Preparing For Final

1. Which topics and theorems do you think are the most important out of those we have studied?
 It seems to me, and this probably isn't a surprise at all, but I think the big ideas here are: primes. Both the number of primes, and whether a number is prime or not. So, it seems that if I can figure out if a number is prime or not, and how many primes are less than it (or relatively prime) or to be able to prove there are infinite primes, I should be in okay shape.


2. What kinds of questions do you expect to see on the exam?
Again, I expect to see questions really similar to those questions we have seen in homework. Assuming that the final is slightly weighted more towards the material we've covered since the second midterm, I should expect to use different algorithms to show that a number is either prime or composite. I also expect some type of cryptography, as well as some elliptic curve stuff.

3. What do you need to work on understanding better before the exam? Come up with a mathematical question you would like to see answered or a problem you would like to see worked out.
Well, I would really like to see number 1 of the last homework assignment worked out. I do not understand the p-1 algorithm at all, and I'm nervous about that.
I also need to work on remembering the names and steps of each primality test. They are all a jumbled mess in my head.

Section 6.3, Due on December 5, 2011

1. What was the most difficult part of the reading for you?
Well, again, there were many things that were difficult. And, admittedly, I'm pretty tired, so I may have missed something. But, specifically I have a question about one thing. I felt like I understood "B-Power Smooth" from the first part of this section... But where I got confused was trying to tell if numbers were B-Power Smooth later on. I mean, from what I understand of the definition of B-Power smooth, it seems like everything is B-Power Smooth to some B... So why is it that in the later parts of this section they'd say that a number "Isn't B-Power Smooth"? Again, I probably just read over what they're saying there, but that's something that confused me.

2. What was the most interesting part of the reading for you?
I know this is going to sound a little lame (I can't help it... I didn't fully understand the reading... so sometimes I have to make stuff up to be interesting) and though I really don't understand this part, I think it's interesting that they can use these elliptic curves to factor big numbers. Seriously, after class I was feeling pretty good and exited about this elliptic curve business, so I'm excited to see what light you'll shed on that subject in class.

Section 6.1-6.2, Due December 2, 2011

1. What was the most difficult part of the reading for you?
Um... Let's blame my confusion on the fact that this is a new book with a new style that feels like a new language being spoken. Yes. Let's blame it on that. I'm still pretty confused about what Elliptical Curves are... but beyond that, I'm confused about what in the world this "Sage" business is. I mean.... what in the world is that? It kind of reminded me of playing Zelda and "Sage" is that annoying helper that beeps and tells you what to do every step of the way... only in this book, since I don't even know what "Sage" is, it's not very helpful to me. But, ignoring the weird Sage business, I didn't understand the condition of -16(4a^3+27b^2) not equaling zero. Also, I didn't understand how figure 6.2 is an elliptic curve... It just looks like dots to me.

2. What was the most interesting part of the reading for you?
Well, I really didn't understand much of what I read... so there wasn't much. I guess that if I had to pick something that caught my eye it would be what the very first paragraph says: It talks about putting keys on stamps and making them short and how these curves help with encryptions... Wow.... I guess it's going to be cool when I understand it...