I lecture on a wide variety of undergraduate level courses, along with working with students on projects at undergraduate and masters level.

Students can find all resources on Blackboard. Some older resources can be found below.

I lecture on three courses, spanning the three undergraduate years: **Introduction to Real Analysis**,
**Cryptology**, and **Complex Analysis**.
I have re-written the Cryptology course, and changed the assessment to be more continuous, thus allowing more student feedback.
I am supervising a group Mathematical Modelling project on **Queueing Theory**, and a masters project on
**Machine Learning**, a blend
between theory and some practical work with the Python ML stack.

I joined uclan midway through the teaching year, but immediately picked up two lecture courses, **Introduction to Real Analysis**
and **Cryptology**, as well as covering for a colleague on the course **Further Real Analysis**.

In my previous lecturing position, I lectured on a wide range of courses including 1st year Analysis (a major re-write of the course), 2nd year Linear Algebra, 3rd year Metric spaces (to a joint-honours cohort), a masters course on Measure Theory, and a first year "Calculus" course. I tutored a variety of student projects, from short projects through to full year masters level projects. I also ran a reading course, see below.

My first lecture course was a measure theory course, for which I produced some materials which are available:

Looking back, I was quite ambitious, both in terms of the material to cover, and the amount of work I put into typing things up.

I typed up notes for various lecture courses as an undergraduate. The only one which is complete is:

In 2012 I lead a reading course on the book "Introduction to Banach Spaces and Algebras" by Graham Allan (an old lecturer of mine). See Amazon link or OUP link to buy the book.

I had a slightly troubled time with this book. Some positives:

- The book is self-contained, and would be accessible to anyone with a basic course in Banach spaces, but without exposure to the Baire Category family of results, nor to any measure theory.
- The book takes you all the way to understanding the basics of von Neumann algebras, with a careful treatment of various functional calculus theorems.
- It's hard to think of any modern book which is similar.

However, there are also some negatives:

- At times, this is not an "introduction"-- consider the treatment of the weak and weak* topologies; or see below for various clarifications which I had to write.
- The decision not to sure measure theory didn't, sadly, make sense from the point of view of the programme at Leeds, at least when I ran the course. Similarly, not introducing nets makes for what feels like a very convoluted treatment of von Neumann algebras.

Various teaching materials, in LaTeX and PDF formats. This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.

- Original advert: the original plan. We ended up covering less material than this. LaTeX Source and PDF.
- Summary: this gives a guided reading of the book which I followed. LaTeX Source and PDF.
- Corrections and clarifications: There are a number of places in the book where it's written: "it's easy to see..." or similar. This is of course a dangerous thing to do, and I think in a number of places very misleading. This document gives some more details. The same applies to some exercises: some of these are much (much) harder than the author(s) must have thought. LaTeX Source and PDF.
- Further exercises: LaTeX Source and PDF.

I helped Richard Elwes give a popular talk, to sixth-form students, on knot theory. This was part of the Leeds Festival of Science. Special thanks to Ruth Holland, Hazel Kendrick and David Pauksztello. We repeated the effort as a "Reach for Excellence session".

The following are some handouts (with LaTeX source) which I produced. The margins of the PDF files are off, probably because I used pstricks, and hence ps2pdf, instead of pdflatex.

- Some knots: PDF file and LaTeX source.
- The writhe: PDF file and LaTeX source.
- The bracket polynomial: PDF file and LaTeX source.
- The Jones polynomial: PDF file and LaTeX source. Experts will notice that we massaged the definition a little!

Recently, again with Richard Elwes, I gave a session as part of the Leeds festival of science on the subject of Pick's Theorem. It is always tricky leading A-Level students through a pure mathematics proof, but it's also very pleasing to see some students (often not those you expect!) suddenly "get" the point, and start to really understand something new.

- Handout (PDF) which should be used with the excellent JAVA applet at: Cut the knot Geoboard
- More spotted paper (PDF).
- Proof of the theorem.

I run a "Quiz night" as part of the annual 6th Form Conference held at the university. Thanks for Alan Slomson, on whose idea this was based. Contact me if you would like further information: I won't post the quiz, to discourage cheating!