Divisibility is a fundamental concept in mathematics, seamlessly integrated into our daily experiences, such as dividing a cake into equal parts or determining if one number is a factor of another. Traditionally, we understand divisibility to mean that a number \(a\) divides another number \(b\) (notated as \(a | b)\) if there exists an integer… Continue reading The Ideal Understanding of Divisibility

## My Solutions to 2023 HSC Mathematics Extension II

Here’s a link to my solutions: https://www.dropbox.com/scl/fi/qwrq9e5ptz5wxgy7f76hi/2023-Ext-2-Solutions-Mok.pdf?rlkey=idnadofksn2n9ehpi3ogtefsh&dl=0 Here’s a video I quickly recorded explaining the solution to the last question in the 2023 HSC Mathematics Extension II paper. This question made the Sydney Morning Herald: https://www.smh.com.au/national/nsw/not-seen-a-question-like-it-the-most-difficult-problem-in-this-year-s-hsc-20231016-p5ecms.html News.com.au also featured my video here! https://www.news.com.au/lifestyle/parenting/school-life/sadistic-hsc-extension-2-maths-question-thats-too-hard-to-solve/news-story/16e1e8eafa486ac15fbf67fa8ffbc2a1

## I’ve Done It! Modules and Reps is done!

In my post I’ve Applied for a Master of Mathematics Degree! I shared that I was most scared of the course in Modules and Representation Theory as I bombed that course in my undergrad degree (I got a 62). The UNSW term ended in May and I got my results back and I got a… Continue reading I’ve Done It! Modules and Reps is done!

## Horology, Slide Rules and Logarithms

Mathematics is obviously one of my interests, but admiring wrist watches is another. There’s something beautiful about the way a mechanical, battery-less contraption built up from miniscule parts could keep time as long as the wearer stays alive (of course taking into account servicing, etc but I digress). Placing a tool such as a watch… Continue reading Horology, Slide Rules and Logarithms

## It’s All Sets

Set Theory underpins the foundations of Mathematics. When all of modern Mathematics is formulated axiomatically with sets, it baffles me how much the syllabus requires us to hide it away from students in the HSC Mathematics courses. At the moment it only rears its head when dealing with topics in Probability and Venn Diagrams, and… Continue reading It’s All Sets

## What Are Random Variables?

Related Content Outcomes: MA-S1 Probability and Discrete Probability Distributions S1.2: Discrete probability distributions HSC, We Have A Problem The HSC Syllabus does not give a clear definition of what a random variable actually is – it rather describes what it does: know that a random variable describes some aspect in a population from which samples… Continue reading What Are Random Variables?

## My Journey In Mathematics

How did I get to where I am today? Here’s a trip down memory lane that I hope is a fun read! Maybe there are some lessons in reflection to be learned here, both for myself and my dear reader. Primary Schooling I’m not going to start with my early childhood days as I don’t… Continue reading My Journey In Mathematics

## Thoughts About Some Mathematical Practices

Here are some of my thoughts about some miscellaneous mathematical practices – some words of advice, warning, interesting insights, contentious disagreements, or whatever else comes to mind. This might become a multipart series as more comments come to mind in the future… Notation of Domains of Functions The domain of a function is a set.… Continue reading Thoughts About Some Mathematical Practices

## I’ve Applied for a Master of Mathematics Degree!

Probably the most exciting thing I’ve done during these last few months in lockdown is apply for the Master of Mathematics degree from UNSW. I’m just waiting on the acceptance and processing of the application, and fingers crossed that I get a Commonwealth Supported Place! I’ve been meaning to go back to university to study… Continue reading I’ve Applied for a Master of Mathematics Degree!

## What Are Numbers? Pt. 4: The Real Numbers

This is the final part on a series on ‘What Are Numbers?’. In this part, we discuss the construction of the set of the real numbers. Part 1: The Natural Numbers Part 2: The Integers Part 3: The Rational Numbers Part 4: The Real Numbers Polynomial Equations In the previous parts, we constructed the Integers… Continue reading What Are Numbers? Pt. 4: The Real Numbers