Undergraduate Course PlansSecond year, Semester 1Key Courses:
Topics include systems of ordinary differential equations, multiple integrals, vector spaces, eigenvalue problems. Topics include theory of finite groups, rings and fields, abstract vector spaces over arbitrary fields, number theory.
Topics include limits and continuity, differential and integral calculus, convergence of sequences and series, Taylor series expansions. Second year, Semester 2Key Courses:
Topics include systems of ordinary differential equations, multiple integrals, vector spaces, eigenvalue problems. Topics include Laplace transforms, Fourier series, phase plane analysis, stability of solutions, partial differential equations. Topics include dynamics of a single particle, Lagrange's and Hamilton's equations of motion, principles of relativity, Lorentz transformations.
Topics include numerical methods for solving nonlinear equations, linear systems, integration, differentiation and data fitting. Topics include the uncertainty priciple, the Schrodinger equation, perturbation theory, the harmonic oscillator, the hydrogen atom, systems of identicle particles. This course does have a laboratory component. Third/Fourth year, Semester 1Key Courses:
Topics include nonlinear ordinary differential equations, existence, stability and bifurcations of stationary points and periodic orbits. Topics include complex numbers, analytic functions, conformal mappings, power series and integration using residues.
Topics include metric spaces, elements of topology, compactness, completeness, normed, Banach & Hilbert spaces, Riesz representation theorem. Third/Fourth year, Semester 2Key Courses:
Topics include heat conduction, fluid flow, potential theory Topics include Lie groups, Lie algebras, the theory of representations. Topics include integrable quantum systems, exact solutions of models, models for quantum tunneling, quantum magnets, superconductivity, boson gas.
Topics include classical chaos, mesasures of chaos, nonlinear quantum dynamics, nonlinear quantum maps. Topics include pseudoRiemannian spaces, tensors, covariant differentiation, geodesics and curvature. Topics include numerical solution of ordinary and partial differential equations as models for physical problems, producing reports using the LaTex environment. 
