When I gave my first course back in 1971, I had absolutely no training in teaching. That's still the case, but at least now I have over thirty
years of experience. The most rewarding part of teaching is interacting with students.
According to my philosphy, there are two kinds of classes:
- Maths service classes.
These are courses in calculus, linear algebra, differential equations etc. for students who will not necessarily be
majoring in maths. Here I have to be on my best behaviour. There are some amazing students in these classes, but most of them are not really
interested in math. There are also some, perhaps many, who would rather not be there. The question "Should nurses be required to learn
Calculus?" comes to mind, and I would have thought not — but the university thinks otherwise.
- Dedicated maths classes. Especially in the honours stream these are a pleasure to teach. The courses are all about concepts and they can be
really challenging for students. Here I am pushing the students as hard as I can because I want them to develop into thinking mathematicians
and that won't happen if I wear kid gloves. There are some truly exceptional students in these classes and they are a constant
inspiration to me.
Over the years I have written many sets of notes for courses. The
following are available for download:
Analysis 2, MATH 255, Analysis in Metric Spaces, Numerical series, Riemann integration, Series of
functions, Power series, Elementary functions.
Analysis 3, MATH 354, Metric spaces. Calculus in several variables and to some extent on Banach spaces.
- Honours Analysis 4, MATH 355, Measure Theory, Abstract Integration, Basic
Functional Analysis, Fourier Series and Integrals.
Complex Analysis, MATH 366, Complex Analysis.
For the maths service classes I am a strong believer in the WeBWorK
developed by Prof. Arnie Pizer and Prof. Mike Gage at the University of Rochester but now maintained by the MAA. WeBWorK
is an internet
based method for delivering homework problems to students over the internet.
WeBWorK enhances the
educational process in several ways. By providing students with immediate feedback as to the correctness of
their answers, students are encouraged to make multiple attempts until they succeed. By individualizing problems, cheating is discouraged. By
providing instructors with real-time statistics, lesson plans can be customized to better serve students. Teaching assistants are released
from the chore of marking written assignments and can spend more time interacting directly with students.
The major way in which WeBWorK differs from other web-based homework systems is in the way problems are written. The PG
language allows the inclusion of both Perl and LaTeX code, allowing problem authors to take advantage of the syntactic efficiency
of Perl and the typographical flexibility of LaTeX (which is pretty much necessary for rendering mathematics expressions).