Update post (July 2019)

It seems that every time I return to write something on this blog, it’s about how infrequently I write (and that I’m awfully sorry, and I promise to write more, but it never happens). I see three main reasons for this:

• I am now in a masters program in the School of Mathematics at the University of Sydney! My honours year went quite well overall, and my supervisor was happy to take me as a postgraduate research student.
• Since March, I have also been working casually for Matrix Education, a private tutoring company that is well-known in particular for its HSC preparation courses.

From the two reasons listed above, you can appreciate that most of my time is spent doing mathematics in some way — reading articles and learning new theory for my research project, working on exercises from textbooks, or preparing tutorials and classes. The third reason is really a blend of two:

This update post will explain this last point further.

Update post (June 2018)

Hey, I almost forgot I have a blog! (Since I’m paying for the site hosting, why not make more use of it).

This post will simply be an update, to let the readers of this blog (the number of which is non-zero) know what I am currently doing. It will be a random assortment of thoughts and comments. Right now, I am busy preparing for the semester 1 exams in the Pure Mathematics Honours program at the University of Sydney, but it is nice to take a break from study and write something here. Needless to say, it has been a very challenging semester, but also quite a rewarding one. Mathematics honours students are required to take a total of 6 courses throughout the honours year, as well as prepare a thesis. Many (?) people opt to take 4 of the 6 courses in the first semester, with the intention that more time can be devoted to the preparation of the thesis in second semester. But naturally, this means that one undertakes a lot of coursework in first semester (4 honours level courses at the same time is no joking matter), and as I am prone to procrastination, the time management has been especially challenging. Fortunately, I get along well with my thesis supervisor — who is conveniently also the honours coordinator this year — and he has been understanding and supportive during the periods when I had many assessments to submit and had not worked on the honours project!

Learning, Unlearning & Relearning

This piece is slightly different from what I usually post on this blog, but I believe I have a unique perspective on the issues concerned, as I will explain in the main text.

I would like to discuss the current advertising campaign from the University of Sydney, and in particular the chosen keyword:

Diversions in Mathematics #2: Hilbert’s Hotel

In this instalment, I introduce the concept of infinity in a simple and (hopefully) entertaining way, which puts into practice the counting concepts introduced in the previous Diversion. In fact, Hilbert‘s infinite hotel was one of the ‘stories’ that got me seriously interested in mathematics in the first place, and so it is a pleasure to share it here. This is a very well-known piece of story-driven mathematics. I hope that experienced mathematicians who happen to come across this blog do not tire of hearing (reading) it again, and that they see the value in telling the story to the general public.

Just before we start: I assume knowledge of the definitions and notations introduced in the previous instalment, namely, the very basics of set theory.

Sight-reading, AMEB exams, and studying maths

I have always been interested in maths, and not only in the subject itself but also the ways in which maths is explained and taught. In general, a crucial part of studying and researching is to be able to communicate one’s findings to other people, who may or may not be knowledgeable in your field. For this reason, I’m all for popular science books and magazines, which (provided that it is done well) serve to explain scientific research in an accessible way, and to promote scientific awareness and appreciation amongst the general public. However, in my opinion, popular science books too often simplify, and even completely skip the mathematics behind the science. There is certainly a cultural aversion to mathematics — at least from my perspective as an Australian, and from my awareness of similar attitudes in the US and UK — which may be part of the reason for the lack of ‘real’ mathematics in popular science writing. Here is an anecdote: apparently Stephen Hawking’s publisher advised the great scientist that every equation he included in his A Brief History of Time would result in reduced sales. (There is one equation though: Einstein’s $E = mc^2$). Of course, this is one of the bestselling science books ever, and sits atop many a coffeetable, but I wonder how many people have seriously read it…