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I will put here an English translation of a course that was taught by Misha Verbitsky and Dmitry Kaledin at the Independent University of Moscow in the fall of 2004. The course was targeted to freshmen. Thus the preliminaries of the course is only elementary high-school mathematics. If you are patient enough to go through all the course you will learn a lot of interesting things (for example, algebraic Galois theory and Galois coverings theory) not to mention the general mathematical culture that you will acquire. The course builds upon simple and straightforward definitions and lots of exercises, so the only serious requirement from you is to be patient and steady.
Although the course is intended for the freshmen, it can be useful to anybody. The rules are simple: read the course and do the exercises, for each chapter of the course you should either solve all the problems without an asterisk or marked with an asterisk (if you think that you are an advanced student or if you get bored solving problems without an asterisk). Problems marked with (!) are vital for development of the course and must be solved by everyone. If you have solved k problems with double asterisk than you can skip 2k problems with a simple asterisk.
And of course you can solve all the problems !
Good luck !
August 30, 2006. Dmitrii Pasechnik started translation of a supplement course in measure theory. The translation will be available on this page under the same license as the rest of "Trivium".
May 2, 2005. I created a wiki for this translation project.
You can find the LaTeX source for Algebra and Geometry here.
You will need listki-mera.tex file to compile from LaTeX source.
This work is licensed under a Creative Commons License.
Last updated: Tuesday, July 10, 2007 17:00:38 +0200