This course is an introduction to the theory of Riemann surfaces. Riemann surfaces naturally appear is mathematics in many different ways: as a result of analytic continuation, as quotients of complex domains under discontinuous group actions, as algebraic ...
P-adic numbers are a number theoretic analogue of the real numbers, which interpolate between arithmetics, analysis and geometry. In this course we study their basic properties and give various applications, notably we will prove rationality of the Weil Ze ...
Singular cohomology is defined by dualizing the singular chain complex for spaces. We will study its basic properties, see how it acquires a multiplicative structure and becomes a graded commutative algebra. We study an algebraic version, namely group coho ...
The course introduces the paradigm of quantum computating in an axiomatic way. We introduce the notions of quantum bits, gates, and circuits. We introduce themost important quantum algorithms. We also touch upon error-correcting codes. This course is indep ...
Algebraic geometry is the common language for many branches of modern research in mathematics. This course gives an introduction to this field by studying algebraic curves and their intersection theory. ...
The course is about the derivation, theoretical analysis and implementation of the finite element method for the numerical approximation of partial differential equations in one and two space dimensions. ...
This is an introductory course on Elliptic Partial Differential Equations. The course will cover the theory of both classical and generalized (weak) solutions of elliptic PDEs. ...
Quantum mechanics is one of the most successful physical theories. This course presents the mathematical formalism (functional analysis and spectral theory) that underlies quantum mechanics. It is simultaneously an introduction to mathematical physics and ...
The monstrous moonshine is an unexpected connection between the Monster group and modular functions. In the course we will explain the statement of the conjecture and study the main ideas and concepts leading to its proof. Our final goal is to study Borc ...