5.2-5.3 due by January 31

A. In considering the example for the proofs by contradiction it appeared to me that the first step is a difficult one to make. First, one has to assume some x in P(x) which makes R false. To get to that point, however it takes practice and familiarity with these problems to be able to identify what would make it false and how to show it. In short, experience seems to be a fundamental key to proving these results. Getting to that point is frustrating at times because of the growing pains and repetition involved but rewarding in the end.
B. This past week I have been wanting to draw up a table or diagram to depict how to proof a result. I like the table in 5.3 because it helped me see visually how the first step can be taken either wrong or right. "A journey of a thousand miles begins with a single step" as they say and it follow that with proofs. The workings of a great proof are made or broke by the efficiency of the first step. I liked that.

4.5,4.6,5.1, due January 29

A. In reading these sections, I think the hardest thing will be remembering the set operations and correctly applying them in proofs. The proofs we have been doing have a lot of steps in order to sufficiently define and clarify. I like the examples we are using and look forward the TA sessions. The proofs of sets operations are hard to follow. I drew a Venn diagram and that helped a little to see what was happening.
B. In 5.1 it was interesting how one disproves a statement. It looks to me that my careful examination and playing with numbers, you can conclude which elements make the statements false. An interesting example is when mathematicians tried to come up with a formula for deriving prime numbers. They had a good one until they found a count-example and latter offered a $1 million prize to anyone who could prove or disprove it.
 ( http://akoaotearoa.ac.nz/ako-hub/good-practice-publication-grants-e-book/resources/pages/using-counter-examples-enhance-learn )

4.3-4.4, due January 26

A. When I was studying chapter 1 and working through the problems, I kind of struggled wrapping my head around the concept of sets. I started to catch on but then we moved on to logic and now we are tying it back in. I think that it will be difficult at first getting going on these proofs.
B. I really like the proof strategies for the examples in the book. They explain the thinking behind the work and I would like to go back and carefully read through these strategies to try and align my thinking with theirs.
C. I usually spend an average of 1-2 hours on a given homework assignment. At times I get frustrated and have to break it up because I cant get my head around certain problems.  Using LaTeX, I find enjoyable but now it is taking a bit more time. I follow my lecture notes for proof strategy examples.
D. I think that working through problems helps a lot. I am excited to have a TA to help with the explanation. I think it will be very helpful to have someone to coach us on to success in the homework and in our mathematical logic lives.
E. Honestly I think that working in groups would help a lot. Having a study session with a TA would do wonders at least for me.

4.1-4.2, due January 24

A. There have been a lot of new definitions and symbols in these last couple of sections. I am really working on keeping up and keeping things straight but it is a little bit tough remembering what things mean and what is the proper way to go about a certain problem.  I enjoyed and found helpful the review we had at the beginning of class. Also is there anything happening in the math lab for our class? It would be great to work in groups to discuss strategies and get better acquainted with these style of proofs.

B. I thought the proofs involving congruence of integers were particularly interesting. It takes the divisibility of integers to the next step. By looking at the result and evaluating what it is saying and thinking about how to do it, they can be taken apart and proved. I like the proof strategy in result 4.12.

3.4-3.5, due on January 22

A. I think because this builds upon the previous things we have learned, the difficult part with be continued familiarity with these proofs. Practice makes perfect and the more we work them out the better we will see and develop on our own mathematical proving strategies and techniques.  In the text, it stated that part of learning mathematics is making mistakes. We all do but what makes the difference is learning from and not repeating them. There were examples of finding mistakes that others have made and that might be difficult if is a similar mistake to the ones I might be making. It would be important and helpful  to be able to identify and correct those types of mistakes.
B.  These problems and exercises that we have done are building blocks in a foundation for more complex mathematics. It was very interesting to me to see how the previous subjects we have studied have been applied and built upon. We have studied sets, basics proof strategy, and logic, and now we are putting them together to prove more complicating exercises that require this foundation.

3.1-3.3, due on January 19

A. I think that it will be challenging is correctly documenting the proof strategy and/or analysis. This is done to show and explain how certain conclusions were reached in the proof. At times, things work out in our heads but getting that on paper can be something entirely different. I think this will be very important to do correctly and recognize that it will take practice and patience.
B. I thought the section talking about Q.E.D. was neat because it brought me back to the 500 hall in Douglas High School sitting in front of the a little old lady who skydives. I remember math class with Mrs. Barnes and first learning about proofs and how to finish them off with Q.E.D.

