Here I shall be uploading my $\LaTeX$ 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)