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I recently completed my Master’s in Mathematics in Pure Mathematics from the University of Waterloo in Ontario, Canada. As you can conclude, this makes me a mathie to the core. On this page I have added several links to math websites that I often visit and some of the work I have done over the last few years. Feel free to email me if you have any questions or would like to discuss anything math related!
Papers Apery’s Recurrences and Beuker’s Integrals I worked on this paper with Prof. Pavlos Tzermias of the University of Tennessee, Knoxville in the summer of my first year (2004) while attending the REU at UTK. The paper lays out an elementary proof of the equivalence of two different rational approximations to ζ(2). A Topological Proof of the Infinitude of the Primes This proof was shamelessly stolen from the excellent book, Proofs from the Book for a talk I gave at the Short Attention Span Math Seminars. Chen’s Theorem says that every sufficiently large even number can be written as the sum of a prime and a number that is the product of at most two primes. It is the closest result to Goldbach we have to date. This paper was written jointly with Adam Felix and Eugene Eisenstein in Fall 2005 for PMATH 744: The Circle Method, taught by Prof. Yu-Ru Liu. This paper is based off the exposition of Nathanson in Additive Number Theory. Reader Beware: the paper is full of typos we never got a chance to fix. Notes on Elliptic Curves and Modular Forms These notes were for CO 690, a course on Elliptic Curves and Modular Forms I took with Cameron Zwarich, Lloyd Eliott, and Koray Karabina in Winter 2007. In the paper on Weil Pairing, I give some corrections to a mistake in Silverman’s, Arithmetic of Elliptic Curves. Koblitz’s Conjecture for Drinfeld Modules A link to my thesis. My thesis work was supervised by Prof. Wentang Kuo and Prof. Yu-Ru Liu and was in collaboration with Lloyd Eliott. A problem set I created for the Fall 2007 Waterloo Math Circles. A Linear Algebra Proof of the Fundamental Theorem of Algebra A paper I wrote for PMATH 800: Lie Groups, taught by Prof. Wentang Kuo in Fall 2007. Though this has nothing to do with geometry or Lie Groups, the proof is still wicked. Notes for a talk I gave for Prof. Liu’s Math 145 class in Fall 2007 on the connections between music and Diophantine Approximations. By no means is this list complete. As I find more talk slides, notes, or pdf’s of papers, I will try to add them.
Links General Math Planet Math Notes These notes were taken by Chris during undergrad and were an invaluable resource. Currently they are being hosted by Cameron Zwarich. These notes are from various courses given at the University of Waterloo by Prof. Cameron Stewart . The notes on Diophantine Approximations are an invaluable introduction. These notes in a variety of topics from algebra and number theory were an invaluable source during my undergrad. I highly recommend the algebraic number theory notes as an introductory text that places proper emphasis on valuations and local theory. Neukirch provides an excellent follow up to these notes.
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