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.

5.1/5.2 (part 1), due Nov 15

1) Corollary 5.2.1 seemed like it was the most confusing.

2) Cryptography sounds really interesting-the science of encoding and decoding secret messages.

Exam 2, due Nov 10

Which topics and theorems do you think are the most important out of those we have studied?
Fermat numbers,Mersenne numbers, Fibonacci numbers, Golden section,Binet formula, infinitely many prime of the form..., Pythagorean Triples,Thrm 3.2.1.1, Fermat's two-square thrm, finite simple continuous fraction, Dirichlet's thrm, Dirichlet character, Lemma 3.3.1, Dirichlet L-series,Thrm 3.3.4, Twin primes, Thrm 3.4.1, arithmetic functions, Thrm 3.6.2, Mobius function, and Mobius inversion formula

What kinds of questions do you expect to see on the exam?
I expect to see some proofs that use some of the things listed above. There may be a questions asking me to compute a certain finite simple continuous fraction, or compute a Mobius function.

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 in class on Friday.
I need to work on understanding things concerning anything having Dirichlet. I would like to see problem 3.20 from the book done.

Are there topics you are especially interested in studying during the rest of the semester? What are they?
I like things having to do with prime, so I would like to see what other things involve primes.

4.2 (part 2), due Nov 8

1) I was hard for me to follow the proof of 4.2.2.

2) It is interesting how divergence keeps coming up and being used.

4.1&4.2 (part 1), due Nov 3

1) I didn't understand the use of the A_1 and A_2.

2) It was easier to understand 4.2 because it talked about things I have seen before like binomial coefficients and the binomial formula.

3.3 (part 2), due Oct 30

1) I had the most trouble understanding the rough outline of Dirichlet's Thrm in this section.

2) I was able to relate some of the things I read to calculus (convergence).

3.3 (part 1), due Oct 25

1) I just really what to know what the phase "runs over" means in this section?

2) I thought the most interesting part of the section was the notation the used to describe Dirichlet characters.

3.2.5, due Oct 23

1) I didn't really understand Lemma 3.2.5.1 and the proof of the infinitude of primes using continued fraction was also a little confusing.

2)I thought it was interesting that you can also prove the infinitude of primes by using continued fraction.

3.2.2, due on Oct 18

1) The proof for Lemma 3.2.2.2 was the most confusing.

2) The most interesting thing I read was that Pythagorean triples can be related to Fermat's two square thrm which involves to quadratic residues.

3.2-3.2.1, due Oct 16

1) I had the most trouble understanding the proof if Lemma 3.2.1. I feel like the left out some of their justification for their steps.

2) I've done some problems having to do with Pythagorean triples, so when I read some of the thrms and things they had to say about them, I noticed that I already knew a lot of what they had to say.

3.1.5, due on Oct 13

1) I had the hardest time understanding the proof of Lemma 3.1.5.5.

2) I didn't realize there are so many lemmas that are variations of the thrm stating there are infinitely many primes.

3.1.4 (Part 2), due Oct 11

1) I had the most trouble understanding Lemma 3.1.4.5 and its proof.

2) I didn't realize and I also thought it was interesting that you can use the Fibonacci numbers to prove there are infinitely may primes.

3.1.4 (Part 1), due Oct 9

1) I had the most difficulty understanding the proof for the Thrm 3.1.4.1.

2) The most interesting thing about the reading was that I didn't realize there were so many shapes that the golden ratio could be used for. It makes me realize that the golden ratio is probably used for a lot more that I know.

3.1.3, due Oct 6

1) I had the most difficulty understanding Lemma 3.1.3.2.

2) I found it interesting that there are different ways of finding certain primes like Fermat primes and Mersenne primes.

3.1.2, due on Oct 5

1) The most difficult part for me to understand was when the thrms and their proofs included 2^(2^(n-1)) or 2^(2^k). I don't know why this confuses me, but I just don't know why it is that particular number that was chosen, and I don't really know how it fits in...

2) The most interesting part about this section was that it uses some calculus-Thrms having to do with convergent and divergent sums. I was not expecting to see that.

Review Questions, due Sept 30

Which topics and theorems do you think are the most important out of those we have studied?

Division Algorithm, Euclidean Algorithm, Fundamental Thrm of Arithmetic, GCD and LMC, Congruences, Fermat's Thrm, Euler phi function, solving polynomial congruences, Chinese Remainder Thrm, quadratic residue, legrendre and jacobi symbols,

What kinds of questions do you expect to see on the exam?

I expect to see some proof of some thrms, also some computation like solving a polynomial congruence. I also expect to see a problem on quadratic residues, maybe also a question using GCD's or LMC's.

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 in class on Friday.

I need to work on understanding proofs involving quadratic residues better.
Show that if p is congruent to 1 (mod 3), then (−3/p) = 1.

3.1.1, due on Sept 27

1) (Difficult) I have no idea what Lemma 3.1.1 is saying and its proof is even more confusing.

2) (Reflective) I thought the most interesting about the reading was that there were so many proofs of the Thrm: There are infinitely many primes. I didn't know there were so many proofs of this thrm.

pg 221-222, due on Sept 26

1) (Difficult)I'm not sure I know what (a/p) or something of that form means.

2) (Reflective) The most interesting thing that I read was that if p is a prime then the Jacobi symbol and the Legendre symbol are identical.

