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

# Category: Maths

## 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

## 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

## The Language of Proof in HSC

Related Content Outcome MEX-P1 The Nature of Proof This post will primarily look at the following dot-point from page 28 of the Extension II syllabus: use the formal language of proof, including the terms statement, implication, converse, negation and contrapositive (ACMSM024) – use the symbols for implication (⇒), equivalence (⇔) and equality (=) , demonstrating a clear understanding of the… Continue reading The Language of Proof in HSC