Making Convincing Arguments-Welcome!
Promo Video
()
Companion e-book
Active Learning
Python Programming Language
Making Convincing Arguments-Why Proofs?
Proofs?
()
Proof by Example
()
Impossibility Proof
()
Impossibility Proof, II and Conclusion
()
Slides
Making Convincing Arguments-Existence Proofs
One Example is Enough
()
Splitting an Octagon
()
Making Fun in Real Life: Tensegrities (Optional)
()
Know Your Rights
()
Nobody Can Win All The Time: Nonexisting Examples
()
Slides
Making Convincing Arguments-Acknowledgements (Optional)
Acknowledgements
How to Find an Example?-How to Find an Example
Magic Squares
()
Narrowing the Search
()
Multiplicative Magic Squares
()
More Puzzles
()
Integer Linear Combinations
()
Paths In a Graph
()
Slides
How to Find an Example?-Optimality
Warm-up
()
Subset without x and 100-x
()
Rooks on a Chessboard
()
Knights on a Chessboard
()
Bishops on a Chessboard
()
Subset without x and 2x
()
Slides
How to Find an Example?-Computer Search
N Queens: Brute Force Search
()
N Queens: Brute Force Solution Code
N Queens: Backtracking: Example
()
N Queens: Backtracking: Code
()
N Queens: Backtracking Solution Code
16 Diagonals
()
16 Diagonals: Code
Slides
Recursion and Induction-Recursion
Recursion
()
Coin Problem
()
Hanoi Towers
()
Two Cells of Opposite Colors: Hints
Slides
Recursion and Induction-Induction
Why Induction?
What is Induction?
Arithmetic Series
Plane Coloring
Compound Interest
Inequality Between Arithmetic and Geometric Mean
More Induction Examples
Where to Start Induction?
Triangular Piece
Proving Stronger Statements May Be Easier!
What Can Go Wrong with Induction?
Logic-Examples, Counterexamples, Logic
Intro
Examples and Counterexamples
Logic
Summary
Logic-Reductio ad absurdum
Reductio ad Absurdum
Balls in Boxes
Numbers in Tables
Pigeonhole Principle
An (-1,0,1) Antimagic Square
Handshakes
Invariants-Double Counting
Double Counting
`Homework Assignment' Problem
Invariants-Invariants
Coffee with Milk
More Coffee
Debugging Problem
Invariants-Termination
Termination
Arthur’s Books
Invariants-Even and Odd Numbers
Even and Odd Numbers
Summing up Digits
Switching Signs
Advanced Signs Switching
Solving a 15-Puzzle-When and Why a Solution Does Not Exist
Reading
The Rules of 15-Puzzle
()
Permutations
()
Proof: The Difficult Part
()
Mission Impossible
()
Classify a Permutation as Even/Odd
()
Bonus Track: Fast Classification
()
Slides
Solving a 15-Puzzle-The Project: Programming 15-puzzle
Project: The Task
()
Even permutations
Bonus Track: Finding The Sequence of Moves
Quiz Hint: Why Every Even Permutation Is Solvable
()