Minority Effort: Teaching Lesser Known Mathematical Physics

I have posted less and less in social media because I find many posts to be distracting, intrusive and sometimes annoying. Most posts are opinions that tend not to matter. So I'm taking lessons from these. I am limiting my posts there for information that are probably more useful to my group and friends and are also of immediate interest. If I post here, there is a high chance that it will not get read. The posts here are really for those who are really interested in what I personally think. If not, they won't probably reach here.

The last few days have been busy preparing solutions to mathematical physics problems that might help the students for their final. Since the course is an advanced course for graduates and most books do not have solutions to the problems in the books, I have to work them out on my own. Some of which I fumble as my students discovered (of course, rectifiable). One can try to search solutions online (if they are there) but even so, one still need to internalise them to one's own thought patterns. Otherwise, one would be parroting - have experienced these in my early teaching days and one felt dreadful.

When I first started planning for this course, I was discussing with Dr. Nurisya on what one should teach because one can approach mathematical physics in zillion of ways. One thing clear in my mind, was not to repeat much of what was taught in undergraduate mathematical physics. I have taught the subject twice (I think) years ago in two different styles - computational mode using Mathematica (one student made the remark right to my face, it was a waste of time), and another calculational mode involving non-theoretical students that had me repeat some undergraduate stuff (finally was given to a different lecturer). This time, I had the opportunity to start afresh with the students attending are theoretical students. The book adopted was Szekeres' book. Peter Szekeres was my lecturer in Adelaide, teaching relativity and differential geometry. The book started off with set theory all the way up putting more structures. 

The book had 19 chapters altogether. Of course, I could not teach the whole book in one single semester - it needs at least, two semesters. So, one needs to pick and choose. Dr. Nurisya wanted me to delve into Lie Groups ad Geometry. Nice idea and was hoping to do so. But the relevant chapters in Szekeres' book are Chapters 15-19, right at the end of the book. I had to improvise. I thought that I should teach relatively unfamiliar topics like throwing in logic with set theory, delve more into rings, integral domains and fields, take a swing at algebraic numbers and quadratic extensions, introducing less familiar language of rings and modules instead of vector spaces. The second last one, was something that I stumbled into when doing quantum theory on hyperbolic surfaces and more recently theoretical computer science and cryptography. Alas, I did not get into differential geometry; it was already too much. There was a cursory glance on Lie groups during topics of groups and algebras. So, it was not perfect. I offered myself to the students to teach (unofficially) further Lie groups and Lie algebras using William Goldman's lecture notes that ties up nicely with differential geometry (including hyperbolic geometry). Not sure whether they want it or not.

All the efforts above would not be visible for my annual assessment. No marks or recognition goes to the hard work of understanding and lecturing a difficult subject. No marks or recognition goes to unofficial teaching. Do I care? Well, no and yes. No, since my intent is to teach everything I know before I leave. Yes, if people start making a fuss over me being busy with 'unofficial' things that does not 'benefit' the department.

Here is something I felt all these years.

Credit to Duncan Sabien FB post from where I pinched this pic.