0, due January 17

A. I had previously read this part in previewing the book and a couple of things caught my attention. The way we present our information and proofs are critical in communicating correctly and effectively right solution. If stated improperly it could be hard to interpret or most likely incorrect. The language of correct notation for answering problems is difficult. In my first homework assignment I struggled with this because I was very unsure of how to do it. Now, I feel I have more practice and I am trying harder but still I would like to greatly improve and get it right.
B. As stated in a previous post, the new symbols caught my attention. I thought in was interesting the how and why of using the symbols. Also, I thought it was challenging but interesting the wording and mathematical definitions of words in writing (example: or, that vs. which, since/then, etc.) and I look forward to being able to correctly use it. 

2.9-2.11, due on January 12

A. I got my first homework back and one of the things that is challenging to me is the notation. These sections have a lot of theorems and ways to make statements in which the correct notation is critical. I found this to be a bit difficult to follow and to effectively carry out in a problem. The examples in the quantitative statements seem to have a procedure that ensures correctness and shows clarity and I want to be sure to understand and able to do it.
B. When first flipping through this book for the first time, the upside down and backwards letters definitely jumped out at me. It made me chuckle because I had no idea what they meant and what the symbols were. Now, reading through the sections I came upon them again and this time was able to get an idea of how I could use the neat backwards and upside down letters to make mathematical statements through quantification.

2.5-2.8, due January 10

A. In reviewing the exercises for the sections I read, there was a lot of work that would require careful organization and mastery of the principle and rules of logic. I feel this could be a challenge in doing the work correctly if I don't understand fully how use the rules of logic. I think the biggest hold up is making the connection between the use of sets and the statements were are studying and getting it right. Sometimes, when I do the set problems I have a hard time understanding where to start and what I am doing. Now, taking it a step further will require more practice and dedication.
B. In the previous homework and in the reading I loved the use of the truth tables. They helped me so much and I understood them. They make the organization and visualization a lot more clear. It seems that that is key to working through the problems and getting the desired result.

2.1-2.4, due January 9

A. The part that I feel will be most difficult will be getting a good handle on the vocabulary and the proper use of it. As I read, I was impressed by the importance of clearly presenting information so that it makes sense to not only you but to others. That is a point that is very important and I feel that it will take some getting used to and a lot of practice to reach that proficiency and accuracy but it is needed and expected.
B. The part that interested me were the truth tables. I liked the visual representation of what was being stated and the options for the statements. This technique is a helpful tool in organizing thoughts and verifying the statements. For example, in the section on implications it was discussed what it is and how to write it. It was seen clearly as a table was drawn and the story backed it up. Very applicable too. How often are worried about our grades and now we can draw a cool table to show our options. Art is a great stress reliever right?

1.1-1.6, due on January 5

A.    As I read through the first chapter, there was a lot of new terminology that I was unfamiliar with. Also remembering some of the terms that I have not used for over 2 years was a bit challenging. The book moved really fast through these concepts and new terms which was a bit tough to keep straight. However, with practice and reading some parts out loud I will get a handle on it.

B.     To me, I found interesting the use of Venn diagrams. At times when some concepts were a bit hard to follow, the use of the Venn diagrams help a lot. Visually, sorting out the information in a way that is easier to read and to see the operations being made was neat.

Introduction, due on January 5

My name is Derrik Jenkins and I am a mechanical engineering major.
I studied for 1 year, then completed a two year mission, and I have just returned to begin my sophmore year at BYU.
I took AP calculus in high school and Math 113 at BYU my freshman year.
I am very interested in attaining a minor in math to go with a degree in mechanical engineering. I enjoy math and would like to get a firm grasp on mathematical concepts that will build a solid foundation for further engineering and mathematical application to what I study and work with.
I greatly enjoyed the examples that were used by previous professors. They explained the concept, then showed how to work out the problems. Problems similar to those we would face later on in the homework or in test situations. Also the past final exams were available to review and study.
I feel that the lectures were at times vague and the why of certain application of principles weren't explained very well. The concepts we covered were shown but not explained very well. However, the TA's did a fantastic job reviewing the material and helping with homework questions.
Well, not my last name. So, I love to be in the outdoors- running, biking, climbing, hiking.. also, I can tear a phone book in half.
I have class until 3pm, so any time after 3 or before 10am would work for me.