# Teaching

I have started keeping a teaching diary of sorts. Skip to things below:

- Reading course: Introduction to Banach Spaces and Algebras
- Lecture courses
- Popular talks
- Video mini-lectures

## Year 2014/15

I continue to be the admissions tutor. I am tutoring a group for
**MATH1025 Number Systems** and for
**MATH1225 Introduction to Geometry**.

## Year 2013/14

I am now the (full-time) admissions tutor, and so have a much reduced
teaching load. I tutored a group for **MATH1025 Number Systems**.

In the 2nd semester, I had a project student on **MATH3083**, and
a number of students working on essays for **MATH3000**.

## Year 2012/13

I continued to be the deputy admissions tutor, working with Dr Daniel Read.
I gave the 2nd half of the course **MATH1010 Mathematics I**, this time with
a slightly re-written linear algebra section, and worked with Dr Phil Walker,
pioneering e-assessment on this module. I tutored a student on the project module
**MATH5004** and run tutorials for **MATH1010** and **MATH1225**.

In the second semester, I ran workshops for the new module **MATH2016 Analysis**,
tutored on **MATH3000**, and continued tutoring on **MATH5004**.

## Year 2011/12

I lectured the 2nd half of the course **MATH1010 Mathematics I**,
a new course--my part featured partial differentiation and an introduction to
matrix algebra. I also tutored students for this module.
I also tutored students on the project module **MATH3083**, and
ran workshops for **MATH2015, Analysis 2** (the final time this module ran), tutored
students for **MATH1060** and finally helped out with **MATH3000** again.

I also ran a reading course **MATH5002** based around the book
"Introduction to Banach Spaces and Algebras" by Allan. Please
see below for some teaching resources associated
to this.

I also began my new job as the deputy admissions tutor, working with Dr Daniel Read. Not strictly teaching, but rather recruiting the next generation of undergraduates.

## Year 2010/11

I lectured the first semster of **MATH1035, Analysis I** (which is the final year
this course is running) and also the course **MATH2200, Linear Algebra 2** (now
lectured by Dr Schuster). As ever, I also supervised students on the project
modules **MATH3000** and **MATH3083**, and tutored on **MATH1060**.

## Year 2009/10

I lectured **MATH5015, Linear Analysis I**, and **MATH1035, Analysis I,**
in the first semester, and
**MATH3181, Inner-products and Metric spaces** in the second semester.

## Year 2008/09

I lectured **MATH5015, Linear Analysis I**, in the first semester, and
**MATH3181, Inner-products and Metric spaces** in the second semester.

## Year 2007/08

I lectured **MATH5015, Linear Analysis I**, in the first semester.

## Introduction to Banach Spaces and Algebras

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 doesn't, sadly, make sense from the point of view of the programme at Leeds. 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.

## Popular talks etc.

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 recently 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!

## Video mini-lectures

As part of taking the ULTA2 teaching course at Leeds, I have been experimenting with making video mini-lectures: basically narrated PDF files of small, important sections of my current lecture course, MATH3181.

I plan to post more details here in the future, but for now, the bare minimum of details.

I produced PDF files using the standard LaTeX package Beamer. I then recorded the beamer presentation with my narration using the free package CamStudio. This produces AVI file output, and can also produce Flash output.

CamStudio refused to record the window of Acrobat Viewer, so I had to use my DVI previewer, YAP. Audio was recorded using an old, very cheap clip-on microphone. I uploaded the video to the University of Leeds video hosting project, LuTube. You can see my mini-lectures:

On the VLE I also added the PDF file and an MP3 of the extracted audio, so students could download the files and use them away from an internet connection. Obviously the PDF is no longer syned to the audio, but an advantage of this system is that it's not at all hard to see where in the PDF I am narrating.

# Links

- MAGIC group - Postgrad teaching based out of Sheffield.
- iSquared magazine - Of interested to undergrads.

# IT links

I'm a bit of a cynic about the possibility of using IT in teaching mathematics. So here I'm trying to prove myself wrong by collecting links to uses of computers in teaching.

- How to invert a sphere - Great video, which is long and goes into a lot of detail, but without becoming tedious, about some basic topology. Would be a fun way to motivate a first course on algebraic topology, but is so long that students would essentially have to watch it in their own time (or maybe you could break it up and make a whole lecture out of it -- assuming you had a spare lecture going...) Anyone else think that the woman sounds just like Marina Sirtis? (Hat tip to John Baez).
- Moebius Transformations Revealed.