All my unimelb teaching sites are on canvas now.

This year I am:

  • content coordinator for Real Analysis, MAST20026
  • lecturing Partial Differential Equations, MAST90133

First and second year undergraduate mathematics majors should consider taking the "advanced" subjects, including Real Analysis: Advanced, MAST20033, a subject I helped create.

Animations: I like making interactive tutorials and mathematics visualizations. Check out my github with matplotlib animations here. I also made a related interactive tutorial on sequence convergence that you can find here. In Real Analysis, students learn mathematically rigorous notions of convergence. Here is a video showing a sequence of points in the plane converging to the origin.

The video shows the points in the sequence \[x_n = \frac{4}{(n+1)^{3}} + \frac{2}{(n+1)^2}, \quad y_n = \frac{2}{(n+1)^2},\] plotted in order \(n = 1, 2, \dots \). This sequence converges to the origin \((0,0),\) which means that, for each ball around the origin, all but finitely many of the sequence points lie within it. That is to say, for any radius \(\epsilon > 0,\) there is a sequence index \(N\) (the one indicated in the video) such that the \(N^{th}\) point and all subsequent points lie within distance \(\epsilon\) of \((0,0)\).