On this page you will find a collection of some of my past work and random interesting downloads I've come across. I intend to update this periodically with some of my short articles, presentations, and talks, as well as my extensive archive of homework sets and solutions from my previous course work.
Articles
This is an article I wrote as a grader for UC Berkeley's undergraduate number theory course explaining the technical details of the RESSOL algorithm provided by Niven, Zuckerman, and Montgomery in their classic text, "An Introduction to the Theory of Numbers", Fifth Edition. The RESSOL algorithm is used to find solutions to the quadratic congruence x^2 congruent to a (mod p). The interested reader can refer to pages 110 - 114 of the text for more information.
Papers
As part of my History of Mathematics course at UC Berkeley, we had to write two papers, both using primary sources. For my first paper, I focused on the work of Diophantus, using a primary source from the 1600's. What's cool was I managed to find a typo --- and the source is in French!
My second paper, which turned out to be an original explanation of one of Gauss' eight proofs of the Quadratic Reciprocity Law. The length requirement for the paper was about 4 pages, double-spaced. This one's 24 pages, single-spaced...ouch! Definitely a very fun and worthwhile project. This material also served as my first Sophex talk at UT Austin. SOPHomore EXchange, Sophex for short, is a weekly seminar targetted at first and second year Math Ph.D. students at UT Austin.
Talks/Presentations
To conclude our undergraduate number theory course, the professor made us give short, 15-20 minute talks on an interesting application of number theory. This one's a sheer delight since it highlights the beauty of simple, elementary number theory.
I took a seminar with Professor Kenneth Ribet titled "Rational Points on Elliptic Curves". We used the book of the same name by Tate and Silverman. I delivered two lectures, but sadly typed up only the second one.
Fun Stuff
There's an interesting anomaly to be explained in the picture. How is it possible to cut up the 8 by 8 square and assemble the pieces, as shown, into a 5 by 13 rectangle?
Problem-Solving
One of the best and most active weekly problem-solving contests is run by the Mathematics Department at Purdue University. Above and below are three solutions I submitted during the Fall 2003 semester.
A collection that only got 2 pages far. This file contains problems and some solutions that I particularly like from Loren Larson's book, "Problem Solving Through Problems".
Contact Information
Gagan Tara Nanda
RLM 12.136
(512) 475-8688