Some of the things I have written about
Graduate
Some notes on Category Theory. An introduction is found in most of the graduate algebra books.
Undergrad
Solutions to some exercises from Tripos, ISIBangalore BMath. A note on the question whether Z[sqrt(2)] and Z[i] are isomorphic.
This article is about a minor modification of a proof in Rudin's Principles of Mathematical Analysis.
Review of some theorems and exercises in Analysis I.
Some theorems and exercises from Abstract Algebra, Dummit and Foote.
Some review notes on General Topology.
An instructive article on uniform continuity.
Some notes, solutions and errata - Bourbaki Algebra I, initial sections
Solutions to some of the problems from UPSC Maths optional.
High School
Review slides of some results in Trigonometry. More results will be added to these slides.
Some review notes on Solid Geometry. More results and problems will be added to these notes.
Review slides of some results in Elementary number theory. More results will be added to these slides. A collection of problems and solutions on the topic of diophantine equations. More will be added to it later. "An introduction to Diophantine equations A problem-based approach (Titu Andreescu, Dorin Andrica etc.)" is a good example of a book that treats the subject, which otherwise seems to be a study of eclectic problems, with a certain method and order. The coverage is complete to a large extent at this level and inspires the readers to solve more such problems.
Review slides of some results in Euclidean/Modern/Projective Geometry as well as geometric transformations. More results will be added to these slides and probably there will be a reordering of the topics. Euclidean refers to the results from the 13 extant works of Euclid. Modern refers to more results about triangles and its associated circles after Euclid. Geometric transformations such as isometries, homotheties, spiral similarities, affinities, projectivities and inversions form groups and are probably more recent than what is referred here as modern. References are Euclid, Durell's Modern Geometry, Yaglom's Geometric Transformations, Russell's Treatise on Pure Geometry.
Review notes on geometry of some plane curves in the real plane.
A note on the use of complex numbers in Euclidean geometry. Will probably add more applications and properties to it later. Professor Titu has written an excellent book on this topic.
A handout on the problem of computing antiderivatives of rational functions using partial fractions.