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transphenomen

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Introduction to Partial Differential Equations. This is not a proof class.

Fourier series, orthogonal expansions, and eigenvalue

problems. Sturm-Liouville theory. Separation of variables

for partial differential equations of mathematical physics,

including topics on Bessel functions and Legendre polynomials.

Elements of Complex Analysis. This is not a proof class.

Complex numbers and functions. Analytic functions,

harmonic functions, elementary conformal mappings.

Complex integration. Power series. Cauchy’s theorem.

Cauchy’s formula. Residue theorem.

Number Theory. Proof class.

Elementary number theory with applications. Topics

include unique factorization, irrational numbers, residue

systems, congruences, primitive roots, reciprocity

laws, quadratic forms, arithmetic functions, partitions,

Diophantine equations, distribution of primes. Applications

include fast Fourier transform, signal processing, codes,

cryptography.

Differential Geometry. Not a proof class.

Differential geometry of curves and surfaces. Gauss and

mean curvatures, geodesics, parallel displacement, Gauss-

Bonnet theorem.

Introduction to Topology. Proof class.

Topological spaces, subspaces, products, sums and quotient

spaces. Compactness, connectedness, separation

axioms. Selected further topics such as fundamental group,

classification of surfaces, Morse theory, topological groups.

These are all undergraduate courses and so should not be too hard. I would like for you guys to help rank them not just in how useful they are for statistics, but how well they would increase my breath of understading of mathematics in general. These courses also have an additional course or two that continue on from the last class in case you guys think that studying a specific subject in depth would be better than just skimming many subjects.