Currently this is a placeholder page: you can find information on courses I teach through Moodle.
Teaching at Lancaster (Jan. 2014 onwards)
In the academic year 2020-21 I am teaching MATH225: Abstract Algebra, and MATH328: Number Theory.
In the academic year 2019-20 I taught Math 317/417: Hilbert Spaces, and Math 328: Number Theory. (No, the change of title is not a typo.)
In the academic year 2018-19 I taught Math 317/417: Hilbert Space, and Math 328: Number Theory.
In the academic year 2017-18 I taught Math 317/417: Hilbert Space, and Math 328: Number Theory.
In the academic year 2016-17 I taught Math 316/416: Metric Spaces, Math 426: Lie Groups and Lie Algebras, and Math 328: Number Theory.
In the academic year 2015-16 I once again taught the first half of Math 225: Groups and Rings, and all of Math 328: Number Theory.
In the academic year 2014-15 I taught the first half of Math 225: Groups and Rings, and also taught Math 328: Number Theory.
In the Lent term of 2014 I taught Math 328: Number Theory.
For my own reference, if nothing else, here is a copy of my old teaching page at the University of Saskatchewan.
Words of wisdom
On rigour and intuition
The point of rigour is not to destroy all intuition; instead, it should be used to destroy bad intuition while clarifying and elevating good intuition. It is only with a combination of both rigorous formalism and good intuition that one can tackle complex mathematical problems; one needs the former to correctly deal with the fine details, and the latter to correctly deal with the big picture. Without one or the other, you will spend a lot of time blundering around in the dark (which can be instructive, but is highly inefficient)
From Terence Tao's weblog. The whole post is worth reading.
Will I ever use this?
If the treadmill is not seen during the actual game, was it just a waste to use it? Were all those trainers wasting their time? Of course not. It produced (if it was done right!) something of value, namely stamina and aerobic capacity. Those capacities are of enormous value even if they cannot be seen in any immediate sense. So too does mathematics education produce something of value, true mental capacity and the ability to think.and
Education is built up with facts, as a house is with stones. But a collection of facts is no more an education than a heap of stones is a house.
From an online essay by Robert H. Lewis, which is worth reading, albeit with a sceptical alertness to rhetoric and anecdote.
Learning from lectures?
We do not learn to play the violin by playing the violin or rock climbing by climbing rocks. We learn by watching experts doing these things and then imitating them. Practice is an essential part of learning but unguided practice is generally useless and often worse than useless. People who teach themselves to program acquire a mass of bad programming habits which (unless they wish to remain hackers all their lives) they then have to painfully unlearn. Mathematics textbooks show us how mathematicians write mathematics (admittedly an important skill to acquire) but lectures show us how mathematicians do mathematics.
From T. W. Körner's 2004 essay In Praise of Lectures, available on his webpage under the blunter title "How to listen to a maths lecture".