Topological Spaces Courses and Certifications

Point Set Topology

Explore fundamental concepts in point set topology, including topological spaces, continuous maps, metric spaces, connectedness, compactness, and metrization, with a focus on practical examples from mathematics.

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

Beijing Jiaotong University

点集拓扑

该课在数学人才培养过程中有着重要的作用。该课对极限与连续做了最一般的推广。学完该课再回望微积分有一览众山小之感。

• XuetangX
• On-Demand
• Free Online Course

Surfaces

4 ratings at OpenLearn

Surfaces are a special class of topological spaces that crop up in many places in the world of mathematics. In this free course, you will learn to classify surfaces and will be introduced to such ...

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

IIT (ISM) Dhanbad;  NPTEL

Essentials Of Topology

Explore foundational mathematics, delving into topological spaces, connectedness, compactness, and separation axioms. Develop a deeper understanding of mathematical concepts beyond computational exercises.

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

BIMSA

A Morse Model for Stable Homotopy - ICBS 2024

Explore stable homotopy groups, framed bordism, and Morse theory in topological spaces. Gain insights into Floer homotopy foundations and the Pontryagin-Thom construction.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Floer Homology with DG Coefficients - Applications to Cotangent Bundles

Explore Floer homology with DG coefficients and its applications to cotangent bundles. Gain insights into symplectic geometry and dynamical systems through advanced mathematical concepts.

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

Friedrich–Alexander University Erlangen–Nürnberg

Geometrical Anatomy of Theoretical Physics

Comprehensive exploration of advanced mathematical concepts in theoretical physics, from set theory to Lie groups, manifolds, and fiber bundles, with applications in quantum mechanics and symmetries.

• YouTube
• 1 day 23 hours
• On-Demand
• Free Video

Models of Consciousness Conferences

Sketches of a Mathematical Theory of Qualia

Exploración matemática de los qualia: definición, estructura y relación con la teoría cuántica. Propone un modelo de conciencia basado en principios abstractos del comportamiento de dispositivos que detectan qualia.

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

Applied Algebraic Topology Network

Antonio Rieser - Algebraic Topology for Graphs and Mesoscopic Spaces

Explore algebraic topology for graphs and mesoscopic spaces, covering homotopy, homology, and metric cohomology. Learn about pseudotopological spaces and their applications in various mathematical categories.

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

Applied Algebraic Topology Network

Wanted- Topologists for Autonomous Robots Community

Exploring topological complexity in robotics: from path planning to task spaces. Insights into rigorous formulations for robotic autonomy, emphasizing environment topology and combinatorics in cooperative motion.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

A Counter-Example to Hausmann's Conjecture

Explore a counter-example to Hausmann's conjecture on Vietoris-Rips complexes, challenging long-held beliefs in algebraic topology using persistent homology.

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

ICTP Mathematics

Topology - Lecture 2

Explore fundamental concepts of topology, including topological spaces, continuity, and homeomorphisms, with a focus on mathematical rigor and abstract reasoning.

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

ICTP Mathematics

Topology - Lecture 3

Explore fundamental concepts of topology, including continuous functions, homeomorphisms, and topological properties, in this advanced mathematics lecture.

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

Applied Algebraic Topology Network

Simplicial Neural Networks

Explore simplicial neural networks, a generalization of graph neural networks for multi-dimensional data, and their applications in imputing missing data on coauthorship complexes.

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

Insights into Mathematics

Introduction to Homology in Algebraic Topology - Part 2

Explores cycles, boundaries, and homology in algebraic topology, focusing on graph modifications and using commutative group theory to analyze formal combinations of geometric elements.

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