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N J Wildberger - University of New South Wales
AlgTop0: Introduction to Algebraic Topology
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Topology Introduction - 06:34
AlgTop1: One-dimensional objects
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
One-dimensional Objects - 01:07
Circles in Moduli Space - 09:06
Polygonal Representations of C... - 19:48
AlgTop2: Homeomorphism and the group structure on a circle
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Homeomorphism - 00:56
Group Structure of a Circle - 14:57
Pappus's Hexagon Theorem - 29:43
Desargues' Theorem - 33:37
Pascal's Theorem - 37:24
AlgTop3: Two-dimensional surfaces: the sphere
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Links - 06:58
Two-Dimensional Surfaces - 11:08
Affine Plane - 11:21
Spheres - 18:59
Properties of Stereographic Pr... - 31:40
Inversive Plane - 38:45
AlgTop4: More on the sphere
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Inversive Plane - 00:36
Riemann Sphere - 12:50
Riemann Surface - 24:30
Sphere as Projective Line Over... - 33:10
AlgTop5: Two-dimensional objects- the torus and genus
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Cylinders - 00:29
Torus - 12:01
N-Holed Torus - 18:55
Genus - 20:09
Torus as Configuration Space - 26:35
Torus as Orbit Space - 32:09
AlgTop6: Non-orientable surfaces---the Mobius band
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Non-orientable Surfaces - 00:25
Mobius Band - 00:49
Non-orientability - 05:24
Cross-Caps and Handles - 31:10
AlgTop7: The Klein bottle and projective plane
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Mobius Band as Moduli Space - 00:37
Klein Bottles - 12:18
Projective Plane - 20:05
AlgTop8: Polyhedra and Euler's formula
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Polyhedra - 00:16
Platonic Solids - 00:21
Euler's Formula - 12:37
Archimedean Solids - 15:41
AlgTop9: Applications of Euler's formula and graphs
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Total Number of Platonic Solids - 01:00
Deltahedrons - 14:24
Platonic Solids in Higher Dime... - 19:05
Graphs (Topology) - 35:02
AlgTop10: More on graphs and Euler's formula
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Graphs (Topology) - 00:25
Planar Graphs - 00:25
Kuratowski's Theorem - 07:08
Five Color Theorem - 08:51
Six Color Theorem - 17:51
Pick's Theorem - 24:44
AlgTop11: Rational curvature, winding and turning
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Winding Numbers - 30:32
Turning Numbers of Smooth Curves - 40:54
AlgTop12: Duality for polygons and the Fundamental Theorem of Algebra
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Turn-Angles - 00:36
Dual Polygons - 11:33
Applications of Winding Numbers - 26:34
Fundamental Theorem of Algebra - 26:48
AlgTop13: More applications of winding numbers
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Applications of Winding Numbers - 00:06
Retraction - 04:07
Brouwer Fixed-Point Theorem - 14:29
Antipodes - 20:40
AlgTop14: The Ham Sandwich theorem and the continuum
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Borsuk-ulam Theorem - 11:55
Consequences of Borsuk-ulam - 17:34
Ham Sandwich Theorem (Stone-Tu... - 19:40
Continuum - 32:34
AlgTop15: Rational curvature of a polytope
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Polytope Curvature - 00:46
Spherical Triangle Area - 23:06
Girard's Theorem - 23:07
Polytope Vertex Curvature - 36:59
AlgTop16: Rational curvature of polytopes and the Euler number
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Polytope Curvature - 00:31
AlgTop17: Classification of combinatorial surfaces I
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Classification of Combinatoria... - 00:26
AlgTop18: Classification of combinatorial surfaces II
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Combinatorial Surfaces - 00:22
Classification of Combinatoria... - 04:21
Euler Number of a Combinatoria... - 50:09
AlgTop19: An algebraic ZIP proof
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Classification of Combinatoria... - 01:02
Conway's Zip Proof - 01:02
Combinatorial Surfaces - 14:01
AlgTop20: The geometry of surfaces
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Classical Geometries - 02:17
Euclidean Geometry - 05:06
Reflections in Spherical Geometry - 14:53
Hyperbolic Geometry - 22:59
AlgTop21: The two-holed torus and 3-crosscaps surface
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Advantages of Hyperbolic Geometry - 00:20
AlgTop22: Knots and surfaces I
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Knots - 00:32
Types of Knots - 02:52
Reidermeister Moves - 10:51
Knot Diagrams - 10:53
Knot Invariants - 20:28
Alexander-Conway Polynomial - 35:36
AlgTop23: Knots and surfaces II
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Knots - 00:09
Surface With Boundary - 04:18
Euler Characteristic And Cuffs - 23:20
AlgTop24: The fundamental group
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Fundamental Group - 00:14
Homotopic Paths - 03:20
Equivalence Relation - 10:08
Path Multiplication - 19:52
AlgTop25: More on the fundamental group
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Fundamental Group - 00:13
AlgTop26: Covering spaces
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Homomorphism of Fundamental Group - 00:35
Classical Geometries - 08:01
Covering Spaces - 08:01
Torus Knots - 36:05
AlgTop27: Covering spaces and 2-oriented graphs
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Covering Spaces - 00:14
2-Oriented Graphs - 21:30
AlgTop28: Covering spaces and fundamental groups
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Covering Spaces - 00:23
Covering Spaces of Torus - 01:53
Covering Spaces And Fundamenta... - 12:47
Lifting Path Lemma - 12:47
Lifting Homotopy Lemma - 24:22
AlgTop29: Universal covering spaces
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Universal Covering Space - 18:41
AlgTop30: An introduction to homology
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Homology - 03:43
Chains(Topology) - 13:24
Cycle Definition - 26:22
AlgTop31: An introduction to homology (cont.)
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Homology - 00:12
Quotients (Homology) - 15:48
AlgTop32: Simplices and simplicial complexes
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Simplicies - 00:27
Simplex Standard Form - 11:34
Simplical Complexes - 18:00
Simplex Orientation - 29:18
AlgTop33: Computing homology groups
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Homology - 00:19
Chains(Topology) - 00:20
Measuring Connected Components - 27:11
AlgTop34: More homology computations
Topic:
Topology
Teacher:
N J Wildberger
AlgTop35: Delta complexes, Betti numbers and torsion
Topic:
Topology
Teacher:
N J Wildberger
Concepts In This Lecture:
Torus Homology - 00:39
WildLinAlg1: Introduction to Linear Algebra
Topic:
Linear Algebra
Teacher:
N J Wildberger