PhD Course - Proofs from The Book

Organisers: 

Associate Professor Riko Jacob, PhD student Tobias Lybecker Christiani and PhD student Matteo Dusefante 

Lecturers:

Collaborative, discussion-based lectures. Participants present mathematical proofs followed by a discussion.

Dates of the course:

Week 3 to week 8 in 2018 (6 weeks)

Time:

Tuesday and Thursday 13:00-15:00

Room: 

4A09

Course description: 

The course is a reading of "Proofs from The Books" - a collection of mathematical proofs that embody the concept of mathematical beauty. The proofs are divided evenly among five fields: number theory, geometry, analysis, combinatorics, and graph theory. The goal of the course is to obtain an understanding of the proofs in each of these areas, to discover new proof techniques, and to discover potential applications and connections to theoretical computer science. 

Before each lecture participants will read half a chapter and prepare a presentation of one (or more) proofs on the whiteboard. Participants should make at least five presentations during the course. 

Programme: 

Week 3: Number Theory

Week 4: Geometry

Week 5: Analysis 

Week 6: Combinatorics

Week 7: Graph Theory 

Week 8: Exam week 

Prerequisites:

 Undergraduate profiency in linear algebra, calculus, probability theory, number theory, and discrete math. 

Exam: 

Supervised oral examination (seminar). Presentation of one or more open problems related to the course topics. Students must present individually. 

Credits:

5 ECTS 

How to sign up:

Write an email to rikj@itu.dk