Additive Combinatorics Courses and Certifications

Graph Theory and Additive Combinatorics

This course examines classical and modern developments in graph theory and additive combinatorics, with a focus on topics and themes that connect the two subjects.

• MIT OpenCourseWare
• 34 hours
• On-Demand
• Free Online Course

Graph Theory and Additive Combinatorics

Explore classical and modern developments in graph theory and additive combinatorics, connecting the two subjects and introducing current research topics and open problems.

• MIT OpenCourseWare
• On-Demand
• Free Online Course

Ryan O'Donnell

Analysis of Boolean Functions at CMU - Additive Combinatorics

Explore additive combinatorics in Boolean functions, covering subspaces, cosets, Hamming balls, and the Fryman region conjecture. Gain insights into advanced theoretical concepts.

• YouTube
• 1 hour 22 minutes
• On-Demand
• Free Online Course

Institute for Advanced Study

Associativity Testing - Ben Green

Explore associativity testing in discrete mathematics, covering key concepts, theorems, and applications in group theory and additive combinatorics.

• YouTube
• 58 minutes
• On-Demand
• Free Online Course

International Centre for Theoretical Sciences

The Selberg Sieve and Large Sieve - Lecture 1

Explore the Selberg Sieve and Large Sieve in number theory, covering linear algebra, duality principles, and applications like the Bombieri-Vinogradov theorem in this advanced mathematics lecture.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Online Course

International Centre for Theoretical Sciences

The Selberg Sieve - Lecture 1

Explore the Selberg sieve method in number theory, covering heuristics, probability, and applications to twin primes. Learn about sieve techniques for detecting primes in sequences.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Online Course

International Centre for Theoretical Sciences

Basic Lower Bounds and Kneser's Theorem by David Grynkiewicz

Explore set addition, basic lower bounds, and Kneser's Theorem in additive combinatorics. Learn key proofs, including Cauchy-Davenport theorem, and applications to field extensions.

• YouTube
• 54 minutes
• On-Demand
• Free Online Course

Hausdorff Center for Mathematics

Mathematics of Signal Design for Communication Systems and Szemerédi’s and Green-Tao’s Theorems

Explore signal design for communication systems, focusing on orthogonal transmission schemes and their dynamics. Delve into mathematical connections with functional analysis and additive combinatorics.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Online Course

Simons Institute

Strong Bounds for 3-Progressions

Explore advanced additive combinatorics, focusing on 3-term arithmetic progressions in integer sets. Learn about recent breakthroughs and their implications for number theory.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Online Course

Simons Institute

Structure of Communication - Richard M. Karp Distinguished Lecture

Explore communication complexity, its applications, and structural conjectures in theoretical computer science with Shachar Lovett. Gain insights into efficient communication and its connections to various mathematical domains.

• YouTube
• 1 hour
• On-Demand
• Free Online Course

Simons Institute

Structures in Random Graphs - New Connections

Exploring structures in random graphs, including cliques and independence numbers in Cayley graphs, thresholds for monotone properties, and edge-colorings of bipartite graphs.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Online Course

Simons Institute

Larger Corner-Free Sets in High Dimensions

Explore high-dimensional corner-free sets in additive combinatorics, examining recent advancements in upper bounds and their connection to communication complexity theory.

• YouTube
• 35 minutes
• On-Demand
• Free Online Course

Institute for Pure & Applied Mathematics (IPAM)

Discreteness of Asymptotic Tensor Ranks

Explores discreteness in asymptotic tensor parameters, proving general theorems and new lower bounds for asymptotic subrank of tensors, with applications in algebraic complexity and quantum information.

• YouTube
• 40 minutes
• On-Demand
• Free Online Course