Sec 16.5, due Dec 9th

Well, today is the day (I mean tonight is the night ;) ) the very last blog entry. It is a sad day and one that I wished would never come, but it is here and the last blog must be written. First, I just wanna say, Thank you for such a wonderful class! This was by far my favorite class all semester and I wish there were more classes I could take and more that I could learn! You've be a great teacher, one of the favorites! Thank you for everything, and I'll see you in our last class today. :(
1. I was curious as to how alpha multiplied by a was comparable to a discrete log. I know we learned about this is section 16.2, but it was brought to my attention again today for the reading and last night in the homework. In section 16.2 (I think) it talks about discrete logs for elliptic curves, and how beta=a*alpha may not look like a discrete log, but it was.. or something like that, I was just a little confused on that. Anyway, these have all been great sections, and I've really enjoyed this entire book! I can't believe that it's already over!! Thanks again for everything!
2. I really liked this section a lot. It was fun to see how all the cryptosystems that we have learned and used before can now be done using elliptic curves! I think that this is why I understand this section pretty well, because I've seen the basics of this all before, and that's really cool, because it's easier to understand and interesting!

Sec 16.4, due Dec 7th

1. I felt like I pretty much understood everything in this section, but seeing the examples done in class always help me understand everything better, so I'll be looking forward to that.
2. This was a really good section, and it was pretty easy to understand. It's nice how the examples used the finite fields that we've been using as examples all semester, it really helps to understand.

Sec 16.3, due Dec 4th

1. The Singular curves part in this section was kind of confunsing for me, I just had a hard time following the example, probably because I'm tired, but that was what confused me. i'm sure I'll be able to understand it better in class.
2.This section was really cool! I love learing new ways to factor large n's, and now we have an even newer one, with elliptic curves! Also, it's always fun to learn new definitions, such as smooth and B-smooth (which is kinda funny cause it sounds like you're telling the elliptic curve to "be smooth" around this lady curve that it's going to intersect...ok, jk, I'm tired :) ) ANYWAY, this was a great section and I love learning about these elliptic curves!

PS Loved the cryptography pictures!!! They were awesome! :)

Sec 16.2, due Dec 2nd

1. I really liked this section, but I was a little confused on how to represent plaintext as an elliptic curve and mapping the message on to a point on that curve. The example on page 356 was just a tad confusing, but when we go over it in class I'm sure I'll understand!
2. I really enjoy reading these sections! It's fun to learn about elliptic curves and how many different uses that they have! You can use them for discrete logs and for representing plaintext! I love learning about this stuff!

Sec 16.1, due Nov 30th

1. This section was great! Really interesting! There were a few things that were a little confusing, but for the most part I felt like I understood it. I thought that the example on page 350 was a little confusing for me at some parts, and for some reason, I don't understand how infinity is the identity element of the group E, that was also confusing to me. Other than that, I really enjoyed this section!
2. I thought that this was a really cool section! Learning about elliptic curves and how they can factor integers, or how a huge bit key size can be reduced by a lot smaller bit size elliptic curve system is really cool! Although I didn't get everything in this section, I felt like I understood a lot, and I'm excited to learn more about elliptic curves.

Sec 2.12, due Nov 24th

1.Although I really liked this section, it was a bit confusing for me. I know that they had diagrams and stuff, but I just couldn't follow what they were saying :( I was confused on how they encrypted and decrypted things, and I just didn't really understand it. Anyway, I'll be able to understand it in class :) See you then
2. I really liked this section! It was fun and interesting to read about this enigma machine and what it did, and it was really cool to read about the history that surrounds it. Like how the Polish guys broke it and gave it to the British and they used it all during WWII and and the Germans didn't even know! Suckers... :) Anyway, it was a lot of fun to read and I also liked how it talked about cycles, that was fun. I remember cycles from 371, I loved those things. Anyway, great section! I'll be in class today, sorry for missing yesterday! If I don't get to tell you in class, Have a happy Thanksgiving!

