Probability Theory To start with an analogy, what is money? Textbooks and Wikipedia say that money is a medium of exchange, and a store of value, and a unit… To start with an analogy, what is money? Textbooks and Wikipedia say that money is a medium of exchange, and a store of value, and a unit of […]
“I went through fire on my first.” While still a graduate student at Princeton University in 1940, Richard P. Feynman (1918–1988) gave his first lecture in a seminar on electrodynamics, the topic that would eventually earn him the 1965 Nobel Prize in physics. In front of a prestigious audience consisting of Nobel laureates Albert Einstein (1879–1955), Wolfgang Pauli (1900–1958), and Eugene Wigner (1902–1995) […]
Analysis Ways of determining when an equation is equal to zero 11 Feb 2020 — 13 min read As every schoolchild knows, the solutions of a quadratic polynomial equation ax²+bx+c=0 are given by the quadratic formula: But in the real world, we don’t just have to deal with second degree polynomials. Finding the roots of […]
We are going to tackle a problem. The journey we take solving it will teach us how to differentiate ‘with respect to a function’, and even understand the Fundamental Lemma of Calculus of Variations. (Crikey). We are given the function f, and want to pick a function y such that we minimise the integral. In […]
Radicals Developing an Intuition for Radicals The word radical is overloaded in the vernacular probably because it is important. Catchy as the title may appear, our concern is math radicals! Pun aside, they are a mathematical construct — a product of the human mind. Their serendipitous emergence in natural laws is a curious fact. Is that coincidence? It […]
The British writer, mathematician and logician Charles Lutwidge Dodgson (which was Lewis Carroll’s real name) worked in the fields of geometry, matrix algebra, mathematical logic and linear algebra. Dodgson was also an influential logician. (He introduced the Method of Trees; which was the earliest use of a truth tree.) For some time Dodgson was Mathematical Lecturer at Christ […]
In probability theory and statistics, Markov’s inequality gives an upper bound for the probability that a non-negative function of a random variable is greater than or equal to some positive constant. The inequality is named after Russian mathematician Andrey Markov (1856–1922) and is useful for relating probabilities to expectation by providing bounds for cumulative distribution of a stochastic variable. Introduction […]
Mathematics An entry-level primer on “rubber-sheet geometry” 06 Aug 2019 — 12 min read An entry-level primer on “rubber-sheet geometry” When I studied topology as an undergraduate, I always found it difficult to answer the inevitable question from family and friends: “What on Earth is topology?” Every time, I would give them a slightly different […]
Welcome back! In my last article Formal Truth and Logic we introduced many fundamental concepts (e.g. “What precisely is a ‘statement’?” or “How can we compose logic statements?”) of logic in Mathematics. If you require extra context on the notations or definitions used throughout this article, I highly recommend reading the previous article in case you have […]
This article flows out of a video conversation between the YouTubers and mathematicians Grant Sanderson and Matt Parker (references below) and an email conversation between myself and a friend of mine: Peter Gaffney as we explored our own solutions to this beguiling puzzle. Exploring different approaches to this seemingly impossible problem reveals some interesting connections […]
In the late 1800s, mathematics was undergoing a radical shift. Led by David Hilbert (among others), a new group of mathematicians became more interested in abstracting ideas rather than solving problems. Initially criticized for lacking practicality, this difference in philosophy has led to a vast amount of interesting results, one of them being Category Theory. […]
If you haven’t read part 1, you can find it here. The general gist of it is that we look at our data and have a guess at what sort of model would fit it best, then we find the parameters for that model that are the most likely to have generated our data. As promised, […]
Fibonacci numbers are one of the most captivating things in mathematics. They hold a special place in almost every mathematician’s heart. Throughout history, people have done a lot of research around these numbers, and as a result, quite a lot of interesting facts have been discovered. Let us see how they look like – Any number […]
Electromagnetism as compared to gravitoelectromagnetism (GEM) was formulated by the proponents through painstaking observations on the behavior of real objects, i.e. magnets and inductors in their respective electric and magnetic fields. A similar observation on a gravitational field, while it would seemingly be easy, is on the contrary counterintuitive, especially when the supposed objects possesses […]