RESEARCH (Tab above for more details)
TEACHING, NOTES etc. (Tab above for more details)
High School Years 11-12: Online RSA mini-mooc, Introduction to Contemporary Mathematics, Why Study Mathematics?, 1962 High School Exams and Solutions
First Year University: Foundations of Calculus
Second Year University: Introduction to Analysis, Problems, Solutions
≥ Third Year University: Analysis 2, Measure Theory, Elliptic Systems, Finite Elements
A series of talks on the foundations of quantum mechanics, leading to quantum computation.
Meetings Seminar room 1.33, Hanna Neumann Building 145, ANU. 3-5pm some Fridays.
31/5/19 “Entanglement: Conundrum or Resource?” Discuss/review: Notes pp1,2 Grothendieck, Socrates/Plato perspectives on QM; Ch 3 Bell States (invariance properties, preparation, measurement), quantum circuits (CNOT gate and entanglement), tensor product of operators and applications, superdense coding and teleportation, comments on CHSH experiment.
If you missed any of the first 3 talks, (and ideally in any case) have a quick look through Chapter 3 and you should be fine.
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
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.