Trinity Essay - Over the past two years I have gained a...

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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 
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