AlgTop0: Introduction to Algebraic Topology
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop1: One-dimensional objects
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop2: Homeomorphism and the group structure on a circle
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop3: Two-dimensional surfaces: the sphere
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop4: More on the sphere
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop5: Two-dimensional objects- the torus and genus
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop6: Non-orientable surfaces---the Mobius band
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop7: The Klein bottle and projective plane
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop8: Polyhedra and Euler's formula
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop9: Applications of Euler's formula and graphs
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop10: More on graphs and Euler's formula
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop11: Rational curvature, winding and turning
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop12: Duality for polygons and the Fundamental Theorem of Algebra
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop13: More applications of winding numbers
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop14: The Ham Sandwich theorem and the continuum
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop15: Rational curvature of a polytope
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop16: Rational curvature of polytopes and the Euler number
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop17: Classification of combinatorial surfaces I
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop18: Classification of combinatorial surfaces II
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop19: An algebraic ZIP proof
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop20: The geometry of surfaces
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop21: The two-holed torus and 3-crosscaps surface
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop22: Knots and surfaces I
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop23: Knots and surfaces II
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop24: The fundamental group
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop25: More on the fundamental group
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop26: Covering spaces
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop27: Covering spaces and 2-oriented graphs
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop28: Covering spaces and fundamental groups
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop29: Universal covering spaces
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop30: An introduction to homology
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop31: An introduction to homology (cont.)
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop32: Simplices and simplicial complexes
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
AlgTop33: Computing homology groups
Topic: Topology
Teacher: N J Wildberger
Concepts In This Lecture:
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:
WildLinAlg1: Introduction to Linear Algebra
Topic: Linear Algebra
Teacher: N J Wildberger