Ill be a 3rd-yr physics student next year, and due to course conflicts, Ill have to study one of these three math classes on my own (ie, without going to lectures). Which of these would be more useful for theoretical physics (probably in String, LQG and the likes): Analysis III - Real numbers; completeness properties. Metric spaces; compactness and connectedness, continuous functions. Contraction mappings. Sequences and series of functions; modes of convergence, power series. Topics on function spaces such as: Weierstrass approximation, Fourier series and L2 spaces. Analysis III is also a prerequisite to Manifold Theory and Lie Groups Applied Linear Algebra - Vector and matrix norms. Schur canonical form, QR, LU, Cholesky and singular value decomposition, generalized inverses, Jordan form, Cayley-Hamilton theorem, matrix analysis and matrix exponentials, eigenvalue estimation and the Greshgorin Circle Theorem; quadratic forms, Rayleigh and minima principles. The theoretical and numerical aspects will be studied. General Topology - Countability, Compactness (Local, Para, Sequential), Projective Spaces, Zoo of Quotient Spaces Ive taken: ODE Calculus I/II, Analysis I/II Linear Algebra Intro / I Group Theory Applied Algebra Intro to Topology Thanks.