From jacobson@math-cs.cns.uni.edu Thu Sep 27 15:44:12 2007
Date: Thu, 27 Sep 2007 15:44:12 -0500 (CDT)
From: Mark Jacobson <jacobson@math-cs.cns.uni.edu>
To: 810-080-02-fall@uni.edu
Subject: Test on Thursday, NOT TUESDAY...  :-)


Hi Discrete Structures students,

     The exam will be on Thursday, October 4th, one week from today.

     It will NOT be on Tuesday, October 2nd.
             ---

     On Tuesday we will review past homeworks and my 14 page handout
of solutions to HW #1 and HW #2 (reduced to two sheets of paper due to
miracle of photocopy reduction of the images!).

     I will probably hand out or post a solution/key to HW #3 by or
on Tuesday too.

     Great job at the induction discussion today.

     If the following two STEPs can be established and proven,

        P(1) is true (*** BASIS STEP ***)

        P(k) -----> P(k + 1) is true (*** INDUCTIVE STEP ***)

     ----------------------------------------------------------

     Then P(n) is proven true for all n >= 1.

     Our P(n) today was:
                                      2
      3 + 7 + 11 + ... + (4n - 1) = 2n  + n

    Read section 2.3 of the textbook for more about Mathematical Induction.

    Study over the homework #1 and homework #2 solutions and key and
       compare it to your answers.  Excellent test preparation would
       be to redo some problems to see if you do them better and faster
       after studying the HW key I handed out today.

    http://cns2.uni.edu/~jacobson/c080.html

    See week number 6 for links to three Flash links:

  webspace.ship.edu/deensley/DiscreteMath/flash/ch2/sec2_3/suminduction.html

    is just one of the hypertext links.

    1.  Try the Inductive Proof textbook online exercise (Flash player).
        Note that (n(n + 1)) / 2 can be written as:

         2
        n  +  n       n (n + 1)
       ----------  = -------------
           2               2

    2. Proof practice from the textbook web site.

    3. The Proof Scrambler is excellent practice also.

    Mark