Fourier Analysis Courses and Certifications

International Mathematical Union

Larry Guth- Decoupling Estimates in Fourier Analysis

Explore recent developments in decoupling, a Fourier analysis technique with applications in harmonic analysis, PDE, and number theory. Survey key applications and proof concepts.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Terence Tao- The Circle Method from the Perspective of Higher Order Fourier Analysis

Explore higher order Fourier analysis and its application to the circle method, offering new perspectives on multilinear averages and complex mathematical problems.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Ryan O'Donnell

Fourier Analysis of Boolean Functions - Lecture 8a of CS Theory Toolkit

Explore Fourier analysis of Boolean functions, focusing on real-valued functions and their Fourier transforms in this graduate-level theoretical computer science lecture.

• YouTube
• 32 minutes
• On-Demand
• Free Video

Instituto de Matemática Pura e Aplicada

Fourier Analysis and Beyond I (2025)

Explore advanced Fourier analysis techniques and their applications across mathematical disciplines through expert mini-courses and research presentations from leading specialists.

• YouTube
• 12 hours 11 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Hans Feichtinger- Fourier Analysis via the Banach Gelfand Triple

Explore Gabor analysis foundations using MATLAB, focusing on finite Abelian groups and matrix analysis methods. Learn to apply abstract harmonic analysis concepts to signal processing problems.

• YouTube
• 59 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Music Applications of Fourier Analysis

Explore Fourier analysis applications in music, covering signal processing techniques for audio analysis, synthesis, and music information retrieval. Gain insights into the intersection of mathematics and music.

• YouTube
• 1 hour 25 minutes
• On-Demand
• Free Video

Simons Semester on Dynamics

Automatic Sequences from the Point of View of Higher Order Fourier Analysis

Delve into advanced mathematical concepts exploring automatic sequences through higher order Fourier analysis, featuring insights on nilpotent structures and topological dynamics.

• YouTube
• 48 minutes
• On-Demand
• Free Video

Instituto de Matemática Pura e Aplicada

Some Open Problems in Fourier Analysis - Lecture 3

Explore open problems in Fourier analysis through advanced mathematical techniques and theoretical frameworks presented by a leading expert.

• YouTube
• 46 minutes
• On-Demand
• Free Video

Instituto de Matemática Pura e Aplicada

Some Open Problems in Fourier Analysis - 01

Explore open problems in Fourier analysis through advanced mathematical techniques and theoretical frameworks presented by a leading expert.

• YouTube
• 53 minutes
• On-Demand
• Free Video

Instituto de Matemática Pura e Aplicada

Some Open Problems in Fourier Analysis - 02

Explore open problems in Fourier analysis through advanced mathematical techniques and theoretical frameworks presented by a leading expert.

• YouTube
• 48 minutes
• On-Demand
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Almost Orthogonality in Fourier Analysis: From Singular Integrals to Function Spaces to Leibniz Rules for Fractional Derivatives

Delve into the mathematical world of Fourier analysis, exploring almost orthogonality concepts from singular integrals to function spaces and fractional derivative Leibniz rules with Rodolfo Torres.

• YouTube
• 50 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Workshop on Dynamics, Discrete Analysis and Multiplicative Number Theory

Explore advanced research in dynamics, discrete analysis, and multiplicative number theory through expert presentations on conjectures, polynomial patterns, and ergodic theory.

• YouTube
• 14 hours 18 minutes
• On-Demand
• Free Video

Ryan O'Donnell

Analysis of Boolean Functions

Dive into Fourier analysis, noise stability, social choice theory, and computational complexity through 23 graduate-level lectures covering Boolean function analysis fundamentals.

• YouTube
• 1 day 5 hours 49 minutes
• On-Demand
• Free Video

IIT Bombay;  AICTE

Fourier Analysis and its applications

Explore Fourier analysis theory and applications in mathematics, physics, and engineering. Rigorous proofs, convergence issues, and diverse mathematical applications are covered, including geometry, celestial mechanics, and number theory.

• Swayam
• 12 weeks
• On-Demand
• Free Online Course

The Fourier Method in Euclidean Space - Lecture 4

Explore how the Fourier method adapts to Euclidean space while considering multiple scales in this advanced mathematical analysis lecture.

• YouTube
• 1 hour 20 minutes
• On-Demand
• Free Video