Last day due by April 11

A.Some of the most important topics this semester: Logic, Direct Proof and Proof by Contrapositive, Existence and Proof by Contradiction, Mathematical Induction, Prove or Disprove problems, Equivalence Relations, Functions, Cardinalities of Sets, Number theory algorithms,

B. One of the things that I would like to review is proofs involving the union of sets.
Also a review of the properties for a question like
Let R be a relation defi ned on the set Z by a b if and only if a2 + b2 is even. Then R is
(remember to choose the most correct answer)... transitive, symmetric, and/or reflexive.

C. This semester I have learned how grateful I am for the mathematics we have today. It is a beautiful thing to be able to solve life's problems and make it a better place by analyzing numbers and making calculations. I have learned that some of the simple rules and theorems we enjoy today are actually very difficult and complicated to prove. Some of the number theory we have covered has been my favorite thing we have studied.

Thank you Professor Jenkins for your help and teaching.

12.4 and 12.5 due by April 8

A. In the previous sections of this chapter I was able to follow the format of the proofs. However finding the real numbers ceilings has been difficult. The following sections require more of this. I would appreciate reviewing the steps to getting these problems started. The side work we do is great and I would like to be able to do it myself.
B. The other day I was able to have a chalk board to myself and it was great working out the problems. I could visually get a grasp on the arithmetic and process that was required to prove these limits.

12.3 due by April 5

A. I liked that there were a lot of examples. It seemed that it came down to rearranging terms and finding the right delta so that we can use some math to come prove by the closeness the limit. It looks like the trick to get things going is this first part of finding the right delta and placing it correctly in the inequality.
B. I like to rearrange terms and see how things simplify. These examples used a lot of this and I am excited to work through these and prove the limits.

12.1 due by April 4

A. It has been a while since I have studied Calculus and i feel that I have forgotten a lot of it. I am excited for this chapter though to help bring it back and be able to use it again.
B.Looking through this section there is a lot of arithmetic that looks very interesting.  A lot of working with the numbers and determining the divergence or convergence.

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.