Sec 19.3 and article, due Nov 23rd

1. I really enjoyed the article and this section in the book. However, the section was a bit confusing, and I'm still trying to get used to the new notation that we're using and stuff. I'll be sure to read the section again so that I can understand it better since I might not be in class today.
2. I really enjoyed reading the article, the author is a pretty funny guy and it was really easy to read and understand! So today we're going to talk about what we could do with a quantum computer if we had one? I suppose I will think about that a lot today, since I might not make it to class :( Also, I really enjoyed reading this section, although, I prefer the article over it, just because the article wasn't as long or quite as confusing, but I'm trying really hard to understand this stuff because it is very interesting to me!

Sec 19.1-19.2, due Nov 20th

1. Alright, I'm not gonna lie. This stuff sounds sooooo cool! It really does, I love the thought of using quantum mechanics to break ciphertexts and stuff because I love science and these kinds of these, but I am definitely not a physicist and this pretty much confused the heck out of me. I understand what they're trying to do I think and stuff, but I am not getting how they're doing it, but I can't wait for you to explain it in class today in a way that I'll understand it better!! Then I'll get way pumped for this!
2. I really did enjoy reading these two sections and the idea behind it, I just need a little help understand the concepts and stuff better.

P.S. No class next week?? :)

Sec 14.1-4.2, due Nov 18th

1. These sections were super interesting! I love all the real life examples that they give to! I mean, if this stuff can help not get my credit card info stolen, I'm all about it! :) I was confused about a couple of things. In section 14.2, the procedure that victor and peggy follow, I was confused at step 2, where Victor gets his b_i from {0,1}. So, can all the b_i's just be 0 or 1? They're not allowed to be fractions right? Other than that, I really enjoyed these sections and am excited to learn more!
2. Man, this stuff just keeps getting cooler and cooler! I love this idea of Zero-Knowledge techniques! I think that it is really interesting and fun to read about! I was confused about some stuff, but I'm excited to learn about it in class!

Sec 12.1-12.2, due Nov 16th

1. I really enjoyed reading these sections, and I thought that secret splitting is vey interesting and cool, but there were a few places that I got a little confused. Basically half way through section 12.2, where it started talking about hte matrices, and the sums of all the products and stuff, I kinda got a little lost, but I still think it's really cool!
2. These sections were extremely interesting and really fun to read about! I like the idea of secret splitting, and I think it's really cool how many different ways there are to do it!

Questions for Test

Which topics and ideas do you think are the most important out of those we have studied?
The most important things that I think we've studied are the computational problems that you can do by hand, and also knowing the steps and general idea of each of the cryptosystems we've learned about in this last section. I think that if I know how to do the computational stuff like chinese remainder theorem and know the steps and ideas of RSA, ElGamal, etc, and the definitions and theorems, that hopefully it'll be ok :)


What kinds of questions do you expect to see on the exam?
Just as I said before, I think that there will be a couple computational, some that show we know the steps and general idea of the cryposystems we've learned, and maybe some proofs, but hopefully not :)

What do you need to work on understanding better before the exam?
I think that I just need to focus on those things that I don't quite understand. Especially if it's on the study guide and I don't understand it. That includes a few of the cryptosystems we've learned, so I'll need to go over those and raelly understand them before I get near that test.


Are there topics you are especially interested in studying during the rest of the semester? What are they?
No, I've been very interested in what we've been learning so far. If the class continues like this, then I'll be very happy, I like this class a lot and I find most eveything very interesting!

Sec 8.3,9.5, due Nov 11th

1. Ok, I'm not going to lie, the secure hash algorithm was a little confusing to me... especially all the new symbols on page 225. I was also confused about how to know the block length that you would divide your message up in to. They had to add like a bunch of 0's and all sorts of stuff to finally get 6 blocks of length 512. So yeah, this section got me.
2. I really liked section 9.5 though. It was clear and I understood it, and it's nice because I've seen all that stuff before. I really liked learning about digital signatures, because not only is it interesting, but it's something that we can all relate to personally. Anyway, good sections for today, just a little confused on 8.3.

Sec. 9.1-9.4, Due Nov 9th

1. I felt pretty good about these sections, but if I had to choose something that was a little confusing to me, I would probably choose the section on ElGamal signature scheme. The process was a little confusing and I wasn't sure where they got some of the stuff.
2. These sections were are very interesting to read about and I really liked them! It was fun reading about digital signatures and all the different ways to keep them safe using RSA, ElGamal, Hash functions and Birthday Attacks. It made me think about all the things that I sign, and wonder if everything is safe. But like you said in class last time, if we're paranoid, we can always do what Alice did during the birthday attack section and put in a comma or something so that we completely changes the hash. So yeah, I really liked reading these section, they were a lot of fun!

