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**Unformatted text preview: **Over the past two years I have gained a significant amount of knowledge in mathematics. So far, I have taken courses in Calculus, Linear Algebra and Differential Equations, Real Analysis, Number Theory, and a research seminar on Cryptography, taught by Professor Ken Ribet. I am currently taking courses in Linear Algebra and Abstract Algebra, although I have picked up a lot of information on Abstract Algebra from the work I did in Cryptography. I have also done research under a math education graduate student at UC Berkeley involving abstract algebra and computer programming. I have become particularly interested in Number Theory and Algebra this past fall. Using An Introduction to The Theory of Numbers by Niven, Zuckerman, and Montgomery, I learned about Divisibility, Congruences, Quadratic Reciprocity, Quadratic Forms, and Simple Continued Fractions. The cryptography seminar I took also really allowed me to explore number theory Fractions....

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