11.3-11.4 due Nov 15, 2012

1. The hardest thing to understand was the proof for Theorem 11.8 which was the one with the 2 conditions.
2. Right when I read the section title for 11.3 I thought of elementary school when we learned about greatest common factors. I love how we yet again bring up concepts that I learned years and years ago. 

11.1-11.2 due Nov 14, 2012

1. The most difficult thing to understand was the proof for the The Division Algorithm, especially the 2nd half.
2. I found these sections to be much easier to understand that the previous 2 weeks. The examples in here are actual numbers and help me to understand the concepts. It is also nice that we are reviewing thing that I have already learned, where chapter 10 was all new.

10.5 part 1 due 11/9/12

1. I assume that "up to" means up to and including so I read theorem 10.18 in addition to the pages before it and I would have to say the most difficult thing to understand was The Schroder–Bernstein Theorem, then again it was all difficult.
2. I found it very difficult to understand anything in this section. This is probably because I have a hard time understanding all of chapter 10. Math is all about building on idea on another. If we can't understand how to add/sub and mult/div then we can not understand how to do algebra. Same concept applies to me with this class. I need to be able to understand the section before or how can i expect to understand this new section.

10.4 due Nov 7

1. Most difficult thing to understand was the The Continuum Hypothesis
2. I found theorem 10.14 very interesting about how P(A) and 2^A are numerically equivalent.

10.1 due Oct 31

1. I understood the description of numerically equivalent sets, but once I got to the Theorem, it was hard to understand.
2. I thought that it was interesting that we could determine if 2 sets have the same cardinality if they are bijective. I have never thought of that and now it is easy to remember.

8.3-8.4 due Oct 12

1. The proof that was for Theorm 8.4 was the most confusing
2. I find these sections very interesting. So far I have enjoyed learning about relation proofs and they seem to make a lot of sense. I thought most of the examples for this section were very clear and easy to understand. It makes it easier to follow the discussion in class if the reading was easy to understand.

8.1-8.2 due Oct 3

1. symmetric and transitive relations were most confusing subject in these chapters.
2. Section 8.1 was very easy to understand and it reminded me lot of math in elementary school and middle school. Back then math came very easy and I didn't have to work at all to understand what was going on. It has been difficult in college not always understanding as I did in those earlier years, but I find I feel a great sense of accomplishment when I understand math that at one time was confusing (aka. this class :) )

6.2 due Oct 5

1. Theorems Theorem 6.14 (The one about Complement of A1 U a2...) and 6.15 (If A is a finite set of cardinality n ≥ 0, then the cardinality of its power set P(A) is 2n) were really confusing.
2. My major is Family History and it is really hard to relate it to what we learn in class. However, I know this section is going to be difficult for me to understand and complete the proof, but I know that if I work hard I can be successful. I can relate this principle to my major and to my life.

6.1 due Oct 3

1. I always have a difficult time with summations and that was hard for me to understand.
2. I thought that it was interesting that there was yet another way to prove some of the proofs that we have been solving all semester. I have been quiet surprised at how many different ways there are to prove something.

5.4-5.5 due Sept 26

1. Proof 5.21 was confusing and I doubt I could do a problem like that on my own and understand it.
2. The example of the student X with more hairs that everyone else helped me to understand what an existence proof is. I really liked that

5.2-5.3 due Sept 24

1. The most difficult thing was trying to remember how to do all the proofs that we have learn so far.
2. I really liked the story of the 3 prisoners. I like questions like that and trying to figure out the answer. It also helped me to understand better proof by contradiction.

4.5-4.6 and 5.1 due Sept 21

1. The most difficult thing to understand was proofs using set products.
2. I like how things we have learned in elementary school are still being used in our class today: Commutative Laws, Associative Laws, and Distributive Laws. I love how math always builds upon itself and you need everything that you have previously learned. It isn't like you learn something and you never use it again, but you build on it and extend your knowledge on it.

4.1-4.2 due Sept 17

1.The congruent/modulo was confusing and the notation is really different.

2. I thought it was interesting that we can write an integer is even and odd by the divides notation. I have never seen this notation before, but it is easy and quick and useful.

3.4-3.5 due Sept 14

1. The most difficult thing to understand was sub cases.
2. I found that proof evaluations was very interesting. I feel that doing these evaluations will really help me to know how to do proofs better and keep me from making mistakes. It will be good practice.

3.1-3.3 due Sept 12

1. The thing I found most difficult to understand was probably proof by contra-positive.
2. I have always had a hard time with proofs, and now that we are really starting them, I am getting a bit nervous. Granted this is the beginning, and the proofs we do now are the easiest, I still am nervous and hope I can do well. 

Chapter 0, Pg 5-12 due Sept 10

1. Reading about the rules in writting proofs were pretty straight forward, but it's one thing to read them and another to be able to use them correctly. So the most difficult thing would be how to use them in the right way and still proving the problem correct.
2. I found it interesting that we would be asked to write out the symbols in words instead of just using the symbols. For all the proofs I have done in the past we just used the regular sumbols, but I guess writing out the words make it easier to understand.

2.9-2.11 due Sept 7

1. One thing that really confused me was quantified statements, universal quantifier, and existential quantifier and their notation.
2. In theorem 2.18 we see Commutative Laws, Associative Laws, and Distributive Laws. I remember years ago learning about associative property of addition and subtraction, distributive property, etc and I love how it is still being tied into the math I am learning now. I love how math builds in layers and no matter how many times you have seen it or how long ago you learned it, math repeats itself, but in different ways.

2.5-2.8 due Sept 5

1. Today when I read, the thing that got me most confused was all the symbols and trying to figure it all out in my head. With negations, implication, etc it hurts my head to figure it out. I think I just need more time practicing understanding it at a glance.
2. I really like the section about bi-conditionals. I really liked how it all came together like in the triangle example. The statements with works instead of #'s make more sense to me and I though this was very interesting.

2.1-2.4 due Aug 31

1. The most difficult thing for me to understand is implication. It is clearer if it is in a story like in the example about the kid getting an A in the class, but when it is with 7/34 being rational and sqrt2 being rational, it can get confusing.
2. The most interesting part of the chapter was implication. Even though it is confusing, it is a new and interesting concept that I enjoyed learning about.

1.1-1.6, due on August 29

1. The most difficult section for me to understand was 1.4- Indexed Collections of Sets. The notation was a bit confusing and I could quite get my head around what the notation meant. 

2. Something that really helped my to understand the information were the Van Diagrams that were used in this chapter. It helped me to better understand concepts because it was a visual way to see it. It helped to learn certain concepts in 2 different ways. 

Introduction, due on August 29

1. I am a Senior and I am a Family History Major
2. I have completed Math 112, 113, 313, 314, 334
3. This is the last class I need for a Math Minor
4. Good- I had a math teacher in high school who was amazing. He knew exactly what to teach and how to teach to help the student to learn best. He also was open before school, lunch, and after school if a student ever needed help. He knew how to explain things in different ways so you could understand.
Bad- I had a college professor who was a very smart man but didn't know how to teach. Everything was confusing and he got off subject a lot so there was little time for him to teach. We were left to figure things out for ourself most of the time.
5. Between 10 and 2 most days