Due Wednesday, Feb 1

For Wed:

Proof for feedback:



  1. You have a proof test on Wednesday.  (See “Grading” tab for all the grading details.)  To study, I suggest reviewing example proofs (we’ve done several in class now) by trying them yourself and them comparing to the author’s solutions.  It’s ok for solutions to differ!  Here are some exercises from Hammack that may be good (and have solutions in the back):
        1. Use the definition of an “odd number” to be an integer of the form 2k+1 where k is another integer.  Show that if x is odd, then x^2 is odd.  The solution to this is written in great detail on pages 119-120 of Hammack.
        2. Chapter 8, Exercise 1.
        3. Chapter 7, Exercise 7. (This is an “if and only if” which means it goes both ways:  if A then B and if B then A.  Therefore we can state this as two theorems:  Suppose x, y \in \mathbb{R}.  If (x+y)^2 = x^2 + y^2 then x = 0 or y=0.  Furthermore, if x = 0 or y=0 then (x+y)^2 = x^2 + y^2.  So it’s actually two review problems in one!
        4. Examples 8.5, 8.6 on page 160.  This uses the symbol \mid for “divides” (Definition 4.4 on page 116).
  2. Announcements:
        1. I have posted office hours (“About” tab above)
        2. I have posted some solutions to Jan 27 daily post (“Materials Archive” tab above)
  3. Try Hammack Exercises from Section 3.2, particularly 1, 3, 7, 9 (answers are in the back), more if you want more practice with the multiplication principle.