# 401-3055-64L  Algebraic Methods in Combinatorics

 Semester Autumn Semester 2017 Lecturers B. Sudakov Periodicity non-recurring course Language of instruction English

### Courses

NumberTitleHoursLecturers
401-3055-64 VAlgebraic Methods in Combinatorics2 hrs
 Wed 10:15-12:00 HG D 5.2 »
B. Sudakov
401-3055-64 UAlgebraic Methods in Combinatorics1 hrs
 Mon 15:15-16:00 CAB G 11 »
B. Sudakov

### Catalogue data

 Abstract Combinatorics is a fundamental mathematical discipline as well as an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years. This course provides a gentle introduction to Algebraic methods, illustrated by examples and focusing on basic ideas and connections to other areas. Learning objective Content Combinatorics is a fundamental mathematical discipline as well as an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years. While in the past many of the basic combinatorial results were obtained mainly by ingenuity and detailed reasoning, the modern theory has grown out of this early stage and often relies on deep, well-developed tools.One of the main general techniques that played a crucial role in the development of Combinatorics was the application of algebraic methods. The most fruitful such tool is the dimension argument. Roughly speaking, the method can be described as follows. In order to bound the cardinality of of a discrete structure A one maps its elements to vectors in a linear space, and shows that the set A is mapped to linearly independent vectors. It then follows that the cardinality of A is bounded by the dimension of the corresponding linear space. This simple idea is surprisingly powerful and has many famous applications.This course provides a gentle introduction to Algebraic methods, illustrated by examples and focusing on basic ideas and connections to other areas. The topics covered in the class will include (but are not limited to):Basic dimension arguments, Spaces of polynomials and tensor product methods, Eigenvalues of graphs and their application, the Combinatorial Nullstellensatz and the Chevalley-Warning theorem. Applications such as: Solution of Kakeya problem in finite fields, counterexample to Borsuk's conjecture, chromatic number of the unit distance graph of Euclidean space, explicit constructions of Ramsey graphs and many others.The course website can be found at https://moodle-app2.let.ethz.ch/course/view.php?id=3770

### Performance assessment

 Performance assessment information (valid until the course unit is held again) Performance assessment as a semester course ECTS credits 6 credits Examiners B. Sudakov Type session examination Language of examination English Repetition The performance assessment is only offered in the session after the course unit. Repetition only possible after re-enrolling. Mode of examination written 180 minutes Written aids It is an open books exam. This information can be updated until the beginning of the semester; information on the examination timetable is binding.

### Learning materials

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### Groups

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### Restrictions

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### Offered in

ProgrammeSectionType
Doctoral Dep. of Information Technology and Electrical EngineeringDoctoral and Post-Doctoral CoursesW
Electrical Engineering and Information Technology MasterRecommended SubjectsW
Computer Science MasterFocus Elective Courses Theoretical Computer ScienceW
Computer Science MasterFocus Elective Courses General StudiesW
Mathematics BachelorSelection: Mathematical Optimization, Discrete MathematicsW
Mathematics MasterSelection: Mathematical Optimization, Discrete MathematicsW