__Ch. 1 topics and documents__

1. Difference method examples

2. Difference method wksht.

3. Cubic cut ups sheet. Challenge yourself, and see how many different patterns emerge from this problem!

Over 100 proofs of the pythagorean theorem! Check on this link! And this is just the tip of the iceberg.......1000s of valid proofs exist! Could you find the next one?

Proof By Mathematical Induction: Click here for a few extra examples. There are also several good examples in your text book (ex. 18,19,20,21 and 22)

4. Check out the Khan Academy lesson below for an example of proof by mathematical induction.

2. Difference method wksht.

3. Cubic cut ups sheet. Challenge yourself, and see how many different patterns emerge from this problem!

Over 100 proofs of the pythagorean theorem! Check on this link! And this is just the tip of the iceberg.......1000s of valid proofs exist! Could you find the next one?

Proof By Mathematical Induction: Click here for a few extra examples. There are also several good examples in your text book (ex. 18,19,20,21 and 22)

4. Check out the Khan Academy lesson below for an example of proof by mathematical induction.

## 5. HW 5 Solutions

I have hand written the solutions in detail for the homework 5 involving proof by induction. When you turn in your take home quiz, I expect the proof to look very similar to the ones I have written here. You should be neat, include all steps, and always end your proof with something like:

"Since P(1) is true, we assume P(k) is true, and P(k+1) is true, by the principle of mathematical induction P(n) is true also."

"Since P(1) is true, we assume P(k) is true, and P(k+1) is true, by the principle of mathematical induction P(n) is true also."

## 6. Topic 1.6 Counting principles

1. Introduction to Permutations and Combinations Power point.

2. Check out some of the KHAN ACADEMY links on combinations and permutations.

3. Investigation for HW 6 involving circular permutations.

(note: We will not address the last combination in this course)

2. Check out some of the KHAN ACADEMY links on combinations and permutations.

3. Investigation for HW 6 involving circular permutations.

(note: We will not address the last combination in this course)

## 7. TOPIC 1.6 and 1.7 Counting principles and the Binomial Theorem

a. Alternative Text book Packet (distributed in class.....if you lost your copy, please ask me for a new one)

b. Alternative Text book Packet SOLUTIONS

b. Alternative Text book Packet SOLUTIONS

## 8. CH. 1 ISA SOLUTIONS

Full worked solutions to the take home quiz: Use this as a study guide as you prepare for the ch. 1 test.