Category Archives: elementary

## Graphing the Mandelbrot Set

A class of fractals known as Mandelbrot sets, named after Benoit Mandelbrot, have pervaded popular culture and are now controlling us. Well, perhaps not quite, but have you ever wondered how they are drawn? Here is an approximation of one: From now on, Mandelbrot set will refer to the following set: for any complex number […]

## 60 Linear (Matrix) Algebra Questions

I sometimes am a teaching assistant for MATH 133 at McGill, and introductory linear algebra course that covers linear systems, diagonalisation, geometry in two and three dimensional Euclidean space, and the vector space $\mathbb{R}^n$, and I've collected a few theoretical questions here that I like to use in the hope that they may be […]

## One Fair Coin and Three Choices

A few nights ago as I was drifting off to sleep I thought of the following puzzle: suppose you go out for ice cream and there are three flavours to choose from: passionfruit, coconut, and squid ink. You like all three equally, but can only choose one, and so you decide you want to make […]

## Nonnegative Sums of Rows and Columns

For any $n\times n$ matrix $A$ with real entries, is it possible to make the sum of each row and each column nonnegative just by multiplying rows and columns by $-1$? In other words, you are allowed to multiply any row or column by $-1$ and repeat a finite number of […]