July, 2020

Ask Uncle Colin: A Sum With An Unknown

Dear Uncle Colin, My textbook gives me an arithmetic sequence that starts $3 + 8 + 13 + \dots$, and asks me to find where the sum is 1575. I’ve got it down to $\frac{-1 \pm \sqrt{63,001}}{10}$, but I don’t know how to work out that square root without a

Read More

The Mathematical Ninja and Logs Base 2

The student’s shoulder twitched slightly as he said “So I need to work out $\log_2(10)$…” and the crash of the cane against the table reminded him that the calculator was off-limits. “I think you can estimate that yourself,” said the Mathematical Ninja. “Uh… ok. There’s a change of base formula,

Read More

Ask Uncle Colin: Factorising

Dear Uncle Colin, How would you go about factorising $6x^2 - xy - y^2 + 7x - y + 2$? - Argh! Getting Nowhere. Expression Simplification Impossible. Hi, AGNESI, and thanks for your message! I have, historically, not been a fan of these. However, I’ve recently come across a method

Read More

Summing with Generating Functions

A nice challenge puzzle via Reddit: Find $\sum_{n=1}^{\infty} \frac{n2^n}{(n+2)!}$ There was a video attached to it that I didn’t watch, something about telescoping sums, but the moment I saw this, I thought: generating functions! Why would I think such a thing? The thing that jumped out at me was the

Read More

Ask Uncle Colin: Why does the $ac$ method work?

Dear Uncle Colin, A while back, you shared an easy way to factorise nasty quadratics. Why does it work? Dutifully Indulging Students’ Curiousity & Reasoning In Maths. I’m Not A Nasty Teacher! Hi, DISCRIMINANT, and thanks for your message! Let’s start by recapping the method in the post, go through

Read More

Captain Holt’s Seesaw

When Jake’s father (Bradley Whitford) comes to town, Jake is excited to see him, but Charles is wary of his intentions; Holt challenges Amy, Terry, Gina and Rosa with a brain teaser in exchange for Beyonce tickets. Brooklyn 99, S02 E18, Captain Peralta “Surely it isn’t that hard?” I have

Read More

Ask Uncle Colin: Dividing Decimals

Dear Uncle Colin, I’m trying to work out $0.03 \div 0.1$. The answer is apparently 0.3, but I don’t understand why a division would make something bigger! Division Isn’t Very Intuitive, Decimals Especially Hi, DIVIDE, and thanks for your message! There are several ways to tackle this. I’ll start with

Read More

Dictionary of Mathematical Eponymy: The Sieve of Sundaram

I am not a number theorist. I mean… well scratch that. I am not an especially knowledgeable number theorist1 but I do enjoy number theory when it’s around my level. The Sieve of Sundaram is about my level. What is the Sieve of Sundaram? OK, let’s start with the Sieve

Read More

Ask Uncle Colin: The Area Between Two Curves

Dear Uncle Colin, I need to find the area between the graphs of $y=\sin(2x)$ and $y=\cos^2(x)$ in the interval $0 \le x \lt 2\pi$. I’ve found four solutions, but I think that means I need to do five separate integrals! Is there an easier way? Trigonometric Expressions: Double Integration Of

Read More

Sign up for the Sum Comfort newsletter and get a free e-book of mathematical quotations.

No spam ever, obviously.

Where do you teach?

I teach in my home in Abbotsbury Road, Weymouth.

It's a 15-minute walk from Weymouth station, and it's on bus routes 3, 8 and X53. On-road parking is available nearby.

On twitter