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.

Sec. 7, 11.3-11.4 due March 23

At the moment I'm rather sleep deprived, so not very much of the sections made much sense.  Finding the GCD was the most confusing thing for today.  The proof puzzled me, but the application thereof made enough sense.  Hopefully I understand better in class.

Sec. 7, 11.1-11.2, Due March 21

The proof for the division algorithm was slightly confusing, but the existence of such a thing does seem logical.  It's nice to be moving back to more familiar things though.  If there is enough class time further review of chapter 10 would be appreciated.  Thus far chapter 11 doesn't seem to horrible.