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

Hausdorff Center for Mathematics

Facets of High Dimensional Random Polytopes

Explore asymptotic behavior of high-dimensional random polytopes, analyzing facets and their geometric properties as dimensions and data points increase, revealing insights into spherical approximations and tessellations.

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

Hausdorff Center for Mathematics

The Transfer Operator Method

Explore the Transfer Operator Method in dynamical systems, focusing on its applications in topology and number theory within the context of advanced mathematical research.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Erik Palmgren: A Constructive Examination of a Russell Style Ramified Type Theory

Exploration of ramified type theory in Martin-Löf type theory, examining functional reducibility and its applications in constructive mathematical analysis. Introduces an intuitionistic ramified type theory.

• YouTube
• 32 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

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

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

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

International Mathematical Union

Finitary Analysis in Homogeneous Spaces

Explore finitary analysis in homogeneous spaces with Amir Mohammadi, delving into advanced mathematical concepts and their applications in this specialized field.

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

International Mathematical Union

Charles Smart - Unique Continuation for Lattice Schrodinger Operators

Explore unique continuation for lattice Schrodinger operators with Charles Smart, delving into advanced mathematical concepts and their applications in quantum mechanics.

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

Institute for Pure & Applied Mathematics (IPAM)

Self-Consistent Transfer Operators for High-Dimensional Expanding Coupled Maps

Explore self-consistent transfer operators in high-dimensional expanding coupled maps, examining equilibrium measures, stability, and the relationship between thermodynamic limits and finite-dimensional systems.

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

IMSA

Linearized Instability for Neutral Functional Differential Equations with State-Dependent Delays

Lecture on linearized instability for neutral functional differential equations with state-dependent delays, presenting recent research findings in advanced mathematics.

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

IMSA

Functional Inequalities and Improvements: Stability - Part 1

Explore functional inequalities, their applications, and recent developments in stability theory. Learn strategies for optimizing constants and functions in various mathematical fields.

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

International Mathematical Union

Mathematical Analysis and Numerical Methods for Inverse Scattering Problems

Explore mathematical analysis and numerical methods for inverse scattering problems, covering applications, challenges, algorithms, and recent progress in stability analysis and deep learning approaches.

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