Quantum Mechanics Cats and Collapses: Interpreting Quantum Mechanics Everyone’s heard of Schrödinger’s Cat. But what can it tell us about the meaning of Quantum Mechanics? Quantum Physics Schrödinger’s Equation “So do any of you guys know quantum physics?” Paul Rudd in Avengers: Endgame Quantum Mechanics What is Wave-Particle Duality? Why we need quantum physics. History […]
In this time of deep political, economic, and public health crisis, another terrible ill has recently befallen us: the death of a great and prolific mathematician, Ronald Graham (1935–2020). We were blessed with his presence and genius from October 31, 1935 to July 6, 2020. While this is truly a sad moment for mathematics, I […]
Using only elementary methods we will prove the Fundamental Theorem of Algebra. Along the way, we’ll befriend some key ideas from elementary analysis and catch a glimpse into the beautiful world of complex numbers. Motivation Regardless of anything else, it’s been a great quarantine project for me:) The aim of theory really is, to a great extent, […]
Ever wondered what happens to a raindrop during its journey from clouds to the ground? It does not stay intact. It deforms and breaks as it comes down. According to Villermaux and Bossa, the raindrop flattens as it comes down and forms a bag-like structure before it breaks (I strongly recommend watching the supplementary movie on this page for the […]
Relativity A Light Intro To Tensors A Framework For Defining Geometric Objects In Space Relativity The Lorentz Transformation And how to repair physics Relativity How to Compute the General Relativistic Correction to Time General relativity is one of the most technically difficult physics theories, as it requires uncommon knowledge and mathematical skills. However, it is […]
An omnipresent problem observed by all scientific intellectuals from Aristotle to Galileo is that modeling the real world is, well, nearly impossible. While dot-diagrams, differential equations & vector calculus bring us closer & closer from theory to reality, it’s clear that an additional degree of complexity lurks. A fascinating branch of discrete math that attempts […]
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 […]