High School Years 11/12

See High School material for

• The text Introduction to Contemporary Mathematics: a course for selected Year 11 and 12 college/high school students, from 2006--2025.  Topics: An introduction to number theory and RSA cryptography; real number system, a hierarchy of infinities; fractals, chaotic behaviour; geometry and topology.
• Videos and an online RSA mini-mooc: EdX style course, number theory and the mathematics of RSA cryptography, starts from Year 10 mathematics.
• Teacher Workshop material.
• 1962 upper level mathematics exams, when there was one less year of high school.  Questions, solutions, comments and general information.

Undergraduate

See Undergraduate material for

• Foundations of Calculus: The theoretical underpinnings of calculus -- for the upper level first year mathematics stream.
• The text Introduction to Analysis, together with Problems and  Solutions: for the upper level second year mathematics stream.
• Occasional other notes, including self-adjoint, unitary and normal matrices.

Honours, Graduate, Seminars

See Graduate material for

• Analysis 2: Third Year Honours Level course.  Topology, Axiom of Choice, Measure Theory, Lebesgue Integration, Hilbert spaces, Lebesgue’s differentiation theorem.
• Finite Elements: A brief introduction assuming a little background in Sobolev spaces.
• Measure Theory: 5 lectures at a graduate student workshop.
• Elliptic Systems: Another 5 lectures at the same workshop.
• Axiom of Choice: Proofs of the equivalence of 5 standard versions of the Axiom of Choice.
• Mathematical Economics: Basic terminology, Edgeworth box, core of an economy, Walras equilibrium.
• Probability Basics: Measure theoretic approach. Borel-Cantelli lemma, weak and strong versions of the law of large numbers, renewal theorem, continuous-time jump Markov processes [CJM].
• History of Foundations of Mathematics: 2024 MSI colloquium. From 1870 to current. Some material is more technical than given in the colloquium. But at least the history and the individuals involved will be interesting! Extensive annotated bibliography.