High School Years 11/12

Online RSA mini-mooc  EdX style course, number theory and the mathematics of RSA cryptography, starts from Year 10 mathematics.  (When you first click the link you will be prompted to sign up for an edge.edx.org  account.  This is necessary even if you already have an edx.org account. The platform is essentially the same in both cases).

Introduction to Contemporary Mathematics  This is the main text for a course for selected Year 11 and 12 college/high school students, which has been running since 2006.  Topics: An introduction to number theory and RSA cryptography; real number system, a hierarchy of infinities; fractals, chaotic behaviour; geometry and topology.

Why Study Mathematics?  Slides for a 2015 talk to Canberra Grammar students in Years 8 to 12.

1962 High School Exams and Solutions  1962 upper level mathematics exams, when there was one less year of high school.  Questions, solutions, comments and general information.

First Year University

Foundations of Calculus  The theoretical underpinnings of calculus -- for the upper level first year mathematics stream.

Second Year University

Introduction to Analysis, Problems, Solutions  For the upper level second year mathematics stream. 

Third Year University & Higher

Analysis 2,  For the upper level third year mathematics stream. 

Measure Theory  A series of 5 lectures presenting an overview of measure theory, emphasising motivation and ideas, with minimal required background.

Elliptic Systems  A series of 5 lectures presenting an overview of elliptic systems of partial differential equations, their singularities and their partial regularity. Ideas and techniques for simple model problems, with minimal background required.

Finite Elements From a couple of seminars when I was putting together my thoughts on finite elements.