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Handouts

• Mapping of Text Chapters

• First Day Lecture

• Topology Midterm Solutions

• Topology Paper

Notes from Logic and Sets to Topology

• Introduction to mathematical arguments, Hutchings

• Logic and Set Theory - H. D. Pfister

• Summary of Point Set Topology, J.P. May

• A Quick Review of Point Set Topology - Terence Tao

• Concise Algebraic Topology - J.P. May

• Topology Without Tears - S. A. Morris

Topological Spaces

• A Few of My Favorite Spaces: The Real Projective Plane

• Quotient Topology

• Jos Leys' Gallery - Movies of quotient spaces

Glomes

• Hopf Fibration

• Hopf Fibration Video

• MATLAB hopfcircles.m, hopfmap.m, glome.jpg

• An Elementary Introduction to Hopf Fibrations

Historical

• Vorstudien zur Topologie - Johann Benedikt Listing 1848 - PDF

• Scottish Physics and Knot Theory's Odd Origins PDF - D. D. Silver

• Birth of P G Tait, Pioneer of Knot Theory - APS News

• Orbits of Asteroids, a Braid, and the First Link Invariant - M. Epple

• The modern legacies of Thomson's atomic vortex theory in classical electrodynamics - S. J. Lomonaco

• Life and Scientific Work of Peter Guthrie Tait - book

• History of Knot Theory - J. H. Przytycki

• Kelvin's Brilliant Vortex Atoms

• Königsberg Bridge Problem

• The great vectors-versus-quaternions debate

Fun Reads

• What is Topology?

• Ten Signs a Claimed Mathematical Breakthrough is Wrong - Scott Aaronson

• The Alternative-Science Respectability Checklist

• Euler Characteristic

• Knot Lecture

• Tori Story and From Mobius Bands to Klein-Knottles and Torus Eversions

Advanced Reading

• Topology in Physics lecture notes

• A Tale of Topology by G. Foland

• Reflections on the History of Topology I. M. James

• Topology and physics-a historical essay C. Nash

• Geometry, Topology, and Physics M. Atiyah

• Knot Theory Links

Videos (also in Links)

• Peter Guthrie Tait: A Knot's Tale - J. Collins

• Virtual Knot Theory - L. Kauffmann

• Topology Lecture - F. P. Schuller

• Topology - B. Zimmerman

• Topology Without Tears - Morris

  • Video 1 - Pure Mathematics

  • Video 2a - Infinite Set Theory: Part (a) - See 1:45

• A Vortex Tied in Knots: UChicago physicists succeed in creating a vortex knot

• Knotted vortices in real fluids

• Jonny Evan's Video Lectures on Topology and Groups

• History of Algebraic Topology - Pierre Albin and Other Lectures

• Visualizations of the Hopf fibration

• Hmmm ...  Topology of Countries - but the second is also interesting