This course covers a wide range of cool math topics accessible to a diverse audience. The learning outcomes include understanding concepts like metric spaces, non-Euclidean geometry, and the Banach Fixed Point Theorem. Students will also learn about mathematical models for pandemics, combinatorial proofs, and the Borsuk-Ulam Theorem. The course teaches skills such as using Bayes' Theorem, dimensional analysis, and set theory in mathematics. The teaching method involves exploring various mathematical concepts through lectures and examples. The intended audience for this course is individuals interested in exploring intriguing and accessible math concepts beyond traditional academic courses.
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
