4.5-4.6 and 5.1, due on January 30

1. I thought that proofs involving sets would be fun, but adding in the cartesian products is giving me a headache! There are just a lot more variables to keep track of than I had originally thought. I think 4.6 might be a challenge for me.

2. I think I will like disproving things. It seems like finding one example of why something doesn't work is a lot easier than showing why all cases should work.

4.3-4.4, due on January 27

1. I'm a little bit worried about doing proofs with real numbers, because it looks like we will be using a lot of inequalities, and those always confused me when I was in algebra. The same thing goes for absolute values. I never remember if I can divide things by each other, and what will make the inequality change direction.

2. I thought the section on doing proofs with sets was interesting. It didn't really occur to me that being able to prove set relations would be a useful skill, but now that I think of it I think it might be fun to try on the homework.

I feel like I don't spend very much time on the homework. I probably spend about an hour, maybe more if I'm typing it up in LaTeX. So far I feel like I have understood everything, and that the reading and lectures have helped prepare me for the homework assignments.

4.1-4.2, due on January 25

1. The modulo phrasing is very hard for me to work with. I think after the lecture and the homework it will probably get clearer, but it takes me a while to look at some sort of modulo and know what it actually looks like in n|(x-y). And then it takes me a little while to figure out what that means! Hopefully it will become more natural with practice.

2. I think I've heard of modulations (?) before in another class. I think I remember one of my past professors saying that it would be really good to know about for future math classes. Is that true?

3.1-3.3, due on January 20

1. I think the most difficult thing for me to grasp is when to use a lemma. In the last example of section 3.3, I understood why using a lemma made the proof easier, but I don't think I would really think about that as a proof strategy. Hopefully it's one of those things that gets easier with practice!

2. I liked what it said in the reading about how a theorem can be beautiful to a mathematician. I usually don't like proofs, but I'm hoping that I can change that attitude through taking this class.

Chapter 0, due on January 18

1. This section seemed pretty straightforward. I think I probably misuse i.e. and e.g. a lot, so I will have to be careful about them! I will try to refer to this section as I do the homework, because it has a lot of helpful clarification about proper mathematical writing. It's something I've never really done much of before, so I'm sure I'll make a lot of mistakes!

2. This doesn't really have to do with the reading, but I noticed that we're going to be learning about LaTeX tomorrow, and I have a website that might be a helpful resource. I've worked with LaTeX in another class, and one of the students showed us this website called Detexify. The way it works is you draw the symbol you are trying to create in a box on the page, and on the right side suggestions come up for which symbol you might be looking for and what the command is. The URL is http://detexify.kirelabs.org/classify.html

2.9-2.10, due January 13

1. I can tell that I am going to get confused when I start trying to negate statements. I could understand all of the examples, but I don't know how I would negate something that was like, "(P or Q) and (not P implies Q).

2. The universal quantifier is going to trip me up! I almost always put a little cross on my conjunction symbol and accidentally make it an "A." I have a feeling my disjunction symbol is going to start having the same problem! But at least I understand what it means.

2.5-2.8, due January 11

1. The most difficult section for me was on tautologies and contradictions. It's hard for me to wrap my mind around checking if a sentence is a tautology or a contradiction, because I want to just check if it is a true or false statement. For the statement, "2 is odd or 2 is even," I know that 2 is even, so it is hard for me to entertain a case where 2 is odd.

2. I really like how much we are using truth tables right now. Last year I took a computer science class, and we learned how to program in binary. It was pretty cool to see how much you can do with simple logic. What we are learning right now kind of reminds me of that class.

2.1-2.4, due on January 9

1. The most difficult part of this reading was the last part of the section on implications. Some of the alternate wordings seemed a little bit confusing. Like if P implies Q, you can say "If P, then Q," but you can also say, "P only if Q." At first I struggled with how that is different from, "P if and only if." The more I thought about it, the more I understood it, but I think it could trip me up on a test if I wasn't careful. Maybe I shouldn't give you any ideas!

2. I've never used the term "disjunction" for the OR statement before. It doesn't really seem to describe what it does. Disjunction is like separating two things, but OR-ing two things is like taking both of them and mixing them up together.

1.1-1.6, due on January 6

1. The most difficult part of this section to understand was the index set. I understood what an indexed collection of sets would be, but it took a while for me to get what I was.

2. Right now the stuff we are learning corresponds a lot to my statistics class from last semester, so it is nice to see some familiar concepts. We used a lot of sets and set notation, so I am comfortable with the material right now.

Introduction, due on January 6

I am a junior and I am a math major, although my minor is actuarial science, which is what I plan on doing for a career. I've taken calc 1 and 2, linear algebra, and I'm enrolled in math 314 right now.

I can't think of any college math professor I have had who has been very effective. My high school teachers were really good because they knew the names of all their students and seemed to care about how we did in the course. I understand that professors here are expecting us to act like adults, and are treating us accordingly, so it doesn't bother me that they ignore students who stop turning in homework and coming to class. But I kind of prefer being treated like a high school student, maybe just because I don't have very much discipline on my own haha.

I'm from Alaska, which is not as unique here as I thought it would be. I've met a lot more people here who were from AK then people from eastern states. Maybe I just notice Alaskans more. I'm taking this class with my little sister Anne, which could potentially be embarrassing for me.