Syllabus

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: 14.04.2025 - 28.05.2025

Teacher in charge (valid for whole curriculum period):

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

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

CEFR level (valid for whole curriculum period):

Language of instruction and studies (applies in this implementation):

Teaching language: English. Languages of study attainment: English

CONTENT, ASSESSMENT AND WORKLOAD

Content

• valid for whole curriculum period:

  Here is tentative content (each part is 2-week long):

  • Part I: Extremal combinatorics & computation: We cover extremal combinatorics (e.g., Ramsey's theory) through the lens of graph algorithms and data structures.
    
    
  • Part II: Probability & computation: We introduce probabilistic combinatorics through the lens of algorithms. We show applications such as streaming algorithms and graph sparsification. You will also see the boundaries between constructive and nonconstructive methods in combinatorics, which highlight the transfer of techniques between combinatorics and computation.
    
    
  • Part III: Linear algebra & computation: In the final part, we go through linear algebra concepts via applications in spectral graph algorithms and (time permitting) analysis of Boolean functions. You will see the applications of random walks, spectral clustering, average case analysis, etc. 
  There will be handouts for all the materials.

Assessment Methods and Criteria

• valid for whole curriculum period:

  Contribution to the course wiki. Exercises. Independent project. 

Workload

• valid for whole curriculum period:

  Lectures. Exercise sessions. Independent work.

DETAILS

Study Material

• valid for whole curriculum period:

  Lecture notes and selected book chapters.  

Substitutes for Courses

• valid for whole curriculum period:

  Substitutes for Courses

Prerequisites

• valid for whole curriculum period:

  Prerequisites

FURTHER INFORMATION

Further Information

• valid for whole curriculum period:

  Teaching Language: English

  Teaching Period: 2024-2025 Spring V
  2025-2026 Spring V

Description