1. Welcome to CPS 130 Yu Chen

2. Overview Proof by contradiction Proof by induction -Mathematical induction -Structural induction

3. For those of you who are bored 4 coins You can flip one coin at a time You will know the end of the game, if all the coins are of the same side How many steps will you need at least to guarantee the end of the game?

4. Proof by Contradiction

5. Flowers and People 5 people How many flowers at most? 2 of them will get the same number of flowers

6. More Maths! Irrational Number

7. Proof by Induction Mathematical Induction Structural Induction

8. Difference Equations Fibonacci: f(x)=f(x-1)+f(x-2) Where f(0)=0, f(1)=1 Closed form? What about f(x)=af(x-1)+bf(x-2)?

9. Tree

10. Thank You!