Sorry- I would like to study some 2nd-year courses that I have the prerequisites for but not the time/credits to study next year, so I am looking for material at a fairly introductory level. There are no recommended books and the lecture notes are not made public, but these are some of the main topics included according to the course webpages:
Algebra:
Abstract vector spaces, linear transformations, multilinear algebra of determinants, eigenvectors and eigenvalues, fields, rings and modules, quotients, isomorphism theorems, Sylow theorems, Cayley-Hamilton theorem, inner product spaces, spectral theorem, Jordan normal form, Galois groups.
Geometry:
Curves in Euclidean space, Frenet-Serret frame, curvature and torsion, vector fields, differential forms, Poincare’s lemma, connection forms, structure equations, surfaces, isometries, geodesics on surfaces, integration of forms, Stoke’s theorem, Gauss-Bonnet theorem, Euler characteristic
Statistics:
Random walks, stirling’s approximation, moment generating functions, Fourier transform of probability distribution, central limit theorem, error function, least squares fitting, residuals, error analysis, Kolmogorov-Smirnov test