Sec 8.4-8.5,8.7, Due Nov 6th

1. I really enjoyed reading about these sections! As I was reading, I go through and put little question marks next to the things that I don't understand as I'm reading. The first thing that I didn't understand was on page 231, when they said that "the probability of exactly i matches is approximately λ^ie^-λ/i!. I just don't understand where they got this equation from. The next part that was a little confusing for me to understand was section 8.5 about the multicollisions. I was wondering if there is any certain size block that we know to split the message M into? Then the big paragraph on the bottom of p 234 became a little confusing. Oh and then my last question is for the last section. I was wondering, what if Bob and Alice can't get together to agree on a shared secret key KAB? Will it just not work? Ok, I think that was about it! I really liked these sections!
2. Yea!!!! The time has finally come to learn about Birthday attacks!! And I think that it was worth the wait! I really enjoyed reading about them, and learning all the cool stuff that it does! It's like I want to go find the probability of a ton of stuff now and then test it, like they said to in traffic. Or I want to ask all the people in my class what their birthdays are and see if there is a match, it's so fun! I also liked how we can use birthday attacks to solve discrete logs! Now we have a few methods to solving those. Multicollisions were fun to read about, but got a little confusing for me about half way through. And then learning about using the hash functions to encrypt was pretty sweet I thought! It's just so fun and cool to learn about what people can come up with when it comes to encrypting messages and stuff! I love it!

Sec 8.1-8.2, due Nov 4th

1. I got a little confused with the proposition on page 221, and also, there were a few things about the simple hash example that I could use a little more explanation on, but you always do a great job at explaining things well in class
2.I really liked reading about hash functions! I think that they're really cool, and they seem pretty secure to me with those 3 conditions that they have to follow. I'm excited to learn more about them!

Sec 7.3-7.5, due Nov 2nd

1. The thing that I was most confused about was the ElGamal Public Key Cryptosystem. I think that I was just confused with some of the wording and the steps. I'll read over it again, but that was the most confusing to me.
2. Now this is what I'm talking about! Relating math to football! Haha, now this is easy to pay attention to and fun to read about! I love how they related the bit commitment to football, and it made it so much easier to understand! I also enjoyed the other two sections, they were quite interesting to read about.

*If this comes in late, please don't count it late! My internet has been messing up :(

Sec 7.2, due Oct 30th

1.This section was very long and had a ton of information in it. The thing that I thought was a little confusing was the Pohlig-Hellman Algorithm. There were just a lot of steps to follow and I might have gotten a little lost. I'm very upset that I'm missing class tomorrow, because I really need to learn about these things. Beth/Braden better take dang good notes! Call them out if they're not, or if they talking or doing anything but paying attention and taking notes :)
2. I really liked this section a lot. I think it's cool how we can compute discrete logs, and the different methods we have to do so. On page 207 at the very top, it talks about how the baby step, giant step process works for primes up to 10^20, or slightly larger, and then it says that it's impractical for very large p, and when I read that I was thinking, "seriously? I thought that primes up to 10^20 was huge... but I guess not." So that was kinda funny :) Well, I'm sorry I'm missing class, some family matters came up that I have to attend to. I hope that your baby boy is doing well and your wife. I'm so happy for you! Have you guys come up with a name yet?? Well, I'll see you on Mon! Have a great weekend, and make sure to let your kids get lots of candy on Halloween! :)

Sec 6.5-6.7, 7.1, due Oct 28th

1. These sections were great. I really liked the public key concept, I think I understood most of it, but maybe I didn't. I like the trapdoor idea, I think it's pretty cool. Now I understood the first example for discrete logarithms that they gave in the book, but then again that was just a very small and easy example, so I'm wondering how hard it's going to be with a very large number... maybe we'll learn that in class.
2.These sections were all really cool and interesting! The RSA challenge was cool, I can't believe that they came up with 524339 small primes! That is a ton! I'm also interested in learning more about the RSA signature scheme, but I guess that I'll have to wait til section 9.1, because there is no way that I could just go an read it by myself :) I wouldn't want to get ahead of the class :) JK, I probably will do that. All in all, I really enjoyed these sections, and I learned a lot!

