Approximation Theory Courses and Certifications

Michael Penn

Every Right Triangle is Almost Pythagorean

Explore the concept of "almost Pythagorean" right triangles, uncovering a fascinating mathematical property that extends beyond the classic theorem.

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

Wrath of Math

Exploring the Best Approximation of Euler's Number e

Discover how Richard Sabey created an extraordinary approximation of Euler's number e using digits 1-9, achieving accuracy to over 18 septillion digits, and learn the mathematical principles behind verifying this feat.

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

MindYourDecisions

The Mystery of 355/113 and Pi

Uncover the untold history of 355/113 as an approximation for π, exploring ancient Chinese mathematicians' contributions including Liu Hui and Zu Chongzhi, and learn how this mysteriously accurate fraction was derived.

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

Sloppy Models, Differential Geometry, and Why Science Works

Explore how complex systems can be modeled despite parameter uncertainties, using differential geometry to understand 'sloppiness' and its implications for scientific comprehension and prediction.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Insights into Mathematics

Real Numbers and Cauchy Sequences of Rationals - Math Foundations 112

Explores the concept of real numbers, challenging their existence and examining how quantities like length, area, and function values are inherently approximate rather than exact 'real' values.

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

Simons Institute

Approximation Power

Explore deep learning's approximation capabilities, focusing on theoretical foundations and practical implications for neural network design and performance optimization.

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

Alan Turing Institute

A Function Space View of Overparameterized Neural Networks - Rebecca Willet, University of Chicago

Explore function spaces of overparameterized neural networks, focusing on weight-bounded networks and their approximation capabilities. Insights from Radon transform analysis reveal novel perspectives on learning with ReLU networks.

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

Imperial College London

Making Decisions with Known Unknowns - Professor Eric Kerrigan's Inaugural Lecture

Explore decision-making under uncertainty, covering aerodynamics, electrical engineering, and energy systems. Learn optimization techniques for real-world problem-solving.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

NPTEL-NOC IITM

The Stone-Weierstrass Theorem

Explore the Stone-Weierstrass theorem, a fundamental result in functional analysis and approximation theory.

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

NPTEL-NOC IITM

Introduction to the Finite Element Method: 1D Basis Functions

Explore 1D basis functions in finite element method. Learn key concepts and applications for numerical analysis and engineering problem-solving.

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

Michael Penn

Why Are These Numbers Close to Pi? - Mathematical Analysis and Exploration

Uncover the mathematical mystery behind numbers that surprisingly approximate pi through elegant mathematical analysis and pattern recognition.

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

Centre International de Rencontres Mathématiques

CEMRACS 2021 - Mathematical and Computational Methods for High-Dimensional Problems

Explore advanced mathematical methods including Bayesian data assimilation, deep neural networks theory, tensor networks, and high-dimensional function approximation techniques.

• YouTube
• 14 hours 37 minutes
• On-Demand
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Learning Theory and Computational Microscopy - IPAM at UCLA

1 review

Explore learning theory applications in computational microscopy, focusing on advanced techniques for image analysis and reconstruction in scientific research.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Urysohn Width

Explore the 100-year history and applications of Urysohn width, a metric invariant quantifying space approximation by simplicial complexes. Discover its role in dimension theory and modern geometric challenges.

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

Fields Institute

Mini-course on Hardy Spaces - Part 3

Explore Hardy spaces with a focus on rotation, generalization, and approximate identities. Delve into uniform boundedness, Poisson PR constructions, and harmonic functions.

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