I recently found a food photography blog called foodporn.net. Now don't let the name scare you! It's a fun website that has a lot of great pictures of food. It has a really good, clean layout. There isn't much to distract from the pictures of food. Clicking on the "details" button under each picture will take you to a page that gives a bigger picture, a title, and a link to the website with a recipe. On the side of the page are categories you can use to narrow your search, like "Asian" or "Fried." The only thing that might make this page better is if each picture had a caption with what the food actually is. It is hard to tell from some of the pictures what exactly it is a picture of. Also, a login feature with ability to tag favorites might add, but isn't really necessary.

11.6-11.7, due on March 28

1. These sections didn't seem to be too difficult. I haven't looked at the homework yet, but the sections seemed straightforward. I like the Fundamental Theorem of Arithmetic. I feel like the prime factorization of numbers is something that I have been doing for a while, so these sections felt a little bit like a review.

2. Wow, it's been a while since I've done one of these posts! I kind of got off track over the last month, but I'm hoping to start doing better and finish the semester strong. I know that late homework is not accepted, but is there any way I can make up for all the assignments I missed? I've really missed a lot of points, and I would be willing to put in a lot of effort over the next few weeks, even if I can only get partial credit.

8.5-8.6, due on February 22

1. 8.5 doesn't seem too bad, kind of just a review of old material, but showing how it is an equivalence relation. 8.6 had me totally lost, though. There were so many new terms, like residence classes, closed under addition or multiplication, and well-defined. Actually most of it made sense after rereading it, but I'm still not quite sure what a residue class is.

2. I thought it was interesting to read that I will see congruence modulo n again, because I had never heard much about that before taking this class, and now it turns out it is some important mathematical concept! Strange.

8.3-8.4, due on February 21

1. I missed Friday's lecture and forgot to do the reading, so I thought that it would be really hard to catch up. Luckily the stuff I missed was about relations, which don't seem to difficult so far. I think what I will have the most trouble with is 8.4, which introduces equivalence classes. Equivalence classes seem to be a lot like sets, which are hard to prove stuff with. Just like with proofs of sets, I understand the examples in the book, but if I tried to do it by myself, it would be really hard.

2. Equivalence relations are actually kind of interesting. It's cool that we can prove things about a relation, without actually having to know what that relation is.

7.1-7.3, due on February 15

1. The first two sections didn't seem very difficult. 7.1 didn't really introduce anything except the term "conjecture," and 7.2 was just like a review of stuff we learned earlier. 7.3 didn't seem difficult to understand, but I think it will take some practice before I am able to easily determine whether to prove or disprove something. It was easier when I knew where I was supposed to be going, because I know that I at least got to the right answer, even if I got there the wrong way.

2. 7.1 has been my favorite section of the book so far. It amazes me how much has been discovered in the math world, but how much there still is to learn. It's weird that right now it seems impossible to prove some conjectures, but we can't even imagine the progress that math, science, and technology will make in the future. Just thinking about how much we have progressed in the past 100 years astounds me.

6.3-6.4, due on February 13

1. These sections both seem really hard. I understood 6.3 for the most part, but I think I will have trouble doing the related problems. 6.4 didn't really make sense to me. In the example on top of page 149, it said that since k+1 is greater than or equal to 3, it follows that: and then a bunch of stuff that followed, but I didn't understand how any of that followed from the previous statements.

2. I think it's interesting that we are doing so much stuff with induction and recursive series. I remember I really liked recursive series in algebra II, but something must have changed between then and now haha.

6.2, due on February 10

1. I didn't really see many differences between this section and 6.1. Was the difference that now, instead of the base case being 1, the base case can be any number that is the least element of a well-ordered set?

2. I thought that the examples for this section were interesting, because they were a lot different from the examples in 6.1. For example, I didn't think about using induction to prove something like 2^n > n. That seems tricky.

6.1, due on February 6

1. Mathematical induction made a lot of sense to me, but only after I thought about it for a while. It seems like it will be pretty easy to set up the proof, but then actually working through it and grouping and rewriting terms to make it work for k+1 will be the difficult part.

2. I think that probably the most important topics we have learned about have to do with direct proofs and proofs by contrapositive, because so many of the other concepts have stemmed from this knowledge. I am expecting to see a lot of questions on the exam that have to do with this. I also expect to see some tricky definition-type questions in multiple choice. I think the sections I had the most trouble with were the ones that involved set proofs, so if I had to choose something to see more examples of, it would be that.

5.4-5.5, due on February 3

1. These sections don't seem too bad. The only new thing we have to do is in 5.5 where we figure out how to turn the proof into something that we can prove using the methods we already know.

2. I feel like 5.4 is the opposite of disproving stuff. It's probably going to take a little more thinking, because it's not too hard to find examples of why something doesn't work, but it's a little harder to find the example of when something is true.

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.