### CS-E4555 - Combinatorics D, 19.04.2021-27.05.2021

Please note! Course description is confirmed for two academic years (1.8.2018-31.7.2020), which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.

#### LEARNING OUTCOMES

In this course, students will get familiar with combinatorics through selected exciting ideas in theoretical computer science (in particular, algorithms and complexity). You will obtain a basic understanding of various types of combinatorial objects and their relationships. Upon completing the course you are able to apply basic combinatorial analysis and proof techniques.

Credits: 5

Schedule: 19.04.2021 - 27.05.2021

Teacher in charge (valid 01.08.2020-31.07.2022): Parinya Chalermsook

Teacher in charge (applies in this implementation): Parinya Chalermsook

Contact information for the course (applies in this implementation):

CEFR level (applies in this implementation):

Language of instruction and studies (valid 01.08.2020-31.07.2022):

Teaching language: English

Languages of study attainment: English

##### Content
• Valid 01.08.2020-31.07.2022:

• Forbidden Structures, Geometry, and Data structures: Davenport-Schinzel Sequences, Zarankiewitz problems
• Algorithms through Ramsey-type results: Independent set and graph coloring
• Concentration Inequalities: Chernoff bound and Martingale, applications in algorithms design.
• Lovasz Local Lemma: Algorithmic Proofs and applications in routing.
• Set systems, VC-dimension, epsilon-nets, and discrepancies: Applications in computational geometry.

##### Assessment Methods and Criteria
• Valid 01.08.2020-31.07.2022:

Contribution to the course wiki. Exercises. Independent project.

• Valid 01.08.2020-31.07.2022:

Lectures. Exercise sessions. Independent work.

#### DETAILS

##### Study Material
• Valid 01.08.2020-31.07.2022:

Lecture notes and selected book chapters.

##### Prerequisites
• Valid 01.08.2020-31.07.2022:

First- and second-year BSc-level mathematics, including an introduction to discrete mathematics (e.g. MS-A040x) and basic probability (e.g. MS-A050x)