Advanced design and analysis methods for algorithms and data structures: Random(ized) Search Trees, Point Location, Minimum Cut, Linear Programming, Randomized Algebraic Algorithms (matchings), Probabilistically Checkable Proofs (introduction).

The course is concerned with approximate geometric methods for the analysis of large data sets represented by point clouds. Concrete topics areLow Distortion Embedding, Approximate Nearest Neighbor Search, Semi Definite Programming, Approximations and Nets, Approximate Smallest Enclosing Balls and Boxes, Directional Width, Support Vector Machines.

This course covers the classic material of computational geometry,concerned with the design and analysis of algorithms and datastructures for geometric problems in low dimensions (mostly twoand three).

This lecture is an introduction to programming based on the language C++;at the same time we present important theoretical concepts that are at the heart of programing. In the first part, we speak about the concepts "Problem", "Program", and "Algorithm" , and we discuss the theoretical limitations of programming. The C++ part is subdivided into "Foundations", "Functions", and "Classes".

In this module, basic paradigms and techniques in working with data will be discussed, especially towards data security, managing data decentrally, and learning from data.

This course provides an introduction to computer science concepts that are foundational for later work in the CAS and MAS programme.

Geometric structures are useful in many areas, and there is a need to understand their structural properties, and to work with them algorithmically. The lecture addresses theoretical foundations concerning geometric structures. Central objects of interest are triangulations. We study combinatorial (Does a certain object exist?) and algorithmic questions (Can we find a certain object efficiently?)

This seminar complements the course Geometry: Combinatorics & Algorithms. Students of the seminar will present original research papers, some classic and some of them very recent.

Introduction to linear algebra: vectors and matrices, solving systems of linear equations, vector spaces and subspaces, orthogonality and least squares, determinants, eigenvalues and eigenvectors, singular value decomposition and linear transformations. Applications in and links to computer science will be presented in parallel.

This course provides an in-depth theoretical treatment of optimization methods that are relevant in data science.

Students present current or classical results from theoretical computer science.

Las-Vegas & Monte-Carlo alg; inequalities of Markov, Chebyshev, Chernoff; negative correlation; Markov chains: convergence, rapidly mixing; generating functions; Examples include: min cut, median, balls and bins, routing in hypercubes, 3SAT, card shuffling, random walks

Presentation of recent publications in theoretical computer science, including results by diploma, masters and doctoral candidates.

Presentation of recent publications in theoretical computer science, including results by diploma, masters and doctoral candidates.