Introduction and development of some basic algebraic structures - groups, rings, fields.

Introduction and development of some basic algebraic structures - groups, rings, fields including Galois theory, representations of finite groups, algebras.The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.

Selected topics concerning fields, including Galois theory.

Galois theory and related topics.

Calculus of one variable: Real and complex numbers, vectors, functions, limits, sequences, series, power series, differentiation and integration in one variable, introduction to ordinary differential equations

Calculus in several variables; differential equations

The lecture course covers basic notions of mathematical logic, set theory, algebra, elementary number theory, graph theory, and combinatorics.

Introduction to differential calculus and integration in several variables.

Complex functions of one variable, Cauchy-Riemann equations, Cauchy theorem and integral formula, singularities, residue theorem, special functions, conformal mappings, Riemann mapping theorem.

No description available.

Introduction to the theory of vector spaces for students of mathematics or physics: Basics, vector spaces, linear transformations, solutions of systems of equations, matrices, determinants, endomorphisms, eigenvalues, eigenvectors.

Eigenvalues and eigenvectors, Jordan normal form, bilinear forms, euclidean and unitary vector spaces, spectral theorem, multilinear algebra, tensor product

This course will give an introduction to various aspects of number theory, both algebraic and analytic.