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Course
| Subject: | Mathematics |
| Views: | 85,950 |
Instructor
Name
N.J. Wildberger
Lecture Description
In this video lecture, Prof. N.J. Wildberger talks about knots and surfaces.
In the 1930's H. Siefert showed that any knot can be viewed as the boundary of an orientable surface with boundary, and gave a relatively simple procedure for explicitly constructing such `Seifert surfaces'. We show the algorithm, exhibit it for the trefoil and the square knot, and then discuss Euler numbers for surfaces with boundaries.
In the 1930's H. Siefert showed that any knot can be viewed as the boundary of an orientable surface with boundary, and gave a relatively simple procedure for explicitly constructing such `Seifert surfaces'. We show the algorithm, exhibit it for the trefoil and the square knot, and then discuss Euler numbers for surfaces with boundaries.
Course Index
- Introduction to Algebraic Topology
- One-dimensional Objects
- Homeomorphism and the Group Structure on a Circle
- Two-dimensional Surfaces: The Sphere
- More on the Sphere
- Two-dimensional Objects: The Torus and Genus
- Non-orientable Surfaces: The Mobius Band
- The Klein Bottle and Projective Plane
- Polyhedra and Euler's Formula
- Applications of Euler's Formula and Graphs
- More on Graphs and Euler's Formula
- Rational Curvature, Winding and Turning
- Duality for Polygons and the Fundamental Theorem of Algebra
- More Applications of Winding Numbers
- The Ham Sandwich Theorem and the Continuum
- Rational Curvature of a Polytope
- Rational Curvature of Polytopes and the Euler Number
- Classification of Combinatorial Surfaces (Part I)
- Classification of Combinatorial Surfaces (Part II)
- An Algebraic ZIP Proof
- The Geometry of Surfaces
- The Two-holed Torus and 3-Crosscaps Surface
- The Two-holed Torus and 3-Crosscaps Surface
- Knots and Surfaces (Part I)
- Knots and Surfaces (Part II)
- The Fundamental Group
- More on the Fundamental Group
Course Description
In this course, Prof. N.J. Wildberger gives 26 video lectures on Algebraic Topology. This is a beginner's course in Algebraic Topology given by Assoc. Prof. N J Wildberger of the School of Mathematics and Statistics, UNSW. It features a visual approach to the subject that stresses the importance of familiarity with specific examples. It also introduces 'rational curvature', a simple but important innovation. NJ Wildberger is also the developer of Rational Trigonometry: a new and better way of learning and using trigonometry.
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