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
Tag: numbers
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
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 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
What Are Numbers? Pt. 3: The Rational Numbers
Welcome to a four part series on ‘What Are Numbers?’. In the previous part, we constructed the Integers by using the equivalence classes of Natural Number ordered pairs that represent equations in the form \(x + b = a\). For example, the Integer we write down in the usual way as \(-2\) describes the set… Continue reading What Are Numbers? Pt. 3: The Rational Numbers
What Are Numbers? Pt. 2: The Integers
In Part 1, we see that the building blocks of numbers start with the Natural Numbers defined through the five Peano Axioms. In this post, we ponder the invention of the Integers. Welcome to a 4 part series (this is part 2) of ‘What Are Numbers?’. Part 1: The Natural Numbers Part 2: The Integers… Continue reading What Are Numbers? Pt. 2: The Integers
What Are Numbers? Pt. 1: The Natural Numbers
In the last few days in the recent Covid Sydney lockdown period, I had a chance to read and revise on some abstract Algebra concepts such Group Theory, Rings, Fields and Galois Theory. I was reading mainly from the book “Abstract Algebra and Solution by Radicals” by John E. Maxfield and Margaret W. Maxfield amongst… Continue reading What Are Numbers? Pt. 1: The Natural Numbers