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Showing posts from August, 2021

Exciting Life Updates

I know I haven’t been updating this blog because I’m too lazy. Years 2 and 3 have been an exciting flurry of business (both work and busy-ness). I constantly spew bite-sized thoughts that stream into my mind on Instagram Stories anyway, and I am remarkably easily bored and excitable, so longer, more considered pieces on Blogger aren’t sustainable. I digress. Many exciting life updates! I’m now officially done with my undergraduate PPE programme at King’s College London. I loved every bit of it: the depth, rigour and intellectual intensity of the course, the international student community, the bustling city of London and all the travel opportunities around Europe. Words can’t do justice to the profundity of the experience. In typical Quincean fashion, I milked everything I could out of the three years: went to Cumberland Lodge (for free) as a photographer with the Philosophy Department in Years 1 and 3, clinched the Principal’s Global Leadership Award (PGLA) in my second year (spending

A New Identity

Identities, even in the form of an email address, assure me of my place in the world and motivate me. It is an inspiring privilege to wear the weight of an institution like an Athenian himation. Do not underestimate the power exuded by meagre glyphs in the address bar; it invites others to pause and pay attention. I was formerly 131416w@student.hci.edu.sg and quince_yq_pan@spf.gov.sg . Since Tuesday, 17 August 2021, I took on a new identity. Neither the anonymous qp8888@ox.ac.uk nor the look-at-my-matriculation-year quince.pan.21@ucl.ac.uk  — phantoms of what could have been. But the legitimate, professional, proper  quince.pan@kcl.ac.uk . One cannot distinguish between student and staff as the email address nomenclature is the same. This is immensely invigorating. Every time I open Outlook, I am reminded that the professors and I are the same in style, if not substance. I can achieve whatever they have achieved. I’ve got one foot in the door, and that fact is stamped on every

Recreational Mathematics, 16 June 2021

On 16 June 2021, I did some mathematics for fun and obtained this result. I explained the proof to my viewers on Instagram Stories that same day, but I only decided to publish it here on my blog today. MathJax works wonders! Consider \(a,b,k \in \mathbb{Z}^{+}\) with \(a < b \). We observe that: \begin{equation*} \begin{split} \sum_{k=a}^{b-1} \sqrt{\frac{1}{k}} - \sum_{k=a+1}^{b} \sqrt{\frac{1}{k}} = \sqrt{\frac{1}{a}} - \sqrt{\frac{1}{b}} \end{split} \end{equation*} By trapezoidal approximation and the convexity of \(\sqrt{\frac{1}{x}}\), \(\forall x \in \mathbb{R}\) and \(\forall n \in \mathbb{Z}^{+}\), \begin{equation*} \begin{split} \int_{n}^{n+1}\sqrt{\frac{1}{x}} \; \mathrm{d}x < \frac{1}{2} \Bigg ( \sqrt{\frac{1}{n}} + \sqrt{\frac{1}{n+1}} \Bigg ) \end{split} \end{equation*} Therefore, \begin{equation*} \begin{split} \int_{a}^{b}\sqrt{\frac{1}{x}} \; \mathrm{d}x < \frac{1}{2} \Bigg ( \sum_{k=a}^{b-1} \sqrt{\frac{1}{k}} + \sum_{k=a+1}^{b} \sqrt{\frac{1}{k}} \Big