This page is home to an English translation a of course that was taught by Misha Verbitsky and Dmitry Kaledin at the Independent University of Moscow in the fall of 2004 (also known under the name “Trivium”). The course was targeted for first-year students, so the prerequisites include only elementary high-school mathematics. It covers a broad range of material that the authors believe is fundamental for one's mathematical education, and culminates in algebraic Galois theory and Galois coverings theory. It builds upon simple and straightforward definitions and lots of exercises, so the only serious requirement from someone taking the course is to be patient and steady.

The students who took this course in Moscow were presented with the following set of rules: for each chapter they had to either solve all the problems without an asterisk or solve all the problems marked with an asterisk (in case they thought that the problems without an asterisk were too easy or boring). Problems marked with “!” are vital for the development of the course and must have been solved by everyone. If one had solved k problems with double asterisk than they had a right to skip 2k problems with a simple asterisk.

But of course you can solve all the problems if you like.

Good luck !

Algebra

Geometry

You can find the LaTeX source for Algebra and Geometry here.

Lecture notes in measure theory

Dmitrii Pasechnik has started translation of a supplement course in measure theory. The translation is available on this page under the same license as the rest of "Trivium".

You will need listki-mera.tex file to compile from LaTeX source.

Creative Commons License
This work is licensed under a Creative Commons License.

Last updated: 2012-11-05 00:36:16 +0400