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!
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:
At the beginning of the year, I promised that I would try to write more regularly. This has clearly not been achieved! In my defence, studying mathematics full-time requires much dedication, patience, and practice — not unlike learning a musical instrument. But now I have time to write since I have completed my semester 1 exams.
(Main article is below)
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.
Announcement of première performance of Three Concert Pieces for piano
I am very pleased to announce that my Three Concert Pieces for piano will receive its première performance in the Utzon Room at the Sydney Opera House on 9 February at 7 pm. The pianist is a good friend and colleague, Nicholas Young, with whom I collaborated frequently during our time at the Sydney Conservatorium. It is a pleasure to work with him again, but this time as a composer!
For more information about the concert and ticketing, click here to be directed to the corresponding page on the Sydney Opera House website.
For some insight into Nicholas’ project, and the rationale behind such a concert, you may be interested in this interview for CutCommon magazine.
The program notes for the concert are available online now.
Dear reader, thank you for visiting the blog, and happy new year! This is an update post, letting you know what I have been up to in the last few months.
This would seem like an awkward mix of topics, but hopefully I can convince you of the similarities. The connection occurred to me recently, as I have been tutoring a student for theory and sight-reading in preparation for a grade 4 AMEB violin exam. (The AMEB is the Australian Music Examinations Board, a bit like the local Aussie version of the ABRSM, which is a world-wide music education organisation). In addition to preparing a set of pieces for performance, the student sitting the exam must also answer questions relating to music theory and history. I have only ever taken one AMEB exam in my life, so I don’t know exactly what kinds of questions are asked during a typical exam. Based on this student’s learning materials, I can deduce that, at this early stage in the progression of grades, they are likely to be questions regarding the fundamentals of music history and analysis, such as: “What is a concerto?”; “What is the form of this movement?” (binary, ternary, ritornello, and “through-composed” are the expected possible answers at this grade — sonata form comes later!); “The music of Mozart is representative of which period of music?”; “You just performed a piece by Handel, can you name some other pieces by Handel?”; “What does allegro moderato mean?; and so on. This is not particularly challenging. A student who is curious and motivated will probably know the answers already, via searching on Wikipedia and other sources on the internet. These basic concepts of Western classical music may also be covered in high school music classes, if the school is fortunate enough to provide them. For the average student, these facts can be imparted easily by the teacher during a lesson, with the additional advantage that explicit examples from the music being practised may be used. With a little more effort, the fundamental concepts of musical analysis and theory can be similarly acquired, or else taught in the lesson too. Remember, at this early stage (grade 5 or below), the student only needs to recall the basic facts.