Undergraduate Material
Books and Notes for upper level first and second year courses.
The 2010 “ANU Last Lecture”.
First Year University
The Foundations of Calculus notes present the theoretical foundations of Calculus. They are an introduction to the methods used in modern mathematics. In the process of working through this material you will prove the major theorems used in the Calculus section of MATH1115 and to a lesser extent in MATH1116 (first and second semester of advanced first year mathematics).
Second Year University
The book Introduction to Analysis provides an introduction to Mathematical Analysis, which roughly speaking is the “in depth” study of Calculus. It begins with informal discussion of a general nature concerning logic and the nature of mathematical proof, and some discussion of set theory.
There are separate booklets of Problems and (some) Solutions.
The mathematics there is basic to most subsequent mathematics courses (e.g. differential equations, differential geometry, measure theory, numerical analysis, to name a few), as well as to much of theoretical physics, engineering, probability theory and statistics. Various interesting applications are included, in particular to fractals and to differential and integral equations.
Various Sets of Notes
Here are some basic notes on self-adjoint, unitary and normal matrices.
Some of the material in the Graduate page might also be of interest.
Last Lecture 2010
In 2010 I was nominated, and then elected by ANU students at large, to give the symbolic “Last Lecture” in the Great Hall at University House: Mathematics, Free Will and the Human Condition. (The “Last Lecture” was an ANU “tradition” that existed from 2006–2018.)
Last Lecture 2010 (Unfortunately there is occasional loud static. The video consists of zooming and panning photographs, together with the slides.)
Last Lecture Slides (Just the slides)