Sec 6.4.1, due Oct. 26

1. This section was actually a little difficult to follow as it transitioned into matrices and stuff. I was kinda confused on a few of their examples. Like the one on the top of page 184, where it shoes the relation of 17078^2 which was congruent to 3 primes raised to powers, and then they transferred those powers into the row of a matrix. What I'm confused about is when we know when to stop, if that makes sense... So I understand that we have (6, 2, 0, 0, 1, 0, 0, 0) and the 6 comes from 2^6, the 2 comes from 3^2 and then I guess 0 for the primes 5 and 7, and then 1 for 11^1, and then I don't know why they out down 3 more zeros. Anyway, that was kinda confusing to me.
2. I really liked this section though, it was very interesting! I like the Basic Principle, I understand that, and we've gone over it in class, so that's great! I just hope to understand the rest of this section tomorrow in class, because it's a little fuzzy after just reading it myself, and I'm excited to see how well it helps us!

Sec 6.4 up to 6.4.1

1. This section was nice and short, and so the only thing it really covered was the p-1 factoring algorithm which was actually a little confusing, just trying to understand all the parts of it and how to come up with B and where people come up with this stuff! So I look forward to learning about it in class tomorrow!
2. I found the part of this section that I read very interesting! I'm excited to learn more about the p-1 factoring Algorithm in class and while I was reading about it, I just wondered like where people come up with this stuff! It's crazy! But also very cool! I hope you wife had your baby!! If so, Congratulations!! I'll ask you tomorrow in class...if there is class :)

Sec 6.3, due Oct 21st

1.I really like learning about primality testing, but one of the things that I thought was a little difficult to understand was the Miller-Rabin Primality test. The Theorem is really long, but when I went over the example it made a lot more sense. I know that when I see more examples in class today, that I'll be able to understand it a lot better too
2.I really enjoyed reading this section, I thought that it was really cool and interesting! And I know that it will helps us because there are methods in this sections that are extremely fast, and so I'm excited to have them!

Sec 3.10, due Oct 19

1. I really enjoyed reading this section and found it very interesting! It was a little disheartening at times when I would go through the examples in the book, and realized that I really needed to know those propositions like the back of my hand because for a large number like on the example on p. 92, it took like 10 steps, which I know is very fast, but it's fast because of all the steps from the propositions, so I just need to make sure that I know those really well and understand them!
2. This section was very interesting and fun to read about! I really enjoyed learning about the Legendre and Jacobi symbols and how they can help us find out whether a is a square mod p or not for a large p. I like seeing examples, and so I'm looking forward to seeing more examples tomorrow in class! Also, if your wife had her baby, then congratulations!! I'll find out tomorrow when I see you! :)

Sec 3.9, Due Oct 16th

1. This was a very cool section and I really liked it a lot! Although I had to read it slowly to make sure that I was understanding it correctly and following along, and really pay attention to the examples and go over them until I understood them, I'm a tad confused on the second to last paragraph on p. 87 where it talks about gcd(a-b,n)=p. I guess I understand it, I just might need a couple more examples :)
2. This section was great! It was very interesting learning about Square roots mod n, and it's nice to have a quick way to factor n. I know that this will help in RSA when n is a very large number made up of two large primes, and so it's all very helpful!

Sec 3.12, 6.2, due OCt 13

1. The RSA attacks were really cool, although I did have a little trouble understand a few of them. I thought that the timing attacks were really cool, but I didn't really understand it completely. I'll probably have to read over that again, but I thought that it was a great idea! Along with the rest of them!
2. I really liked continued fractions, I thought that they were really cool and interesting, and it was great that we had gone over them in class, because I felt like that helped me understand it a ton better! The attacks on RSA were really interesting too! I don't know how some people come up with this stuff, but they do, and it fascinates me!

