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Explore fundamental concepts of algebraic topology including homology groups, simplicial complexes, and topological surfaces through visual, intuitive approaches. Learn from comprehensive YouTube video series by mathematicians like NJ Wildberger, covering everything from the fundamental group to non-orientable surfaces like the Klein bottle.

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Insights into Mathematics
Duality for Polygons and the Fundamental Theorem of Algebra - Algebraic Topology Lecture 12

Explore duality in polygons and a rational proof of the Fundamental Theorem of Algebra using winding numbers. Gain insights into algebraic topology concepts and their applications.
- YouTube
- 46 minutes
- On-Demand
- Free Video
Insights into Mathematics
Rational Curvature, Winding, and Turning in Algebraic Topology - Lecture 11

Explores rational curvature, turn angles, and winding numbers in algebraic topology. Introduces new geometric concepts for describing polygons and planar curves, emphasizing practical applications in mathematics.
- YouTube
- 48 minutes
- On-Demand
- Free Video
Insights into Mathematics
The Ham Sandwich Theorem and the Continuum - Algebraic Topology Lecture 14

Explore the Borsuk-Ulam theorem, Ham Sandwich theorem, and their applications in algebraic topology. Learn how these concepts relate to continuous maps and homeomorphisms in affine spaces.
- YouTube
- 36 minutes
- On-Demand
- Free Video
Insights into Mathematics
Applications of Euler's Formula and Graphs in Algebraic Topology

Explore Euler's formula applications to Platonic solids, polyhedra, and higher dimensions. Learn about planar graphs and delve into advanced geometric concepts in algebraic topology.
- YouTube
- 42 minutes
- On-Demand
- Free Video
Insights into Mathematics
Computing Homology Groups - Algebraic Topology - NJ Wildberger

Explore homology groups in algebraic topology, focusing on examples like circles and disks. Learn about connectivity, loops, and higher-dimensional holes in spaces.
- YouTube
- 41 minutes
- On-Demand
- Free Video
Insights into Mathematics
Simplices and Simplicial Complexes - Algebraic Topology

Explore higher-dimensional geometry through simplices and simplicial complexes. Learn about convex combinations, orientations, and the fundamental concept of homology in algebraic topology.
- YouTube
- 49 minutes
- On-Demand
- Free Video
Insights into Mathematics
An Introduction to Homology - Algebraic Topology

Explore higher-dimensional topology through homology groups, cycles, and spanning trees. Learn to compute and characterize independent cycles in graphs using algebraic techniques.
- YouTube
- 47 minutes
- On-Demand
- Free Video
Insights into Mathematics
The Fundamental Group - Algebraic Topology

Explore the fundamental group in algebraic topology, covering homotopic paths, loop multiplication, and equivalence classes. Understand key concepts for surfaces like disks and circles.
- YouTube
- 43 minutes
- On-Demand
- Free Video
Insights into Mathematics
Classification of Combinatorial Surfaces - Algebraic Topology - NJ Wildberger

Introduction to the classification of connected compact combinatorial surfaces in algebraic topology, covering key concepts like polygons, vertices, traversing, Euler number, and orientability.
- YouTube
- 51 minutes
- On-Demand
- Free Video
Insights into Mathematics
More Applications of Winding Numbers - Algebraic Topology - NJ Wildberger

Explore winding numbers, degree of circle functions, and key theorems in algebraic topology. Learn about retractions, fixed points, and Borsuk's Lemma in this advanced mathematics lecture.
- YouTube
- 27 minutes
- On-Demand
- Free Video
Insights into Mathematics
Non-Orientable Surfaces - The Mobius Band - Algebraic Topology

Explore non-orientable surfaces like the Möbius band, understanding their unique properties and applications in algebraic topology. Learn about crosscaps and key deformations.
- YouTube
- 42 minutes
- On-Demand
- Free Video
Insights into Mathematics
The Klein Bottle and Projective Plane - Algebraic Topology - NJ Wildberger

Explore the Klein bottle, projective plane, and Platonic solids in this algebraic topology lecture. Learn about Euler's formula and its proof using triangulation and sphere flow.
- YouTube
- 40 minutes
- On-Demand
- Free Video
Insights into Mathematics
Polyhedra and Euler's Formula - Algebraic Topology

Explore Platonic solids, Euler's formula, and spherical geometry in this engaging lecture on algebraic topology, featuring proofs and insights into fundamental mathematical concepts.
- YouTube
- 46 minutes
- On-Demand
- Free Video
Insights into Mathematics
Two-Dimensional Objects - The Torus and Genus - Algebraic Topology

Explore surfaces like cylinders and tori, understanding their properties and connections to complex function theory. Learn about genus and how planes cover different surfaces.
- YouTube
- 50 minutes
- On-Demand
- Free Video
Insights into Mathematics
Two-Dimensional Surfaces - The Sphere - Algebraic Topology

Explore the two-dimensional sphere's significance in algebraic topology, including its relation to stereographic projection and the inversive plane in Euclidean geometry.
- YouTube
- 42 minutes
- On-Demand
- Free Video

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