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.
If you want to know what this is all about, read my introduction to the series.
If you have already read the introduction, then welcome to the first Diversion in Mathematics! I emphasise, as I did in the introduction, that I will write with the general public in mind, so don’t be worried if you don’t consider yourself a “fan” of mathematics, or if you’ve totally suppressed all memories of maths classes from high school. And if you are a keen mathematician, whether recreationally or studying seriously at college/university, hopefully you will also find these blogs to be of some interest.