Measure Theory Courses and Certifications

Kyoto-U OCW - Unofficial

面積0の集合と関連する問題 - 2021年4月

Dive into 面積0の集合の数学的探究、Hausdorff測度と次元の概念、そして掛谷予想について学ぶ数学フロンティア講座。

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

Applied Algebraic Topology Network

Bala Krishnamoorthy: Linear Programming in Geometric Measure Theory

Explore geometric measure theory through linear programming, examining integral currents, simplicial flat norm, and polyhedral approximation. Discover applications in median shape analysis.

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

Fields Institute

Local Entropy Theory for Induced Actions on Probability Measure Spaces

Explore advanced concepts in local entropy theory for induced actions on probability measure spaces with expert Hanfeng Li from SUNY at Buffalo.

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

Centre de recherches mathématiques - CRM

Measure Equivalence and Wreath Products in Group Theory

Explore measure equivalence and wreath products in group theory, focusing on nonabelian free groups and orbit equivalence of wreath products.

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

Society for Industrial and Applied Mathematics

Exploring Variational Functions - Calculus of Variations and Geometric Measure Theory

Dive into variational problems and bounded Hessian functions with Luigi Ambrosio. Explore the intersection of Calculus of Variations and Geometric Measure Theory, inspired by machine learning insights.

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

Insights into Mathematics

Computability and Problems with Set Theory - Math History

Explores historical controversies in set theory, Gödel's incompleteness theorems, Zermelo-Fraenkel axioms, and Turing's computability concepts, challenging traditional views on infinite sets in mathematics.

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

Wrath of Math

So, There Are Basically No Fractions - The Measure of Rational Numbers is Zero

Discover why almost all real numbers are irrational by exploring measure theory and proving that rational numbers have zero measure on the number line.

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

Michael Penn

How to Take a Walk and Miss Every Rational Number

Explore the mathematical concept of creating a path that avoids all rational numbers, using clever techniques from real analysis and number theory.

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

Fields Institute

Optimal Transportation, Geometry and Dynamics

Explore advanced mathematical theory connecting optimal transport problems with geometric structures and dynamical systems through 24 comprehensive lectures from Fields Institute.

• YouTube
• 1 day 9 hours 39 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Ergodic Theory and Dynamical Systems 2022

Explore advanced topics in ergodic theory and dynamical systems through expert lectures on Diophantine approximation, homogeneous dynamics, and measure theory applications.

• YouTube
• 1 day 16 hours 22 minutes
• On-Demand
• Free Video

ICTP Mathematics

Real Analysis

Master rigorous mathematical analysis through 20 comprehensive lectures covering limits, continuity, differentiation, and integration theory.

• YouTube
• 1 day 4 hours 56 minutes
• On-Demand
• Free Video

ICTP Mathematics

Ergodic Theory

Dive into the mathematical foundations of dynamical systems through comprehensive ergodic theory principles and applications in this advanced diploma program.

• YouTube
• 13 hours 20 minutes
• On-Demand
• Free Video

Martingales: Definition and First Properties - Probability, Measure and Martingales

Explore the concept of martingales in probability theory, including their definition, properties, construction methods, and Doob's decomposition theorem in discrete time.

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

Probability, Measure and Martingales: An Introduction

Explore key mathematical concepts like conditional expectation, martingales, and measure theory through examples from branching processes, random walks, and mathematical finance in this Oxford Mathematics lecture.

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

Probability, Measure and Martingales - Stopped Martingales and Optional Sampling Theorems

Explore stopping martingales, Doob's optional sampling theorem, and uniform integrability concepts in this advanced probability lecture covering key theorems and their applications in mathematical analysis.

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