| Number | Title | ECTS | Hours | Lecturers |
|---|
| 252-4220-00L | A Taste of Research: Algorithms and Combinatorics  | 2 credits | 2S | B. Gärtner,
J. Matousek,
A. Steger,
E. Welzl,
P. Widmayer |
| Abstract | Students work together with lecturers on open problems in algorithms and combinatorics. |
| Learning objective | The goal is to learn and practice important research techniques: literature search, understanding and presenting research papers, developing ideas in the group, testing of conjectures with the computer, writing down results. |
| Content | Work on original research papers and open problems in the areas of algorithms and combinatorics. |
| Lecture notes | Not available. |
| Literature | Will be announced in the seminar and on the seminar's web page. |
| Prerequisites / Notice | Passed first-year exam. |
| 263-4205-00L | Polynomials | 4 credits | 2V + 1U | J. Matousek,
E. Welzl |
| Abstract | Algebraic methods belong among the most powerful and succesful mathematical tools in computer science and discrete mathematics. The course covers a number of results, some of them fairly recent, whose proofs illustrate general techniques. |
| Learning objective | Extending the knowledge of mathematical methods that proved useful in recent research related to theoretical computer science. The students should understand several successful ideas of applying the properties of multivariate polynomials to various problems. |
| Content | From the wide area of algebraic methods, we focus mainly on applications of polynomials, and we will encounter some of the elementary concepts of algebraic geometry. Here are some of the main themes: Dimension arguments using spaces of polynomials. Matchings and determinants. Randomized testing of polynomial identities. Space partitions using polynomials and geometric incidence theorems. "Contagious vanishing" arguments, geometry of lines in space. |
| Lecture notes | One part of the lecture will follow the book "Thirty-three miniatures" by J. Matousek. The rest will be based on recent research papers and on a book in preparation by Larry Guth. |
| Literature | J. Matousek: Thirty-three miniatures, Amer. Math. Soc. 2010 |
