Graph Theory and Additive Combinatorics (MIT OpenCourseWare)
One of the Best Online Graph Theory Courses is Graph Theory and Additive Combinatorics (MIT OpenCourseWare). This course examines the traditional and modern advancements in additive combinatorics and graph theory, as well as their connections. Aside from the basics, you can look at some of the open challenges and do some studying. After you've completed the course, you may browse the website's course collection to learn more about the subject. Remember to go through our list of the Best Research Methods Courses.
Roth's theorem, which states that every subset of 1, 2,... n without a 3-term arithmetic progression includes o(N) items, is a key finding in additive combinatorics. There are two ways to prove Roth's theorem: (1) a graph-theoretic method, and (2) Roth's original Fourier analytic technique. The duality of structure and pseudorandomness is a major principle in both techniques, and it is one of the course's main themes.
Highlights:
- Videos and lecture notes are available for download.
- Check out the instructor's insights sections to get a better idea of the content.
- Complete the set of six assignments to practice along with the curriculum.
Topics:
- Forbidding subgraphs
- Szemerédi’s regularity lemma
- Pseudorandom graphs
- Graph limits
- Roth’s theorem
- Structure of set addition
- The sum-product problem
Rating: 4.4 out of 5
Enroll here: https://ocw.mit.edu/courses/18-217-graph-theory-and-additive-combinatorics-fall-2019/
