7.2 Due October 29

This section was pretty cool. I thought that the most interesting part was the relationships between solving these types of problems and factoring problems. Like it being harder when p=3 (mod 4). I guess that could be purely coincidence, but it still caught my attention.
The hardest part was 7.2.3. I don't have a very firm grasp of why that method works.

6.4.1 Due October 25

This section was very interesting. I like factoring, and I think it is really cool that we have made so much progress recently in the size of numbers that we are able to factor.
The hard parts for me were understanding how the generating squares that were products of small primes thing worked and understanding why we wanted to put it into a matrix like we did and how that whole dependencies thing worked.

Dr. Dorff Lecture

I thought that the path length/ area minimization problems were pretty interesting to think about. And it was cool that soap bubbles do it all by themselves. In that regard, I thought the lecture was pretty interesting, but he kept things pretty basic, so I didn't see any actual math that was very interesting or difficult to understand. I'm sure that if he would have gone into more details about the actual math that describes these surfaces it would have becoming very challenging though.

John Friedlander Lecture

I know that this post is late, but I did attend the lecture on the 14th.

I had already seen most of the material that Dr. Friedlander discussed in this class or other classes, so there wasn't really anything that was too difficult to understand. But there were some interesting parts. I really like the question of whether every even integer was the sum of two primes. That was something that I had never seen before, and I have been thinking about it a lot since then. I'll let you know if I ever prove it :)

6.3 Due October 20

I found this section very interesting. It was neat to see how the things that we read about in the previous section are applied for primality testing.
The Basic Principle and the Fermat test made sens to me, but I struggled a little bit with the last two methods discussed in the section. It would be good for me to go over those again in class.

3.10 Due October 18

Today's reading was pretty interesting, even though, I didn't really see the practical application of the methods. I mean, I guess that it is good to know when things have solutions and when they don't, but even if (a/n)=+1, that doesn't really tell us that a is a square. And even if it is, we would have to factor n to find the solution. So it seems to me that this didn't help us to progress much, but hopefully this will become more clear in class.
The most challenging part was probably just following some of the proofs. I feel like they did a little more hand waving than usual in this section.

3.9 due October 15

This section was pretty cool. It was neat that it provided such a cool way to factor n quickly. I guess I would be interested to know how often it works out so that you could use this method, or how we can implement RSA in a way that would prevent this attack.
I think that I understood everything pretty well and had a good handle on the proofs, but it would definitely help to go through them again tomorrow.

6.2 Due on October 13

This whole section was very interesting. I thought that the timing attack part was the most interesting just because it took advantage of the physical properties of the encryption machine instead of the mathematical properties of the method. I thought that was very cool outside-of-the-box thinking. Also, I thought it was neat that he was an undergraduate when he thought of that idea.
As far a difficulty goes, there is no part of this section that I completely understand. I am really hoping that tomorrow will bring some serious clarification for me.

3.12 Due on October 11

This was an okay section. The material wasn't very complicated, and the proof for the theorem wasn't included, so I don't think that there was anything too interesting or complicated in this section. It was all pretty straight-forward.

3.6 and 3.7 due on October 6th

The most interesting parts of today's reading for me were:

1. Fetmat's Little Theorem and its proof - I thought the proof for this theorem was really clever. Those are always fun to read.
2. The three pass protocol - We had alluded to this previously in the class, but I never really understood how it worked until I read this section. Now that I understand it, I can see what a cool idea it is.

After the reading, I don't have a good understanding of why Euler's function works or why Euler's theorem is important, but I think that everything else made sense.