Final Test Review, due Dec 7

* Which topics and theorems do you think are the most important out of those we have studied?
GCD, Euclidean Algorithm, modular arithmetic, phi function, Chinese Remainder Thrm, Legendre and Jacobi symbols, Mersenne and Fermat primes, Fibonnoci numbers, Fermat's little thrm, golden ratio, dirichlet's thrm, infinitely many primes mod..., Dirichlet characters, Mobius inversion, pi(x), binomial thrm, Riemann zeta function, cryptography and its different algorithms, elliptic curves, and tangents finding a third point.
* What kinds of questions do you expect to see on the exam?
I expect to see questions related to the topics above, some computation, and some proofs using the concept above.
* 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.
I need to work on understanding things about Dirichlet characters and when to use some of the things we have just learned about elliptic points. In what cases or in what problems to I need to find a third point?

6.3, due Dec 4

1) I had the most trouble understanding the proof of Thrm 6.3.1.

2) This section reminds me a lot of abstract algebra with some linear algebra.

5.4.2, due Nov 29

1)I'm not sure I really understood the RSA algorithm.

2)I'm amazed at all of the different types of cyptosystems. Are there people still trying to find new ways to encrypt messages?

5.4/5.4.1 due Nov 27

1) I had trouble understanding the Alberti code.

2) So I think it is interesting, my husband is majoring in computer science and he is going to do a senior project using cryptography. You can use it in the mathematics field as well as in the computer field.

5.3.2, due Noc 21

1) The proof to the Lucas-Lehmer test is really long and somewhat confusing.

2) For some reason I found this section very interesting. I think it is really cool that through Mersenne primes we have been able to find bigger and bigger primes.

5.3.1, due Nov 20

1) I biggest difficulty I had in understanding the reading was, Thrm 5.3.1.2 and Thrm 5.3.1.5 have really long proofs so I got lost a long the way and didn't quite fully understanding those proofs.

2) Interestingly Carmichael sounds really familiar and I can't figure out why. I thought that maybe I had heard of Camichael numbers before, but now I'm just thinking that I've heard it as someones last name...

5.3, due Nov 17

1) Thrm 5.3.6 was the most confusing-big O of a log...

2) The beginning of this section was nice. I could relate it back to previous sections in this book because the book had already stated Fermat's and Euler's thrm once before.