Algebraic Topology Courses and Certifications

Insights into Mathematics

Algebraic Topology

Explore topological spaces, surfaces, knots, and fundamental groups through geometric intuition and algebraic methods in this comprehensive mathematical journey.

• YouTube
• 1 day 5 hours 1 minute
• On-Demand
• Free Video

Introduction to Algebraic Topology

Explore algebraic invariants of topological spaces through fundamental groups, homology groups, and covering spaces with computational techniques and mathematical applications.

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

Insights into Mathematics

Introduction to Algebraic Topology - Algebraic Topology - NJ Wildberger

Explore the foundations of algebraic topology, its historical roots, and key concepts like homeomorphism and fundamental objects. Tackle challenging problems in this dynamic field of mathematics.

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

Insights into Mathematics

Delta Complexes, Betti Numbers, and Torsion in Algebraic Topology

Explore homology groups of torus and projective plane using delta-complexes. Learn about Betti numbers and torsion in algebraic topology, with practical computations and insights into fundamental concepts.

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

Insights into Mathematics

More Homology Computations in Algebraic Topology - Lecture 2

Explore homology computations for the 2-sphere using tetrahedron and delta-complex models. Learn how linear algebra applies to topological problems and simplify calculations with semi-simplicial complexes.

• YouTube
• 43 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

Insights into Mathematics

Universal Covering Spaces in Algebraic Topology

Explore fundamental groups, covering spaces, and universal covers. Learn about helical coverings, two-fold coverings, and connections between geometry and topology in this advanced algebraic topology lecture.

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

Insights into Mathematics

Covering Spaces and Fundamental Groups - Algebraic Topology Lecture 28

Exploring covering spaces and fundamental groups, focusing on torus examples and key lemmas to understand relationships between covering spaces and base spaces.

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

Insights into Mathematics

Covering Spaces in Algebraic Topology

Explore covering spaces in algebraic topology, including fundamental groups, line-circle coverings, sphere-projective plane relations, and torus knots. Visualize complex topological concepts through practical examples.

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

Insights into Mathematics

Covering Spaces and 2-Oriented Graphs - Algebraic Topology

Explore covering spaces through wedge of circles, examining graphs with labeled edges. Learn about universal covering spaces and their fundamental groups in algebraic topology.

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

Insights into Mathematics

Free Abelian Groups and Non-Commutative Groups - Algebraic Topology Review 4

Explore free abelian groups and their role in algebraic topology. Learn about the Fundamental Theorem of Finitely Generated Commutative Groups and non-commutative groups, including cosets and normal subgroups.

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

Insights into Mathematics

Knots and Surfaces - Seifert Surfaces in Algebraic Topology - Lecture 2

Explore Seifert surfaces, their construction for knots like the trefoil, and learn about Euler numbers for surfaces with boundaries in this advanced algebraic topology lecture.

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

Insights into Mathematics

Sphere Geometry and Complex Analysis - Algebraic Topology Lecture 4

Explore advanced concepts in sphere geometry, including inversive geometry, Riemann sphere, complex analysis, and projective lines, enhancing understanding of algebraic topology.

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

Insights into Mathematics

The Geometry of Surfaces - Algebraic Topology Lecture 20

Explore the connection between 2D surfaces and classical geometries, focusing on isometries and introducing hyperbolic geometry through circle inversions in the Beltrami Poincare disk model.

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

Insights into Mathematics

Rational Curvature of a Polytope - Algebraic Topology Lecture 15

Introduces a new rational definition of polytope curvature, using turn-angle to connect curvature with Euler number. Explores opposite cones and applies Harriot's theorem on spherical triangles.

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