Daniel’s Journey To Pure Mathematics & HSC Study Tips

Meet our Mathematics Mentor: Daniel

Maths is all about understanding the rules of the game and then being able to use them to your advantage.

ATAR:

99.65

Alma Mater:

Christian Brothers’ High School, Lewisham

HSC Subjects:

English Advanced, Mathematics Extension II, Physics, Chemistry, Legal Studies and Studies of Religion I

High school achievements:

Dux of Christian Brothers’ High School, Lewisham

5th in the state for Studies of Religion I

1st in school for Physics, Chemistry, Mathematics Extension 1 and Studies of Religion 1

Can you tell us a bit about your high school experience?

High school was an interesting time to be alive – as it always is.

Academically, I was always interested in Mathematics and Science, especially Physics. I was lucky enough to have excellent teachers throughout high school, hence why I took mainly science subjects. So much so, that up until halfway through Year 12, I wanted to be a high school Mathematics teacher. As such, I took the highest level of Mathematics I could, as well as those other subjects which strongly interested me.

Outside of my studies, I debated, I played the piano and played a lot of (usually open-world role-playing or strategy games (all rather badly).

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What are you studying in University, and what do you want to pursue afterwards?

Once I had gotten about halfway through Year 12, I figured that while teaching at high school would be fun, teaching at a higher level would be even better.

Additionally, the academic path would permit me to make original contributions to my field of choice. Hence, when I finished school, I chose to do my undergraduate in Advanced Science majoring in Physics and Mathematics, with the intention of doing a PhD upon completion.

I am currently in my fifth year, have completed my Physics undergraduate and will complete honours in Pure Mathematics next year, either in operator theory or model theory (I’m still deciding).

During my degree, I have stayed in Theoretical Physics and Pure Mathematics. I completed two research projects with the Atomic Physics group at the University of New South Wales (UNSW) under Associate Professor Julian Berengut over the course of late 2017 – late 2019 (late second to late fourth year), resulting in two publications in Physical Review A. Participating in active research was definitely an amazing, edifying and humbling experience, and I strongly recommend anyone who is interested in it start as early as possible.

After I complete my undergraduate, I will probably take a bit of time off – University has been exhausting. Then, I will most likely apply for a PhD placement, at the moment in Pure Mathematics (though that is, of course, subject to change), with the intention of pursuing an academic career in Mathematics or Theoretical Analysis.

What inspired you to teach at Talent 100?

I was lucky to have excellent teachers.

One cannot overstate the influence good teachers can have in a person’s life, irrespective of what they teach. It soon developed into one of my goals in life to be able to have an impact like this in people’s lives. I’ve been teaching at Talent for 3 years, and have taken two, three and four unit maths, as well as Year 11 two unit and Year 11 and 12 Physics.

Furthermore, my specialisation and my interest is Mathematics. A horrific misconception that is generally ingrained throughout high school is that Mathematics is about algorithms and methods.

Students encounter a question and the first thing they ask is “what method do I use” or what’s the formula.” Mathematics is so much more than just remembering the right bit of alphabet soup. It’s a way of thinking, both critically and logically. It’s about understanding the rules of the game and then being able to use them to your advantage. More fundamentally, Pure Mathematics is about is about abstraction and playing with abstract objects. It often has nothing to do with reality and doesn’t at all need to. It’s weird and fun, and I immensely enjoy both doing it myself and teaching others about it. I find it truly beautiful; I want the world to share in its beauty, and I want to share its beauty with the world.

As such, I like teaching topics where I can explore interesting ideas and topics which are less algorithmic. For instance, I really enjoy teaching the theory of real calculus, complex numbers, or proof and logic.

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What are some of your tips for students sitting the HSC this year?

The best way to learn Mathematics, is to do Mathematics.

For each topic, read over the concepts, including the relevant theorems and their proofs. Don’t underestimate the proofs! While knowing when to apply a theorem is useful knowing why it is true is even more helpful, as it will offer additional insight into its application, and when it can be applied will generally be made clear in the proof. More pragmatically, it can reduce the number of things you need to remember –rather than an entire series of results, a single result and a couple of reminders of how to derive certain things is much more compact.

As you’re reading through the theory, do some example problems. Then, do the exercises until you’re confident with the material. Sitting and memorising pages and pages of formulae is useless without practice in using them.

Doing past papers has limited utility. In my experience, doing papers timed is best for working on your exam technique – how to approach a paper, how to divide your time and keeping your composure during an exam situation. If you’re reasonably confident with your exam technique, then my suggestion is to not bother with doing past papers timed. Use past papers as additional exercises i.e further practice in solving problems. Remember, papers are designed to be completed in the time given; if you’re on top of your content, then time shouldn’t be much of an issue.

The HSC is stressful at the best of times, and these aren’t exactly the best of times.

Remember that the most important thing is to take care of yourselves. When studying, remember to pace yourself, give yourself plenty of time to study and prepare so as to minimise the amount of stress you’re under immediately before and take regular breaks during.

Spend some time with your friends and do some things that you enjoy too – exercise, play some music, make some things, play some games, read a good book, drink some tea and watch the sun rise – whatever makes you happy. If you need help, you’re allowed to ask for it. Take care of yourselves and each other.

What’s something people might not know about you?

I fence sabre in my spare time. I’ve been fencing since the end of 2016 (with a bit of a hiatus from March 2016 to about June 2019) and am the current president of the UNSW Fencing Club.

I also look significantly different to my official Talent photograph – I’ve grown my hair and a beard!

Click here to view our Talent 100 online timetables for Term 3, and enrol in one of Daniel’s classes.