.edu/physics/fundamentals-of-physics/

Course | Modern Physics: Classical Mechanics

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YouTube - Broadcast Yourself.

http://epgy.stanford.edu/courses/physics

MATH E-102 Sets, Counting, and Probability | Harvard Extension School

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MATH E-102 Sets, Counting, and Probability | Harvard Extension School: "Pro"

Set of problems

~1~

MIT 18.01 Single Variable Calculus

MIT 18.01 Single Variable Calculus, Fall 2006 (playlist)

('http://www.youtube.com/p/590CCC2BC5AF3BC1?version=3&hl=ru_RU',)

http://www.archive.org/details/MIT18.01JF07/

p.s. But actually it rather improve my English then math ;)