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.
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