## Discrete Structures Fall 2006 Weeks 6 thru 10

Textbook web site.

### Review: Weeks 1 through 5 web page resources. Back to c080.html page: Discrete Structures Fall 2006 main page.

Week Dates Topics Homework or Quizzes
6 09/25-09/29 Postage STAMP proofs: INDUCTIVE PROOFS examples and resources page, illustrating all the main types of inducitive proofs you need for 810:080 class.

```Page 99 #16, #18  Prove the given statement (for 16 and 18)

#16  An odd integer minus an even integer is odd.
#18  The sum of an integer and its square is even.

TWO CASES involved here in problem #18.

Be sure to translate both of these statements!  Example:  #15 on page 99 is:
The sum of an even integer and an odd integer is odd.
----------------------------------------------------- Translates to:
if x is an even integer and y is an odd integer then the sum x + y is odd.
```
HINTS/Directions for #18, Page 99 and the importance of proving two separate CASES.
7 10/02-10/06
```    The HW problem mentioned in class will be DUE ON Wednesday.
Problem #70 page 117
```

### HOMEWORK DUE on FRIDAY, October 6th

```Textbook Page 112, Problem #6
5n(n + 1)
Prove that 5 + 10 + 15 + ... + 5n = -----------
2
for all n >= 1.
```

Email note: Assignments and Reading from chapter two and chapter three.

Continue coverage of Chapter 3 on Sets,

Permutations (P(n,r), Combinations (C(n,r), pigeons and Ghostbusters counting problems (Principle of Inclusion/Exclusion formula).

8 10/09-10/13 Chapter 4, section 1.

### HW DUE ON WEDNESDAY, October 11th - do either #43 or #44 on page 114 of the textbook. 11 men, and 8 women exercise from Friday class. Here is a 2003 email note that was the HINT needed for students who had trouble figuring out the solution. Study this carefully! To simplify, it uses 4 cars and 3 trucks. No two trucks can be next to each other.

Binary relations can have the following properties: reflexive, symmetric, transitive, antisymmetric, and irreflexive. Study these carefully as you read and do 4.1.
9 10/16-10/20

## EXAM TWO: Review session for test two is on Thursday at 4 p.m.

TEST TWO Friday, October 20th

Here is a PRACTICE QUIZ that is interactive, animated and self-grading.

### STUDY GUIDE for TEST TWO, and class help session.

Another interactive practice quiz about sets, binary relations, properties, and how many ways you can arrange the letters in RADAR, etc.

### EXAM TWO FRIDAY (NOT Wednesday) Football or volleyball game, dance or piano recital: Practice for the Friday exam. Preparation involves repetition.

Binary Relations and the r, s, t, and a properties.
10 10/23-10/27 HOMEWORK: ATM and other Inductive proofs and poker hands HW. For FRIDAY, Monday, and Wednesday.

ATM problem: k + 10 instead of k + 1 is okay to use for the ATM with 20 and 50 dollar bills proof.

Review Counting problems ( C(n,r) and P(n,r) ).

Start Functions, Chapter 4, section 4.

Discrete Structures Curriculum 2001 discussion by ACM/IEEE Ironman Draft.