Here I shall be uploading my notes. More will be updated. Comments are welcome.

- I recently came across (in the Purdue Math library) very old notes distributed in conjunction with a lecture (series?) by Armand Borel titled “Algebraic groups and Arithmetic groups”. I decided it was valuable, with relations of algebraic groups to topology and number theory, so decided to type it. (17/11/2012) [Click to download]

- Notes on the
**Hasse-Minkowski’s Theorem**[Click to download] (Main source was J-P Serre’s*Course in Arithmetic*. Serre is known as one of the best expositors of all time; I clarified explanations and added justifications in his proofs, but didn’t try to improve upon his style and overall presentation.)

- I have prepared a formula-list of the lecture notes on
**Fourier Series**for quick reference. [Click to download] (Last updated: 19/02/2010)

**Dirichlet’s Unit Theorem:**It describes the structure of units of the ring of algebraic integers of a number field, similar to the structure theorem on finitely generated Abelian groups. [Click to download]

- The proof of a beautiful theorem in point-set topology due to Kuratowski. [Click to download]

- Lecture notes in Representation theory by Prof Vijay Kodiyalam. It mainly contains double centralizer theorem and Wedderburn’s classification of semisimple algebras. [Click to download] (Last updated: 26/01/2011)

- Using the
**Universal Mapping property**in proving results in Commutative (Homological?) Algebra. [Click to download] (Last updated: 11/02/2011)

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April 3, 2010 at 12:28

AnonymousGreat work!! But should not have copyrighted it!! 🙂