Date: Wed, 4 Oct 2006 17:05:27 -0500 (CDT)
   From: Mark Jacobson <jacobson@math-cs.cns.uni.edu>
     To: 810-080-02-FALL@uni.edu
Subject: Next two HW assignments...

Hi 080 students,

     Here are the next two homework assignments.  Both are
proofs by mathematical induction, from section 2.2 of book.

-----------------------------------------------------------
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.
-----------------------------------------------------------

-----------------------------------------------------------
    HW DUE ON MONDAY, October 9th -
       do either #43 or #44 on page 114 of the textbook.
-----------------------------------------------------------

     Please read the following sections of chapter 3 of the textbook:

         3.1 Sets
         3.3 Principle of Inclusion and Exclusion: Pigeonhole Principle

             Principle of Inclusion/Exclusion: = (Ghostbuster's Problems)
                                                      Dr. Peter Venkman,
                                                      Dr. Raymond Stantz,
                                                      Dr. Egon Spengler
         3.2 Counting
         3.4 Permutations and Combinations ( P(n, r) and C(n, r) )

     http://www.cns.uni.edu/~jacobson/c080.html

     http://www.cns.uni.edu/~jacobson/inductive.html

          When you finish your inductive proof, go through some example
          inductive proofs and make sure yours is as clear as possible.

          There are lots of examples on the above web page for you to
          study so your Friday HW illustrates the pattern very clearly
          for ANYONE reading your proof.

     http://www.cns.uni.edu/~jacobson/inductive.html

     -----------------------------------------------------------------
     http://www.cns.uni.edu/~jacobson/setsSupplement.html

     The above link is to lots of resources on SETS and GHOSTBUSTERS
     counting problems, aka the principle of inclusion and exclusion.
     Utilize and study it.
     -----------------------------------------------------------------

Mark