5.2-5.3, due on February 1

Difficult: The most difficult section in this reading is section 5.2. However, I would not say that 5.2 is actually a difficult idea to understand. For one, the concept of a contradiction should not be new. Therefore, it is easy to apply previous knowledge and experience regarding what constitutes a contradiction to this mathematical application involving proofs. That being said, I would have liked the example to have been more consistent when it came to the variables that were used. At first the variable used are P and Q, but then the book jumps to R and C which caused me to be confused for a bit.

Reflective: I particularly like section 5.3. I thought that it was very helpful to me regarding how to begin proofs. Sometimes, the most difficult part of a proof is simply deciding how to approach it. I also liked the review of all the different kinds of proofs such as direct, contrapositive, and contradiction. I honestly wish that this section had come earlier in the course.

4.5-4.6,5.1 due on January 30

Difficult: The most difficult section from this reading assignment is section 4.6 about proofs involving Cartesian products of sets. I'm mostly just not sure exactly what the book is trying to say. I think that it is talking about that if A x B then it will equal every integer in set A and every integer in set B. But I'm just not a hundred percent sure.

Reflective: My favorite section in this reading was 4.5, which might come as no surprise. I liked this section because it was familiar since it reviewed Commutative Laws, Associative Laws, and Distributive Laws. All of which I remembered learning about in previous readings. Although, I did not remember De Morgan's Laws, it appealed to my love of history and reminded me of J.P. Morgan, so it was still familiar and less intimidating. Basically, this section was just a review. So I was simply building onto a foundation that I had already learned previously.

4.3-4.4, due January 27

Difficult: I thought that both sections for this reading were not too complicated. However, the one that was more difficult was probably 4.4. I think the main reason why this one was more difficult is because I have less experience with sets and their intersections and unions. I really think that the Venn diagrams help me visualize the different ideas that are being presented. I think what is most difficult is actually knowing when to apply each different method and then simply how to start or approach each proof.

Reflective: I particularly like 4.3 for this assignment. I thought that 4.3 was essentially a review which was nice. I like how the book actually takes the time to make sure that old principles are refreshed and that they are actually understood and a base for any concepts that may relate to them. By having a review it made new ideas that were introduced much easier to understand because I already had a foundation. However I am slightly unsure of what exactly a triangle inequality is.

How long have you spent on homework assignments? Did lecture and the reading prepare you for them?
On average I have spent about 2-3 hours on homework assignments. I think that both the lecture and the reading were helpful. The reading was helpful because, although I may not have understood everything, or even really anything, after reading the chapter, the ideas were still introduced. That way, during the lecture I was not starting from complete scratch. However, I think that the lectures are the most helpful for teaching me the concepts. I understand much better with that type of teaching rather than just reading from the textbook.

What has contributed most to your learning in this class thus far?
I would say that the lectures have probably contributed most to my learning so far. Also, the problems from homework of course have been helpful in practicing the different concepts on my own.

What do you think would help you learn more effectively or make this class better for you?One thing that would be very helpful to me would be to work through a problem on my own for a bit in class and then come back together as a class and work through the problem. That way I would be able to try and see if I knew how to do it and then got to check it and see where I was right and where I may have gone wrong. That way I would have branched out on my own a little before I was completely on my own.

4.1-4.2, due January 25

Difficult: The difficult part of this section's reading was 4.2.  For the beginning of the reading for 4.2 I was on track since it was mostly just review of past sections. However, I started to get a little lost when the book moved to introducing the two terms congruent and modulo. I do not understand what the definitions of these two terms are. I assume that congruent has the same meaning now as it has in previous math concepts, but I was not able to verify that for sure. On the other hand, I have no idea what modulo is. As I continued to study this section on congruence of integers, I started to notice a pattern for modulo. But I do not trust it without a secure grasp on the term's definition.

Reflective: I liked section 4.1. I thought that it was written in a way that it made sense to me. This section was probably also easier to understand because the terms that were introduced here were already familiar words so I just had to understand their application for this situation. The idea of this section relates directly to algebra which is actually one of my favorite areas in math. Therefore, it was easy to draw parallels between the new concepts being introduced with knowledge from previous algebra classes.

3.4-3.5, due January 23

Difficult: Section 3.5 was the more difficult section of the two for me. It was hard for me to understand exactly what was going on with having the result coming first. It seemed like the book was trying to make it be different, but in a way it seems that for most proofs you start with the end result and then go about trying to work your way to prove that result.  So I didn't really understand what they meant by that.

