Explore a captivating series of mathematical concepts accessible to a wide audience, regardless of technical expertise. Delve into intriguing topics such as metric spaces, knot theory, non-Euclidean geometry, and the Banach Fixed Point Theorem. Discover the applications of mathematics in real-world scenarios, including pandemic modeling, COVID-19 test accuracy, and Simpson's Paradox in statistics. Uncover the beauty of mathematical proofs, from the area of a circle to the Borsuk-Ulam Theorem. Investigate the nature of infinity, set theory, and the foundations of mathematics. Engage with viral math problems, explore the world of googology, and learn about the Bayesian Truth Serum. Journey through this diverse collection of mathematical wonders, designed to spark curiosity and appreciation for the subject's depth and versatility.
Overview
Syllabus
Weird notions of "distance" || Intro to Metric Spaces.
Untangling the beautiful math of KNOTS.
The Beautiful Story of Non-Euclidean Geometry.
What is cos( cos( cos( cos( cos( cos( cos( cos( cos( cos( cos( cos(…?? // Banach Fixed Point Theorem.
Stirling's Incredible Approximation // Gamma Functions, Gaussians, and Laplace's Method.
The MATH of Pandemics | Intro to the SIR Model.
The MATH of Epidemics | Variants of the SIR Model.
False Positives & Negatives for COVID-19 tests | Using Bayes' Theorem to Estimate Probabilities.
A beautiful combinatorical proof of the Brouwer Fixed Point Theorem - Via Sperner's Lemma.
My Favorite Theorem: The Borsuk-Ulam Theorem.
Integers & Rationals are both infinite but is it the SAME infinity?.
Integers & Reals have different, infinite sizes! **Cantor Diagonlization**.
Crazy Math Patterns that stop working......eventually.
Why is the area of a circle equal to π r² ??? 2000 year old proof, but with pizza..
Intro to Dimensional Analysis: How Much Energy in an Atomic Bomb? Or a Supernova?.
How SIMPSON'S PARADOX explains weird COVID19 statistics.
Defining Numbers & Functions Using SET THEORY // Foundations of Mathematics.
My #MegaFavNumbers is 2^82589933-1 // The largest Mersenne prime…..yet.
Math Prof answers 6÷2(1+2) = ? once and for all ***Viral Math Problem***.
The Largest Numbers Ever Discovered // The Bizarre World of Googology.
Bayesian Truth Serum // Using MATH to catch liars.
This Infinite Integral Tower Actually Converges? Sorta....
Beyond the Binomial Theorem: The Binomial Series.
Taught by
DrTreforBazett
