TOC
Courses
Blog
Twitch
Shop
Search
Toggle menu
Courses
Blog
Subreddit
Discord
Log in
Sign up
▾
Bridge course
•
Countable and uncountable sets
▾
Proof techniques
•
Example of a nonconstructive proof
•
Direct proof
•
Disproof by counterexample
•
Proof by cases
•
Proving properties of absolute value
•
Proof by contrapositive
•
Proof by contradiction
•
Proof by induction
•
Proof by strong induction
•
Proving de Moivre's theorem
•
Visual proof
•
Challenge
▸
Relations
•
Equivalence relations
•
Intersection of equivalence relations
•
Representing relations using matrices
▸
Combining relations
•
Composition of relations
•
Inverse of composite relation
•
Representing relations using digraphs
•
Properties of relations
•
Proving equivalence relations
•
What is a relation?
•
Finding the inverse of a relation on a finite set
▸
Functions (bridge course)
▸
Injective, surjective, and bijective
•
Intro
•
Is it bijective? (infinite domain)
•
Is it injective?
▸
Is it surjective?
•
Proof: Composite of surjections is surjection
•
Proving properties of injective, surjective, and bijective functions
›
Bridge course
›
Proof techniques
Visual proof
YouTube videos
97
Visualising Pythagoras: ultimate proofs and crazy contortions
Mathologer
361
Visual Proof of the Pythagorean Theorem
Girls' Angle
98
Visual Proof of Pythagoras' Theorem
Eddie Woo
4754
The Sum of Cubes and the Triangle Numbers | Animated Proof
PenguinMaths
4755
Euclid-Euler Theorem | Animated Proof
PenguinMaths