Courses

Topological spaces. Basis for a topological space. Separation and countability properties. Limit points, closure and interior. Connectedness, compactness, subspace topology. Homeomorphism, continuity, metrizability. General product spaces and the general...

(Principle of least action, Hamilton's equation, Poisson brackets. Liouville's equation.) Canonical transformations. Symmetry and conservation laws.
Postulates of quantum mechanics, the wave formalism. Dynamical variables. The Schrodinger equation...

This course covers results of elementary number theory. Topics include:divisibility and factorization; congruences; arithmetic functions; quadratic residues; the primitive root theorem; continued fractions and topics from computational number theory.

Scalar and vector fields, grad, div and curl operators. Orthogonal curvilinear coordinates. Electrostatics: charge, Coulomb's law, the electric field and electrostatic potential, Gauss's law, Laplace's and Poisson's equations. Conductors in...

Probability functions, random variables and their distributions, functions of random variables; basic theorems for functions of independent random variables, characteristic function of a random variable; central limit theorem, random walks and martingales;...

Rigid body motion, rotation about a fixed axis. General motion in a plane, rigid bodies in contact, impulse. General motion of a rigid body. Euler-Lagrange equations of motion.

1-dimensional dynamics: damped and forced oscillations. Motion in a plane: projectiles, circular motion, use of polar coordinates and intrinsic coordinates. Two-body problems, variable mass. Motion under a central, non-inertial frame. Dynamics of a system of...

 Boolean algebra. Combinatorics languages and grammars. Recurrence relations, generating functions and applications. Problems of definition by induction: no closed form, infinite loops and the halting problem. Algorithms: correctness, complexity,...

Multi-dimensional root-finding. Optimization. Non-linear systems of equations. Eigenvalues. Numerical methods for ordinary differential equations and for partial differential equations.

Error analysis. Rootfinding; 1 and 2 point methods. Linear systems of equations, matrix algebra, pivoting. Analysis of algorithms. Iterative methods. Interpolation,polynomial approximation, divided differences. Initial value problems, single and multistep...