This course delves into various intriguing topics in mathematics, aiming to deepen the understanding of curious mathematical concepts. The learning outcomes include gaining insights into symmetry, algebra, geometry, complex numbers, and the Gauss-Bonnet Theorem, among others. The course teaches skills such as problem-solving, critical thinking, and mathematical reasoning. The teaching method involves video lectures exploring different mathematical puzzles and theories. The intended audience for this course is individuals interested in advanced mathematics and those looking to explore unconventional mathematical concepts.
Overview
Syllabus
Using Symmetry to Your Advantage: Some Classic Problems in New Light.
David Wilson's Curious Divisibility Graph -- and more!.
Surprising Algebra in Geometry.
Are Complex Numbers Forced Upon Us? Multiplication in High Dimensions.
The Triatic Formula: Having Quirky Fun making things Quadratic, Triangular.
Not-so-Curvy Curves on Not-so-Curvy Surfaces: Understanding the Gauss-Bonnet Theorem.
A Math Mystery for Young Mathematicians.
Dots in a Circle and Parentheses Numbers: A Sneaky Way into the Catalan Numbers.
Fractions Take Up No Space on the Number Line (Whoa!).
Bee Numbers and the Power of Honeycomb! (via Seven Puzzles).
My Favourite Number Tree (and the sqrt(2) and weird binary, and more!).
An Astonishing Property of the Hemachandra Numbers (and the primes, and the non-squares, and more!).
Theon's Ladder, Squangular Numbers, International Paper, and more!.
Sums of Powers Formulas.
Sums of Powers: Part II. Proving the Whacky Integration Technique from part I (if you are game!).
Lattice Points in Circles: A curious puzzle.
Partially-Filled Latin Squares and Semi-Magic Squares: A Follow-Up Video.
Card Pile Mathematics and Semi-Magic Squares.
Archimedes' Law of Lever.
A Golden Ratio Surprise.
How Archimedes First Deduced the Volume of a Sphere.
A Surprising Appearance of Euler's Famous Formula: V- E + F = 2.
How Round is a Cube? (Answer: Just as round as a sphere!).
Tie Folding and a link to Artin's Conjecture.
Gender Balance Puzzle.
The Citardauq Formula.
Egg Dropping: Going beyond just solving the classic puzzle.
Taught by
James Tanton
