Subspaces – A Quick and Easy Introduction

Dear MATH1115 student, Want to become a master of subspaces? Check this out! Mathematically yours, Adrian. P.S. If "Mathematically yours" is too weird, then please replace it with "yours". P.P.S. I've written the word "yours" too much, and now that thing has happened to my brain where it looks like a funny word.

What’s the Go with Big Oh?

I had a couple of MATH1115 students ask me about big oh notation in maths, and so I wrote up a short help document. Hopefully it's useful. I'l have to spend some more time in the future and make it better.

Primes aren’t that pesky

Prime numbers. One of many sequences of numbers we introduce to innocent school children and their sponge-like minds. However, despite the simplicity of defining what a prime number is, they are tenacious buggers with little regard for the eye of the modern mathematician. They are also the best example of randomness and structure meeting each …

The Divergence of the Reciprocal Prime Series

The Divergence of the Reciprocal Prime SeriesJust a little thing I wrote on my favourite diverging series... Enjoy!

An Irrational Sum

I spent two straight days last week marking midsemester exams with my fellow tutors and the two lecturers for MATH1115. The exam contained a couple of questions on performing operations with irrational numbers, such as "is the sum of two irrational numbers an irrational number?" The answer here is a resounding 'not always', the common …

Irrational Numbers

Cold mornings and bright-faced first year students have signified the start of the teaching year here at the ANU. This semester, I'm running a couple of tutorials for MATH1115 Mathematics and Applications 1 Honours; a first year unit which gives students their first glimpse at analysis and linear algebra, both of which lie at the …

Keeping Away from High School

As a student of maths, I often get popped the question. Nope - not that one! I get asked whether or not I'm going to take to the local high schools and become a secondary maths teacher. I always say no but the suggestion does leave thought-crumbs in my head. So I think long and …

A Cute Paradox (Do Not Apply)

A maths teacher informs her class that the following week she will slap a surprise test on them. This will ensure that they keep up with the work and study every night rather than the night before the test. All of the students gasp in shock horror, except for some young smart-ass up the front who …

Harmonic Subseries and a Problem

I've spent a lot of my time recently thinking about harmonic subseries and whether or not they converge. I came across the paper Summing Curious, Slowly Converging, Harmonic Subseries and I thought it contained a result tasty enough to share on my blog. Remember the harmonic series: $latex \sum_{n = 1}^{\infty} \frac{1}{n} = 1 + …