11.5-6, due March 28

      The proof for the fundamental Theorem of Arithmetic seemed a little complicated.  I will need to review the theorem again before we review it in class.  I followed almost all of it but when dealing with p_1*p_2*p_3*...*p_s = q_1*q_2*q_3*...*q_t.  The part after that was a little complicated.
      I enjoyed reading about the different ways to determine divisibility by 2^n, 9, and 11.  I may have known those in the past but found them interesting and useful as I read about them this time.

11.3-4, due March 26

      Though the proofs are clear for the greatest common divisor, it seems as if the same thing was being stated twice when discussing the 2nd definition of greatest common divisor.  I don't see what the distinguishing part is about the other definition such that it is worth restating differently since we already proved everything to go into that definition.
      I like the Euclidean Algorithm as it is naturally recursive.  I decided that I will write a simple program in C++ to solve for the greatest common divisor.  I am a little frustrated as I do not yet know the conventions for recursion in C++ but I am sure I'll figure it out.

11.1-2, due March 24

      I found it difficult to follow the Division Algorithm proof the first time I read it.  Though being more careful to not the notation, I found it much easier to follow and may be able to replicate it.
      I liked how the division algorithm was related to congruency modulo n.  The division algorithm makes more sense and seems more significant when understanding that connection.

10.5 part 2, due 21 March 2013

      In the proof of Theorem 10.19, it felt as if not every subset was represented in the function f.  Consider for instance {42}.  I do not see how the f(x) ever would result {42}.  I'm not sure what I am missing.  I was also a little confused in the proof for the Schröder-Bernstein Theorem.  I must not be keeping my notation straight.
      I find it interesting that the cardinality of the real numbers is numerically equivalent to the cardinality of the power set of the natural numbers.  I thought that Corollary 10.20 was a nice thought too.

10.5 Part 1, Due 19 March 2014

      I did not understand the proof to Theorem 10.17.  With the introduction of new sets and other information, I lost track of what was going on.  The theorem makes sense but the proof is still a little fuzzy.
      I like the idea of mapping the elements of one set to a subset of that same set.  It starts to make comparing cardinalities more exciting.  I am looking forward to seeing what ideas we can take from this idea.

10.4, due March 17, 2014

      I did understand the proof for Theorem 10.15.  It makes sense by intuition but the proof itself seemed unclear because we defined a function f_S and f_T.  I do not understand yet why.
      I liked the idea that we have proven that there is no largest set.  I also found the Continuum Hypothesis interesting but I'm not sure I understand its significance.  Only that it is an interesting idea, that no set has a cardinality that falls between the the cardinality of the natural numbers and the real numbers.

10.3, due by March 14, 2014

      The most difficult part was the proof strategy when the quadratic equation was used.  It didn't quite make sense why they chose the sign they did.  Suppose it was because the "-" did not fall into the correct range where the "+" sign did.
      I like that we are starting to get into visual representations of the math that we are doing.  It helps me to better grasp what is going on in the section.  I find it exciting to be able to start making more functions like that.