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.