2.5.2, due on Sept 20

1) (Difficult) I had the hardest time understanding Lemma 2.5.2.1.

2) (Reflective) I thought that the most interesting thing about this section is that Thrm 2.5.2.4 uses the quadratic formula. Didn't think that I would see that in this class.

2.5.2, due on

2.5.1, due on Sept 18

1) (Difficult) The most difficult part of the reading to understand was the Chinese Remainder Thrm.

2) (Reflective) The best part about this section is that it reminds me a lot of previous math classes that I have taken like Calculus or below. It reminds me of these classes because it gives a thrm or two and proves them and then uses them to find the solution to an equation.

2.4.5, due Sept 15

1) (Difficult) I had trouble follow the proof to Thrm 2.5.1.

2) (Reflective) After taking Abstract Algebra this last spring, I was pretty familiar with cyclic groups, so this section wasn't too difficult to understand. It was nice.

2.4.4, due Sept 13

1) (Difficult) I had trouble understanding Thrm 2.4.4.5 and I don't know that I fully understand Thrm 2.4.4.6. I don't understand for example how the number 7 in their example can be 7=2,4,p^k, 2p^k for p a prime. I know 7 has primitive roots, but I do not see how that statement is true about seven. I also find it would be difficult to find the primitive roots for a large number.

2) (Reflective) I have seen some of these thrms and proofs before. I am familiar with Lagrange's Thrm and Fermat's Little Thrm. I am also familiar with cyclic groups, abelian groups , and order.

4.2.3, due Sept 11

1) (Difficult) I had trouble understanding what a reduced residue system was and also had a hard time understanding Lemma 2.4.3.4 and Lemma 2.4.3.5.

2) (Reflective) I notice that there were some thrm that didn't quite make sense to me when I first read them, but through reading the proof for the thrm I was actually able to understand what the thrm was saying. For example I was able to do this with Thrm 2.4.3.1.

2.4.2, due on Sept 8

1) (Difficult) I had the most difficulty understanding the concept of a ring of integers modulo n. I think I might need an example in order for me to wrap my head around it.

2) (Reflective) The most interesting thing that I read is that in Thrm 2.4.2.2 the residue class for x was the multiplicative inverse.

2.4.1, due on Sept 6

1) (Difficult) I had trouble understanding what a residue system was. Consequently, I struggled to also understand the lemma associated with residue systems, Lemma 2.4.1.1.

2) (Reflective) Though it was hard to understand the concept of a residue system, when they talked about a residue class, I'm fairly certain that a residue class is also referred to as an equivalence class. If they are the same, then I am most familiar with the term equivalence class ([x]).

2.3, due on Sept 2

1) (Difficult) I struggled to understand Thrm 2.3.4. I have no idea what a noncommon prime is. I also didn't understand the notation.

2) (Reflective) I can connect this material to previous things I have learned. It seems I have seen a lot of these proofs before, like the proof of Lemma 2.3.1, Thrm 2.3.1, and the Fundamental Thrm of Arithmetic. I like seeing things that I have seen before because I confirms that all mathematics is connected. It is not disconnected like some people might think.

Section 2.1 & 2.2, due on Aug 30

1) Difficult - I had most difficulty understanding the proof to Thrm 2.2.2. I also had a bit of trouble understanding how they wrote the Euclidean Algorithm as well as its proof. I've seen that Thrm and proof before, but the way they wrote it, I almost didn't recognize it.

2) (Reflective) - I noticed that in these first two sections I was reminded me of things I have previous learned. I was able to connect rings, groups, integral domains, homomorphism, etc to Math 371. There where other things that I related to originally learning in Math 290 like GCD, LCM, prime, composite, relatively prime, etc. I don't remember Math 341 as well, but I do remember learning things about the division algorithm, Euclidean Algorithm, etc. I'm amazed that this class uses many things that we have previously learned and combines them, but I like that I can finally connect these things together in this class.

Please let me know if you would like me to be more detailed in what I mean or have talked about. Thanks.

Introduction, due on Aug 30

What is your year in school and major?
Senior

What do you plan to do after graduating?
Teaching or tutoring Math, ideally I would want to teacher 8th grade Algebra.

Which post-calculus math courses have you taken?
Do you post Calculus I or post Math 314? Well, I'm going to answer the post Math 314 and you can just assume I have take all the math classes between 112 and 314. I have also taken Math 334, 341, and 371.

Why are you taking this class? (Be specific.) Are there specific topics you look forward to learning about in this class? If so, what are they?
I am taking this class because I need it to graduate. Oh, and I chose this class over the other two I could have chosen, because I've enjoyed classes because that had to do with numbers. I don't know how much of the material we will be learning will be using Math 371, but I look forward to learning anything that uses that class. I really felt like I understood that class.

Tell me about the math professor or teacher you have had who was the most and/or least effective. What did s/he do that worked so well/poorly?
Asking me question while lecturing that connects me back to previous things learned or talked about, this will help me connect concepts. A good example of when a teacher did a really good job of teaching was... Well, I remember having a substitute teacher for my Math 341 this last spring, his name was Paul Jenkins. He did good at doing those things that I described above.

Write something interesting or unique about yourself.
I've been married almost 2 years now and I have a little boy named Landon who is 13 months old.

If you are unable to come to my scheduled office hours, what times would work for you?
Your hours work for me, but if for some reason they eventually don't then 12-1:30 on Tues and Thurs.