I plan to put up articles related to the Olympiads in the following broad categories:
- Introductory articles on number theory, combinatorics, inequalities, polynomials, functional equations, triangle geometry etc.
- Thematic articles on various topics in number theory, combinatorics, inequalities, etc.
The material is suited for self study for students in tenth class and above. It is also largely accessible to younger students, but some guidance may be required as all the necessary prerequisites may not have been covered. It may also form a basis for classroom lectures to students. Those interested in using the material for instruction can mail me so that I can send them an instructor's guide, for deriving maximum mileage from the material.
Introductory articles available right now:
- Introduction to inequalities: This is based on a talk I gave on 15th January 2007 at P.S. Senior Secondary School, Mylapore in an INMO Training Camp organized by the Association of Mathematics Teachers of India.
Thematic articles available right now:
- Co-incidence Problems and Methods (PDF format): An article describing techniques for proving collinearity and concurrence
- Touring Problems : A Mathematical Approach (PDF format): An article describing the knight's tour and related problems
- Optimization methods in planar geometry (PDF format): An article describing various approaches to optimizing functions of points and configurations in the plane.
- Construction problems (PDF format): An article describing various approaches to construction problems, including the contrast between top-down and bottom-up approaches, the use of greedy algorithms, and some other useful tricks.
Part of the subject material of both the articles was covered by me in a training session for high school students under the AMTI (Association of Mathematics Teachers of India) camp, being held in Chennai (July-October 2005).
Also available now are the Miscellaneous problems discussed in the AMTI camp (PDF format). These problems hav already been discussed in the past few weeks, during the AMTI sessions. (The discussion has been updated last on 22nd September, 2005). Further problem discussions shall be incorporated into the file as required.
Those interested in other formats or the LaTeX source of the articles can contact me at my email address (vipul at cmi dot ac dot in).
In case of any queries, comments or suggestions regarding the articles, please feel free to contact me at vipul at cmi dot ac dot in.