Reflective: I like the section about proof by cases and subcases found in 3.4. What I like about this is the idea of breaking things down into smaller pieces. This reminds me of art paintings that are composed of just a bunch of dots. Where when you look up close, all you see are all the different colors of dots, but then when you step back you begin to see the whole picture. This seems to be the same way of these types of proofs where there are a bunch of little pieces, or dots, that come together to form the whole picture.

3.1-3.3, due on January 20

Difficult: I did not really understand what the difference between a trivial proof and a vacuous proof is.  I think I picked up that for a vacuous proof every x that is an element of s for P(x) implies Q(x) but where every element is false for P(x).  But I didn't really get how to define a trivial proof.  So I would like it to be a little more clear as to how to differentiate between the two.

Reflective: My favorite section for this reading was 3.2 on Direct Proofs. I thought that it was helpful how the text introduced a small part of a direct proof, followed by another, and so on.  By breaking up the different aspects for the conditions of the proof I was able to follow the thinking and the explanation easier than in other past times.  I also liked how their addressed the section about properties of integers as something that was "familiar" and "elementary".  It seems sort of ridiculous but just by the text alluding to the simplicity, made the whole thing seem easier to understand.

Mathematical Writing, due January 18

Difficult: This section of reading was rather simple to understand, especially since the basics all relate to writing instructions which have been given in English class since elementary school.  However, perhaps the only semi-confusing portion of reading in this section was the part about the difference between when to use "than" or "which".  It sounds like for the majority of the time, than is usually preferable. Although I liked the example separate from the usual mathematics samples about the favorite math textbook, I would have liked more examples that did directly relate to mathematics and how each of these words would be applied to writing math.

Reflective: The comparisons in this chapter to everything that I have learned in English class for writing the common essay are extensive in this section of reading.  The first part I made this connection was in the discussion about having an outline before beginning to write down anything. How many times have I heard a teacher suggest creating an outline to organize my thought before I began my paper? An even more simple connection was that of simply capitalizing the beginning of a sentence. Then, more importantly, word choice. Whether it's deciding between "than" or "which," this chapter emphasizes the importance of choosing the right words and constructing each sentence's structure correctly so that it reads well and makes sense.

2.9-2.11, due on January 13

Difficult: The most difficult part of this section of reading was 2.10 which is on Quantified Statements.  I don't really understand what it does beyond making an open sentence into a statement. I do not understand what the different symbols for a universal quantifier and an existential quantifier. I understood the part of the section that talked about whether or not a quantified statement was true or false. But I am not sure I could apply it since I don't think I understand what it means to be honest. I also found that I have been getting a little confused about adding R into a truth table. I am not always sure if I am doing it right or not.

Reflective: Section 2.9 about the fundamental properties of logical equivalence mentions commutative laws, associative laws, and distributive laws.  When I read these three different types of laws, they immediately sounded familiar and connected me back to other principles that I remember learning.  Unfortunately, I cannot seem to pin point what exactly they remind me of.

2.5-2.8, due on January 11

Difficult: Although I would not really say the concept is difficult, the hardest idea for me to completely understand in this section of reading is the biconditional that is found in 2.6.

Reflective: The principle of a contradiction found in 2.7 is just like a normal contradiction that would be found in English.

2.1-2.4, due on January 9

Difficult: Probably the most complicated concept to wrap my head around in this section of reading is the distinctions between disjunction and conjunction statements.  Although I understand it just fine, there was just some parts that I had to reread and make sure I understood the different symbols and the conditions.

Reflective: What I like about this section of reading is the fact that it doesn't have to do with theorems or principles necessarily, but yet these statements are so important to the rest of mathematics. Without the use of statements it would be difficult to teach the different concepts and principles that make up math.

1.1-1.6, due on January 6

1. Difficult: the most difficult concept in this chapter was subsets.  I keep thinking I have it down, but then I just get confused.
2. Reflective: In a way sets kinda reminds me of sigma notation that I learned in math 112. It is the same idea of using a list to show a group of objects like a pattern. This connection helps me increase my understanding of both of these principles.

Introduction, due on January 6

• I am a junior and am majoring in Secondary History Education
• I have previously taken math 112 and am currently enrolled in math 113
• I am taking this course for my minor which is math.  I am minoring in math so that I can also qualify to teach the course in secondary schools if a history position is not available.
• My math teacher who was most effective was my calculus teacher in high school. He was kinda crazy and would shoot kids with a water gun which made class entertaining.  But he was effective as a math teacher because he would go over a concept and then assign a lot of examples for that one principle as homework which really ingrained the methods and techniques into my brain.
• I cannot straighten my arm completely. It is always crooked.
• Your office hours work for me.