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


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


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.