Office: 747 Evans
E-mail: kmill at math.berkeley.edu
- Math 55, Spring 2017
- Math 54, Fall 2016
- Math 54, Summer 2016
- Math 54, Spring 2016
- Math 1B, Fall 2015
- Math 1A, Spring 2015
- Math 1A, Fall 2014
- Quandles for the topology topics course. November 2, 2017.
- Spatial graph invariants for the 3-manifold seminar. September 19 & 26, 2017.
- The Alexander Ideal for “Knot Another Seminar”. April 21, 2017.
Math tools has programs for some possibly useful computations.
Notes has some notes.
Toys or demonstrations
- Hopf. Fly through a 24-cell and the Hopf flow in . WASD to move, click and drag to rotate perspective.
- zgraph is a complex function grapher that uses domain coloring. Someday it will have built-in documentation, but in the meantime I’m happy to explain it if you track me down!
- Complex polynomials. Type in a polynomial (for instance, x(x+2i)^2+1), then drag the circle () on the left side around to see its image () on the right. One reason every polynomial has a root is that for large radii the image will wrap around zero times, but for very small radii the image will wrap tightly around — and somewhere in between the image must pass through zero. Arrow keys animate the domain coloring.
- Curves. Just a grid phasing through resolutions of the intersections, inspired by Vassiliev invariants. Tab, space, and ’a’ do something.
- Julia set viewer. See this post for an explanation.
- Trefoil. A rotating tubular neighborhood of a trefoil knot; nothing deep.
- Cat transformation. Experiment with matrix transformations by transforming the image of a cat.
- Cat transformation: eigenvector edition. Shows how the eigenbasis is just scaled by the transformation.
- Basis toy. Experiment with bases of .
- Basis change toy. Experiment with two bases of .
- Heat equation & Wave equation. Click and drag a curve, then watch it evolve.
- Spring cart. A cart coupled by a spring to an oscillator.
- Row reducer. Computes the reduced row echelon form of a matrix mechanically, and displaying every step.
- Interactive cofactor expansion.