Sec. 7, due April 11, 2012

Of the theorems and proof techniques from this semester I would place as the most important induction, those  theorems dealing with the cardinality of sets.  What I need to work on most for this exam are those things covered earlier in the semester that I've probably began to forget.  A problem I would like to see is on dealing with a proof by minimum counterexample.  The most important thing I've learned from this course are the techniques to creating a proof, and the way of thinking that goes with it.  If I go further in mathematics these will certainly be helpful in later classes.

Sec. 7, 12.4-12.5, due April 9, 2012

Continuity is something familiar from calculus classes of the past.  However section 12.4 offered some new properties of limits that I've not seen before.  They make sense though and should offer as little trouble as the sections preceding it did.

Sec. 7, 12.3, due April 6, 2012

When I was in calculus epsilon delta proofs were the bane of my existence.  Hopefully this time around I can understand them more.  Just reading the chapter seems to have already helped with that.  The proofs seem fairly similar to what we were doing in the last section, the main difference being defining some delta.

Sec. 7 12.1, Due April 4

This section is somewhat more familiar.  The trouble will come from not being able to simply take the limit of the sequence as has been taught in calculus classes.  Instead I'll have to prove that the limit is indeed what i find it to be.  It doesn't appear overly difficult though.

Sec. 7, Due March 30, 2012

Of what we've studied for this test, the three most important things are the Schroder Bernstein theorem, the division algorithm and the fundamental theorem of arithmetic.  What I most need to review is problems dealing with the cardinalites of sets.  From this course the most valuable thing I've learned are the techniques necessary to prove something, which will surely be helpful in future math classes.

Sec. 7, 11.6-11.7, due March 28

From these sections I didn't quite understand the proof that shows there are an infinite number of primes.  I understand how they got there contradiction, but not how they saw how to reach it.  Section 11.7 had some cool things to point out, but that was about it.  It said, "Hey, this is cool and interesting, but we've got nothing else to do with it."

Sec. 7, 11.5, due March 26

From this section the only proof that confused me was the one for corollary 11.15.  They are using induction.  It says Now let a1,a2,...,ak+1 be k+1 integers, where p|a1,a2,...ak+1.  It seems as if they skipped a step here.  It seems as if they assume the statement is true for k+1 rather than k.