Mathematical Analysis Courses and Certifications

Metric spaces and continuity

This free course contains an introduction to metric spaces and continuity. The key idea is to use three particular properties of the Euclidean distance as the basis for defining what is meant by a ...

• OpenLearn
• 16 hours
• On-Demand
• Free Certificate

Analysis III: Basic Properties of Riemann Integration - Lecture 1

Explore fundamental properties of Riemann integration, including integral additivity, through rigorous proofs. Gain a solid foundation in mathematical analysis.

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

Simons Institute

Michael Cohen and Self-Concordant Barriers Over L_p Balls

Exploration of self-concordant barriers over L_p balls, discussing Michael Cohen's contributions and proof ideas in the context of high-dimensional optimization and convex geometry.

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

Insights into Mathematics

Logical Difficulties With the Modern Theory of Limits - Real Numbers + Limits Math Foundations

Explores logical issues in modern limit theory, examining extended harmonic sequences and the Collatz problem to reveal challenges in defining limits for infinite computations in mathematical analysis.

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

Insights into Mathematics

The Euclidean Rotation Group and Complex Number Multiplication - WildTrig

Explore the connection between Euclidean rotations and complex number multiplication, introducing the concept of half-slope for a more rational approach to 2D dynamics and graphics.

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

ICTP Mathematics

Standard and Less Standard Asymptotic Methods - Lecture 2

Explore advanced asymptotic methods in mathematics, delving into both standard and unconventional approaches to enhance problem-solving skills and theoretical understanding.

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

ICTP Mathematics

Young Towers for Geodesic Flows on Certain Non-Positively Curved Surfaces - ICTP 2021

Explore Young towers for geodesic flows on non-positively curved surfaces with Yakov Pesin. Gain insights into Sinai-Ruelle-Bowen measures and their applications in surface diffeomorphisms.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

ICTP Mathematics

Nonlocal Equations Under Different Perspectives - Lecture 3

Explore advanced nonlocal equations in mathematics, focusing on applications in geometry, physics, and probability theory with expert insights from E. Valdinoci.

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

ICTP Mathematics

Global Regularity of Solutions to the 4-Species Quadratic Diffusion-Reaction System

Explore advanced mathematical concepts in nonlocal partial differential equations, focusing on global regularity solutions for a 4-species quadratic diffusion-reaction system across all spatial dimensions.

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

ICTP Mathematics

Regularity of the Boltzmann Equation in Bounded Domains - I

Explore the regularity of the Boltzmann equation in bounded domains, focusing on advanced mathematical concepts and applications in geometry, physics, and probability theory.

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

ICTP Mathematics

Dynamics, Symmetry and Asymmetry of Ancient Solutions to Mean Curvature Flow - Ancient Convex Solutions to MCF

Explore ancient convex solutions to Mean Curvature Flow, examining dynamics, symmetry, and asymmetry in this advanced mathematics lecture by Sigurd Angenent.

• YouTube
• 1 hour 15 minutes
• On-Demand
• Free Video

ICTP Mathematics

Heat and Schroedinger Evolution on Degenerate Riemannian Structures

Explore heat and Schrödinger evolution on degenerate Riemannian structures with expert Ugo Boscain. Gain insights into advanced mathematical concepts and their applications.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

ICTP Mathematics

Reaction Diffusion Equations on Evolving Domains: Regularity and Global Existence

Explore regularity and global existence of reaction diffusion equations on evolving domains, focusing on mathematical analysis and advanced theoretical concepts.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

ICTP Mathematics

On the Log-Local Principle for Refined Gromov-Witten Theory

Explore the log-local principle in Gromov-Witten theory, its applications, and recent developments in refined invariants with expert Andrea Brini from the University of Birmingham.

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

Hausdorff Center for Mathematics

The Weighted Energy Dissipation WED Principle for Gradient Flows

Explore advanced variational methods for gradient flows, focusing on the Weighted Energy Dissipation principle and its applications in metric spaces and optimal control problems.

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