Assessment task: An essay EITHER on a mathematical topic of your choice, OR on one of the designated essay topics; see below.
Designated Essay Topics:
Note that our advice and the Criteria for Marking apply to these topics exactly as they do to the choose-your-own topics. In particular, there is room to move in the topics below, and you are permitted to and must choose a suitably narrow aspect of the topic, which will permit you to focus. Try to get properly into the ideas, and read properly scholarly articles so you can do so. A thin overview based on slight rewording of Wikipedia pages will not score well. No particular references are suggested: it’s part of your job to hunt. But if you are really stuck, you can ask for advice.
My chosen topic Why are soap bubbles round?
Word limit: 1500 +/- a little.
The essay should be approximately 1500 words, excluding the references. You should have a title page, which includes a word count (and your name and student number!). We are not overly fussy about the word count, but if you are edging over 1700 words, then that is probably excessive. In the other direction, you will find that 1500 words is really not a lot, and it is difficult to stay under 1500 words. Below 1400 words suggests a pretty thin essay.
Generative AI tools cannot be used in this assessment task
POINTERS TO WRITING A GREAT MATHS ESSAY
Pointer Number 1: Do not be boring
The world is flooded with bad mathematics and science writing: don’t add to the flood. Try to choose a topic that genuinely interests you and that you’d genuinely like to learn more about. Then, your enthusiasm can come through in the essay.
Your essay can be along the lines of a mathematical exposition or it can be more philosophical in nature. In any case, your goal is for your essay to be clear and engaging for non-experts. Think of your audience as your fellow Nature and Beauty students; your aim is to explain some cool mathematics in a manner enjoyable to them.
Pointer Number 2: Do not be too technical
Yes, Marty will be able to understand the technicalities and jargon, but Marty is not your audience. Write for your fellow students, and if you need to take time to gently explain some ideas or language, then do so.
Pointer Number 3: Avoid trendy and done-to-death and lecture topics
The world is full of pseudomathematics, so be careful to avoid such topics, or approach them with a very critical eye. Past essays on fractals, chaos, the golden ratio, sports, Rubik’s cube, RSA and music have tended to be poor and to have scored poorly. If you suggest a topic along these lines it may well be rejected, and you’ll have to think again. If in doubt, just ask me or Marty.
Pointer Number 4: Choose a small topic
1500 words is not a lot, particularly when you have to explain technical concepts to a non-expert reader. It is much better to choose a very small topic and to explore it properly than to give a sky-high overview of some large terrain. Make every word count.
Pointer Number 5: Wikipedia is a good place to start and a bad place to end
General resources such as Wikipedia are great places to get going, but you’re aiming for something a lot more interesting and original than a reproduction of Wikipedia. Electronic databases such as Jstor (available via Monash library) are much better resources.
Popular maths books and articles, and the references they contain, are also a good place to get going. There are many such books, and many are very good. Some of our favourites are
*) The Heart of Mathematics: An Invitation to Effective Thinking by M. Starbird and E. Burger,
*)The Parsimonious Universe by S. Hildebrandt and A. Tromba,
*)The Shape of Space by Jeffrey Weeks, Why do buses come in threes by Rob Eastaway and Jeremy Wyndham,
*) Anything by Martin Gardner
*) The archive of Function magazine.
Pointer Number 6: Choose clear and sensible style and formatting
The essay must be typed, and you must include a full list of references and reasonable footnoting, but other than that the format is largely up to you. Just try to be clear. Headings and subheadings are very helpful. Diagrams – hand-drawn is fine – are very helpful (and they don’t contribute to the word count!) Boldface and italics and colours are good.
A good format to keep in mind is that of an article written for Plus magazine. Also, check out Burkard and Marty’s past maths column for The Age.
Pointer Number 7: Be accurate
Needless to say, everything you write should be correct (not only the individual facts, but also the logical arguments that connect them!). Before you hand in your masterpiece, you should have at least two thoughtful friends proofread it and provide you with feedback. Even if your native language is not English I expect you to produce an essay that is grammatically correct. Use a spellchecker to weed out spelling mistakes.
Pointer Number 8: Enjoy it!
Writing a very good mathematics essay is not easy. It is a lot of work. But it can also be really rewarding, to figure out how some piece of mathematics works so well that you can explain it to basically anybody. If you are doing it right, the essay should be tiring but a lot of fun.
The maximum number of marks for the essay will be 32. Deductions from these 32 marks are based on the rough essay rubric reproduced below. In general, it is comparatively easy to avoid deductions in terms of “clarity” and “nuts and bolts”. It is harder to avoid deductions in terms of “making sense”. It is VERY hard to avoid deductions in terms of maths and originality, particularly for the designated essay topics.
The only way anybody will get full marks for their essay is if we consider it to be publishable in a magazine like New Scientist or the Plus magazine website.
