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Physics

I've taken almost the equivalent of a masters degree in physics during my undergrad. This included a term of classical mechanics, 2 terms of electricity and magnetism, a term of waves, 2 terms of statistical mechanics, 4 terms of quantum mechanics, 2 terms of quantum field theory, and 2 terms of general relativity as well as several mathematical physics classes. I have also done mathematical physics research.

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Guitar

I have been playing guitar for 9 years. I have played several styles of music-- I started off playing rock music, moving to metal and post hardcore. I played for my high school jazz band, and have recently started learning classical guitar. I have played with several music ensembles, including being a song writer and guitarist for a band that played around 70 shows of all original songs.

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Discrete Math

I took 2 terms of the graduate level combinatorics and discrete math at Caltech. Topics covered include graph theory, extremal problems, flows in networks, counting, recursions, generating functions, partitions, posets, latin squares, finite geometry, counting using generating functions, Mobius inversion theorem, Polya enumeration, and Young tableux. Can submit transcript if necessary.

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Differential Equations

I took a term of differential equations at Caltech. This included ODEs and PDEs, difference equations, dynamical systems, and both qualitative and quantitative analysis of population dynamics and physical systems dynamics. I also tutored for the advanced undergraduate/intro graduate level PDEs class at Caltech. Can submit transcript if necessary.

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Linear Algebra

I took a term of basic linear algebra covering the basic things such as vector spaces, subspaces, quotient spaces, orthogonal complements, linear transformations, matrices, determinant, trace, change of basis, Gramm-Schmidt orthogonalization, vector spaces over more general fields, inner products, etc. I have taken 2 years of abstract algebra, which is a generalization of linear algebra, and am going on to get my PhD in algebraic geometry, a heavily linear algebra-based field. Furthermore, I have...
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Logic

I just graduated from Caltech with a BS with Honors in Math. I took one term of logic at Caltech covering basic logic, propositional calculus, first order logic, the syntax and semantics of formal languages, formal proofs, Godels incompleteness, and computatbility theory. I have also tutored other students taking the same class. I can submit my transcript if necessary.

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Electrical Engineering

I took 2 terms of a Caltech class on electricity and magnetism, which included several weeks on circuits, including basic DC circuits, Kerchoffs voltage and current laws, Ohms law, power drop, AC circuits, impedance, inductors, capacitors, dynamics of circuits, and Thevenin and Norton equivalents. Furthermore, I have tutored people in the introduction to electrical engineering class at Uconn.