Test review, due by March 29

A. I think that the Schroder-Bernstein Theorem, division algorithm, and Euclidean algorithm are important topics that we have covered. These are the topics that we have built up to and the smaller theorems have helped us prove and use these.
B. I expect to see definitions, sets where we must prove are denumberable, or uncountable, and apply the theorems and algorithms we've learned.
C.On previous exams I haven't gotten full points on the definitions. This exam that is my goal. I would like to just do a quick run through of the terms we've covered in these chapters.
Thank you.

11.6-11.7 due on March 28

A. The part about perfect numbers didn't make much sense to me. I saw how they took the primes and added them but then wasn't sure where they went from there. It was pretty neat though that there was a connection to sports with the Ruth-Aaron pairs.
B. I find it very interesting the different ways to look at numbers. All of the divisibility tricks are really cool. It is fun to see shortcuts and strategies to determine the divisibility of a number. Its fun to impress friends with as well.

11.5 due by March 25

A. I found in this section and in sections previous, that induction has been used. This is done when there is a a1,a2,...an situation. The wording on these can get a little tricky for me. The proofs in section 11.5 looked a little more simpler but will require practice to get the pattern down.
B. I found it very interesting and fun playing with the numbers. When I have taken the time to dig a little deeper and plug in numbers it is pretty neat. At time it is hard to follow when it is just letters and abstract. But to see it in action is fun.

11.3-11.4 due on March 23

A. This section has a lot more definitions. In the last exams we have had I have struggled with getting the definitions right. I think that for this section I will write down multiple times the definitions in order to get a handle on the specific wording.
B. I thought the use of the Euclidean Algorithm was neat. It was like working through a jawbreaker. At first it appears big but going through layer by layer you get through the flavors and break it down.

11.1-11.2 due on March 20

A. I think the most difficult part will be keeping up in the homework. I haven't been able to devote all the time I would like to this class as I would like to and it becomes difficult when I fall behind. Keeping the proofs straight and doing them correctly for the Division Algorithm it looks will take paying attention in lecture and getting after my homework early.
B. I thought it was interesting that this dates back so far. It has been around almost back until the time Lehi left Jerusalem.

10.5, due on March 19

A. In Theorem 10.19 they ended using the Schroder-Bernstien Theorem to tie it all together but to get to that point it was hard to follow. It looks like they found a 1-1 function that maps from an interval to the powerset of N then defined a function going the other way so that the powerset of N maps to a set of real numbers within the interval. Then showed that that was 1-1 and applied the theorems to wrap it up.

B. From what I could see, Theorem 10.17 was interesting because is shows that just by restricting the range of the function to exclude the elements which make it not onto, it becomes bijective and numerically equivalent. It just takes the elements on the set within a set that make it work.

10.4 due on March 15

A. One of the things I found challenging with this section is the understanding what belongs to each set. It has taken time and practice to see what elements are in the sets we are trying to prove.
B. I think it is very interesting to have different sizes of infinity. Also the continuum hypothesis is interesting. because it can't be proven or disproven. I like the new symbols we get to use too- "aleph null."

10.3 due on March 13

A. I understand the general process for proving a function is bijective and numerically equivalent. The part I find difficult is understanding from the beginning what the problem is asking. Going from seeing the 2 sets then being able to pull that apart and prove they are 1-1 and onto gets tricky and its a bit hard to keep up in class.
B. I like the challenge of writing in LaTex some of the challenging charts and functions. I have found that online there are some helpful tips and hints to get it to come out right.

March 5

A. I think the work we have done studying functions is the most important. Functions are used everywhere and being able to understand them in a mathematical theory way will help with higher level classes.
B. I  think there will be questions addressing the definitions we have covered as well as results to prove by the different methods we have covered.
C. I would like to review the strategies for proof by induction.

9.6-9.7 due on March 1

A. In example 9.12 I had a hard time following the progression of a proof. I think I don't understand too well how to interpret it from the beginning but after that I could see how they collected the terms and got their result. So my challenge is understanding how to interpret that statement and begin but after that I can work through it.

B. I found it interesting that in determining the number of different permutations you can use factorials. I like to be able to see what the total number of different combinations is and then work to fill them in. Kind of like what we do in class with list the beginning and end and then fill in the middle. It is a good guide.