Published in Math Simplified·PinnedMember-onlyGraph Theory 101: Why all Non-Planar Graphs Contain K₅ or K₃,₃An intuitive explanation of Kuratowski’s Theorem and Wagner’s Theorem, with lots of diagrams! — A planar graph is one that can be drawn in a plane without any edges crossing. For example, the complete graph K₄ is planar, as shown by the “planar embedding” below. One application of planar graphs would be designing a rail network without any intersections. …Mathematics7 min read

Published in Cantor’s Paradise·PinnedMember-onlyLeast Squares vs Least Absolute Errors —A 250-Year-Old DebateFrom Gauss and the birth of statistics to modern data science and machine learning — Ordinary least squares (OLS) regression is one of the first items on the menu in an introductory Statistics or Data Science course. But why do we need to square the errors? It’s a common question even high school students ask. …Math10 min read

Published in Cantor’s Paradise·PinnedMember-onlyThe Central Limit Theorem — Why Is It So?An intuitive explanation for why sample means should be normally distributed. There have been many excellent articles and videos about the Central Limit Theorem (CLT). But besides formal proofs, I was not able to find a good intuitive explanation for why it is true. So here goes… Theorem Statement The remarkable and…Statistics7 min read

Published in Predict·Sep 20Member-onlyThe Trailblazing Scientists who Shaped our WorldA Data Visualisation — Charles Darwin’s theory of evolution radically changed the way human beings see ourselves and our relationship with other species on Earth. Albert Einstein redefined concepts of space, time, matter and gravity, influencing not only physics but also science, philosophy and popular culture. The visualisation below highlights some of the most…Science4 min read

Sep 9Member-onlyHow would YOU approach this AMC Geometry problem?Method 3 is my favourite 😊 — This was a problem from the AMC 10 (American Mathematics Competition for students in Years 9 and 10). All the key information is shown in the diagram above, but here is the problem statement: In rectangle ABCD, AB = 20 and BC = 10. Let E be a point on…Mathematics3 min read

Published in Cantor’s Paradise·Sep 3Member-onlyThe Wonderful World of Integer Sequences(and the amazing mathematician who has spent his life curating them) — The image above depicts a sequence game I enjoyed playing as a high school student. Two teams of students sit in alternating places around a sequence of numbers, written on large cards. Only the first few numbers in the sequence are revealed. Students take turns guessing the next number, which…Mathematics6 min read

Aug 25Member-onlyInvestigating Remainders in the British Mathematics OlympiadBMO 2017 Round 1 — Problem 1 — Helen divides 365 by each of 1, 2, 3, . . . , 365 in turn, writing down a list of the 365 remainders. Then Phil divides 366 by each of 1, 2, 3, . . . , 366 in turn, writing down a list of the 366 remainders. …Mathematics4 min read

Aug 3Member-onlyThe Simplest Way to Create a High Quality Math VideoFor most students of mathematics, VIDEO is the way to go. — I have noticed that given the choice between a video and a written explanation, most of my students will go for the video first. I have also noticed that Google is serving video results more than ever before. …Mathematics3 min read

Published in Cantor’s Paradise·Jul 27Member-onlyIMO 2022 Problem 3 — Arranging Primes in a CircleThis was the final problem on Day 1 of the 2022 International Mathematical Olympiad, and the most difficult of the Day 1 problems. — The Problem Let k be a positive integer and let S be a finite set of odd prime numbers. …Mathematics7 min read

Published in Cantor’s Paradise·Jul 19Member-onlyIMO 2022 Problem 1 — Solved by an Uneducated Slave BoyThe beauty of the International Mathematical Olympiad is that the problems are difficult enough to challenge the brightest young minds in the world, while only requiring knowledge of high school pre-calculus mathematics. This video/article presents Problem 1 from 2022 IMO, in the style of Plato’s Meno, where Socrates uses guiding…Mathematics7 min read