9.1-9.2, due February 26

1. (difficult) One difficult thing about this section was that with all the talk of the function mapping the coordinate points in the relation, there was not a single graph given to illustrate the point. Therefore, I must assume that the actual graph matters very little to the purpose of the section. It would have been helpful in illustrating I think.
2. (reflective) It's pretty interesting that the number of sets from A to B is |B^A| = |B|^|A|. It's pretty cool that there is usually a way to calculate these things that would be insane to try and count from just writing down all the possibilities.

8.6, due February 23

1. (difficult) The explanation of the equivalence classes and their operations was super confusing at first, have [2]*[3]=[0] for Z_6, but it definitely makes sense now. The book does a good of job of explaining, especially with its likening the operations to a clock that resets at 12 'o-clock to essentially be a zero hour.
2. (reflective) The idea of being well-defined seems to be of little/no use, or have little application in real life. I would really like to have more application for these things in real life scenarios.

8.1 - 8.2, due February 17

1. (difficult) The most difficult part of the reading to understand is the use of the words Relation, Domain, and Range that departs from any other mathematical and english usage that I have ever used or been familiar with. It is actually very frustrating to try to understand what is being described when the words mean things that my mind does not immediately understand.
2. (reflective) I can't see any application yet for a relation to take on the properties of being reflexive, symmetric or transitive. Is there going to be a way to shortcut to figure that out? Because checking each value to be sure its inverse is also in the set seems to be a waste of time.

5.4-5.5, February 4

1.(difficult) Everything was pretty straight-forward. However, the proof the book gives of Result 5.24 is barely follow able. I could not see where the basis for the proof came from. It was confusing to say the least.
2.(reflective) There is one sentence that would have made all of the difference in my initial interactions with proofs: "In a proof, we are not required to explain where we got the idea for the proof". I often felt like I had to explain where my knowledge of the beginning of the proof come from. This is KEY information!

5.2-5.3, due February 2

1. (difficult) The most difficult concept I ran across in this reading is the in depth look at proof by contradiction. On the surface, and in the problems that they gave as examples, it looked fairly easy. But, after the story problem example, I was thoroughly confused. It seems in the story problem as if the proof by contradiction was shaky, and not totally convincing as a proof. I began to wonder if this is often the case with Proof by contradiction?
2. (reflective) I've  been looking for a chart like the one that is given in 5.3 to help a person to decide what course to take with their proof. I was actually contemplating making a chart myself, but this will be of use instead.

4.5 - 4.6 & 5.1, due January 30

1. (difficult) The difficult part is wrapping my head around the wording of the proof symbols for sets. It will take a little while to note what is actually being stated by set notation. Also, mixing cartesian products with set algebra is confusing.
2. (reflective) We are finally granted a way to disprove statements with the information in 5.1. It was difficult to just push that option in the back of my mind as we were constantly proving the statements given. Counterexample seems to be the only way something can be disproved, but I have been wrong before about what is available. I might get surprised.

4.3-4.4, due January 29

1. (difficult)  I don't understand result 4.16 and the subsequent proof for it. I read over it a couple of times, and I don't see how the proof arrived at. It seems to take the exact same expression and reworks it to prove itself. Something to the effect of: Prove 5x=y. Well, 5x-y=0, so 5x=y. It just doesn't seem very logical to me.
2. (reflective) The set algebra is tricky. I was honestly hoping that we'd left behind the set notations and intersections, differences, subsets, unions, compliments, etc... But of course we will be using them probably on and off through the course.

• How long have you spent on the homework assignments? Did lecture and the reading prepare you for them?
• I have spent roughly one hour on each assignment and one hour on readings and bloggings per assignment. However, the LaTeX assignments usually takes me longer than just writing it. The reading and lectures adequately prepared me for the assignments.
• What has contributed most to your learning in this class thus far?
• reading and writing blog posts about the material
• What do you think would help you learn more effectively or make the class better for you? (This can be feedback for me, or goals for yourself.)
• I often do the homework assignments during class lectures, so I would like to have them done either before or afterward and take that time to listen and ask my questions.