4.3-4.4, due January 29

      I found it difficult to understand the proof that verified a particular equality or inequality.  In the example, Result 4.16, I did not understand why (2x - 3y) squared is greater than or equal to zero was used.  I then realized that it came from working the result backwards until the equality could be shown in a way that was known to be true.  Because (2x - 3y) squared is always greater than or equal to zero, it is a great starting point for a direct proof.  It is now much more clear how to verify an equality or inequality.
      I found it interesting to begin working with proofs within sets because it allows us to solve much more general proofs involving sets of numbers rather than just individual number.  I like that we are expanding the tools that we are using to prove statements and expanding the situations in which those tools can be used.

• How long have you spent on the homework assignments? Did lecture and the reading prepare you for them?
• I have typically spent half an hour to three quarters of an hour on reading and another hour on homework problems.  When I wrote my second assignment in LaTeX, I spent about three hours completing it.  I do not anticipate them taking so long as I improve my skills in LaTeX and as I modify the template so that I do not have to redo so much in the assignments every time.
• What has contributed most to your learning in this class thus far?
• I have found that writing about the most difficult part of the reading has helped me to synthesize the material better.
• What do you think would help you learn more effectively or make the class better for you? (This can be feedback for me, or goals for yourself.)
• I think I would learn more if I could see where this will be applied in the various topics within math.  I sure as we continue through the year it will become clearer.