?? Due Oct 12th

There were no reading assignments given for tomorrow on the website... I'm hoping that it's because your wife had the baby, and if so, CONGRATULATIONS!!!! I'm so happy for you!! I guess I'll find out tomorrow :) Have a good night

Sec 6.1, due Oct 9th

1. It actually took me a little while to really understand this, and I'll probably still need to go over the example so that I can understand it more. I also need a little more help understanding Claim 2.
2. I think that the RSA algorithm is actually really cool! I mean what a good idea! It took me a little while to understand it, but once I read the examples and stuff, it was a lot easier to understand. I also think that Claim 1 is really cool too! Also, PGP seems interesting, and it's a funny name, so it'd be fun to learn more about that.

Sec 3.6-3.7, due Oct 7th

1. The most difficult part of these sections for me was section 3.6.1. When they describe a public channel example with a mathematical realization. I understand the previous example of a public channel (the non-mathematical way :)) but I don't quite understand the mathematical way and the steps 1-5. So maybe if we could go over that more in class I'd understand it better.
2. I really enjoyed these 2 sections. I'm very glad that we were able to go over some of it in class before I read it, because it helped me understand what I was reading a lot better! There are still a couple of examples I wouldn't mind seeing again, but it really helped! I also think primitive roots are really cool. Either I learned about them before and forgot or something, but I think that they are very interesting and helpful! Of course I also like Fermat's Little Theorem and Euler's ?F-unction. All in all, great sections, very helpful to have gone over some of it in class before I read! :)

Sec 3.4-3.5, due Oct 5th

1. I thought that these sections were both very interesting and cool. They will be extremely helpful when it comes to larger numbers; there are some really cool shortcuts! There were a couple things that I didn't understand, specifically the example on page 77 about the x^2=1 (mod 35) I just didn't understand how they got to the answers of 6,29, and 34, but I felt like I understood until then. I will read it again and write it out. The next example that I thought that I understood but didn't towards the end was the example on pg 79 with the modular exponentiation, I think that they're just doing it mod 789, but I didn't know if we were using a calculator here or this was all just coming from our heads, in that case it might take a little longer... I just wasn't sure.
2. Like I said before, these sections were really cool. I really liked how they gave us an opportunity for shortcuts when it came to larger numbers, and they are just really useful theorems and examples that will definitely come in use!

Test Sudy Questions, Due Oct 2nd

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

I think that the most important ideas and topics are the general ideas for each of the cryptography examples we have looked at. I also think that the Euclidean Algorithm, congruences, and finite fields are important as well. Basically everything, except the little tiny details that only apply to one problem at a time.

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

I expect a few ciphertexts, some computations, and maybe a TINY, LITTLE stuff about DES and AES :)

* What do you need to work on understanding better before the exam?

Understanding AES and DES, and refreshing my memory on the other things, even though I felt like I has a pretty good understanding of them, I could always use more practice. Hopefully we'll go over more of what's on the exam in class :)

Chapter 5, due Sept 30

1. I really enjoy learning about all of these things, although sometimes it is hard for me to wrap my brain around it. I think what I struggle the most with is that I don't think I could ever do one of these by hand, well I'm pretty dang sure that I can't. There are a lot of steps to it, and it's easy to mess up, whereas before I could do it and practice it, which helped me understand what I was doing better. I think that if I saw how to do this on the computer or something it would help me understand even more. Like the one-time pad, I understood how it worked and what it was, but I really got it when we were able to use Dr. Doud's website and actually crack a real one. So I think that if there is some sort of system we could use to crazk a real one, it would help out more. But I still like it all alot, and am very interested!
2. I really liked how we went over half of this in class before I read it. It really helped me understand what I was reading! On the other half, I will admit that I was a little lost in class with what we were doing at first, even though I understood what you were saying and as I watched you go throught the process, I just didn't know where it came from and now I do :) This DES and AES stuff is very interesting, and I thought it was cool how they held a competition to come up with something to replace DES.

Reading Assignment due Sept 28th

* How long have you spent on the homework assignments? Did lecture and the reading prepare you for them?

I spend like 2 to 4 hours on the homework. On the last homework assignment, I did like 3 of the encryptions by hand which took quite a while, until I found out that I was allowed to use the applets, so the last homework assignment was like 5 or 6 hours :) So yeah, it varies, but it's good. Of course the lecture and reading prepare me for my homework. I always have my notes open and helping me through the homework. I love the examples that we get in lecture and in the books, they're great!


