# Diversions in Mathematics 3a: The Cauchy-Schwarz inequality (part 1)

### Preface

After a long time, I have decided to resurrect the mathematics part of this blog! I started Diversions in Mathematics as a way for me to try to explain mathematics to the general public. This continues to be the main goal of this series of blogposts — for a more detailed introduction, please read the introductory remarks. I wrote two posts in this series, but then abruptly stopped. Part of the reason was that my studies got in the way, but I was also unsure exactly what material to present, and how to present it. I wrote down some of my thoughts on this matter in a previous update post.

One of the main issues as a writer is to consider the readers’ background in mathematics. For posts targeting the general public (like the previous two Diversions), I have tried to assume as little as possible while maintaining the discussion at an intelligent level, i.e. without “dumbing down” anything) However, this already assumes familiarity with many mathematical concepts taught in high school, or at least, some level of maturity in regard to abstract reasoning. Consequently I have decided to relaunch Diversions in Mathematics with high school mathematics as a foundation.

In this blogpost, I will introduce the Cauchy-Schwarz inequality, one of the most fundamental results in mathematical analysis, with the aim of connecting various topics that are typically studied in the Year 12 HSC maths curriculum in NSW. The main article is below.

Continue reading “Diversions in Mathematics 3a: The Cauchy-Schwarz inequality (part 1)”

# Update post (June 2018)

Hey, I almost forgot I have a blog! (Since I’m paying for the site hosting, why not make more use of it).

This post will simply be an update, to let the readers of this blog (the number of which is non-zero) know what I am currently doing. It will be a random assortment of thoughts and comments. Right now, I am busy preparing for the semester 1 exams in the Pure Mathematics Honours program at the University of Sydney, but it is nice to take a break from study and write something here. Needless to say, it has been a very challenging semester, but also quite a rewarding one. Mathematics honours students are required to take a total of 6 courses throughout the honours year, as well as prepare a thesis. Many (?) people opt to take 4 of the 6 courses in the first semester, with the intention that more time can be devoted to the preparation of the thesis in second semester. But naturally, this means that one undertakes a lot of coursework in first semester (4 honours level courses at the same time is no joking matter), and as I am prone to procrastination, the time management has been especially challenging. Fortunately, I get along well with my thesis supervisor — who is conveniently also the honours coordinator this year — and he has been understanding and supportive during the periods when I had many assessments to submit and had not worked on the honours project!

# Learning, Unlearning & Relearning

This piece is slightly different from what I usually post on this blog, but I believe I have a unique perspective on the issues concerned, as I will explain in the main text.

I would like to discuss the current advertising campaign from the University of Sydney, and in particular the chosen keyword:

# Diversions in Mathematics #2: Hilbert’s Hotel

In this instalment, I introduce the concept of infinity in a simple and (hopefully) entertaining way, which puts into practice the counting concepts introduced in the previous Diversion. In fact, Hilbert‘s infinite hotel was one of the ‘stories’ that got me seriously interested in mathematics in the first place, and so it is a pleasure to share it here. This is a very well-known piece of story-driven mathematics. I hope that experienced mathematicians who happen to come across this blog do not tire of hearing (reading) it again, and that they see the value in telling the story to the general public.

Just before we start: I assume knowledge of the definitions and notations introduced in the previous instalment, namely, the very basics of set theory.