* What have you liked or disliked about the class thus far? What contributes most to your learning?

I have LOVED the class so far! It's so much fun, and so interesting!! It's like the first class that I've really look forward to every day! I love the lectures and the fun thing we learn. It's been a little harder lately with the DES stuff, but I think that just because up to then I was able to do everything by hand and crack the ciphers quite quickly, and the DES stuff just seems like it takes a little more time and thought. THe lectures and the reading both contribute to my learning. If I understand the reading, then that helps me a lot and the lectures just add to my understanding of it. If I don't understand the reading, then I depend a lot on the lectures to help me understand and to see examples so that I can really get it down.


* What do you think would help you learn more effectively or make the class better for you?

I think everything is going great. I think that you're doing the best you can and that it can't get better. The thing that would probably make it better and more effective for me would be to re-read the reading if I don't understand it, and write down the examples and take notes while I'm reading. I should do that so that I understand the lecture better.

Sec 3.11, due Sept 25th

1. It was good for me to review fields. We're learning about them in my number theory class, and so it's cool that I can use that knowledge for two classes. The hardest thing for me to understand was probably section 3.11.2 about GF(2^8). I know that was probably the most important, but there were just a few things in there that I didn't quite understand. I could also use a review and some examples tomorrow in class about section 3.11.3, the LFSR sequences using fields. The only thing that isn't difficult for me to understand, but quite frustrating and long at times is polynomial division and finding the multiplicative inverses of polynomials, yeah that is not very fun. I had to do a few this last week in my number theory class, and they were frustrating, and annoying. :) So I hope we don't have to do any of those!
2. This section was really good. I like having a prior knowledge of fields from 371, and then just barely reviewing it in my other class, so hopefully I understand them ok, and can do well. It's nice how all my classes are offering things that I use in other classes, it helps me stay on top of things and not forget.

Sec 4.5-4.8, due Sept 23rd

1.The most difficult part of the reading for me was section 4.5, about the different modes of operation. It was just a lot to take in at once, and there were so many different equations and diagrams that I felt a little lost.
2. I really liked the other sections though! I thought the section about breaking DES was very interesting, and it fascinates me how long it lasted, like 20 years! And how we didn't break it until just a few years ago. I think it's really cool to have something like that around for so long. I also thought it was neat how they had competitions, and gave out prizes, and in return it helped them make their system stronger. I also thought that it was a great idea to double encrypt something, until I found out that it doesn't significantly raise the level of security, that's a bummer! I also was reminded of Birthday Attacks! I'm sure they just as exciting as they sound, so I can't wait to hear about them someday soon! I also found it interesting to read and learn about the one-way functions, and all that stuff about passwords and salt for computers and everything! It was very interesting to learn about!

Sec 4.1, 4.2, 4.4, due Sept 21st

1. The most difficult thing for me in these sections was probably the expander function, and then the DES algorithm. It was just a lot of information to take in and I think that I just need to see a few examples, but it was a little confusing.
2. I thought that these sections were really interesting! The DES algorithm seems really cool! I also really like block ciphers and am excited to learn more about them and get more practice in using them and breaking them :)

Sec 2.9-2.11, due Sept 18th

1. I had a hard time understanding the Linear Feedback Shift Register Sequences section, probably just because I need to read it again and really focus on understanding it. There were a lot of equations and matrices and stuff, so I should just read it again and try to focus harder, but I'll look forward to learning about it tomorrow in class, because I always understand better in class when you teach it :)
2. I think that the one time pads are really, really cool! It's cool to know that there something out there that is basically unbreakable, unless you screw up and use the key more than once :) I also thought that it was really cool how it was said that they used one time pads for secure communication between DC and Moscow during the Cold War! I also thought about how crazy the Pseudo-random Bit Generation section was, the values for x_j are so huge! Really neat! I love learning about this stuff!

Sec 3.8, 2.5-2.8, due Sept 16th

1. It was difficult at first to remember the matrix stuff, like how to find the determinant, and inverse of larger matrices, but after a couple examples I got it down! The next thing that I didn't really understand was on pg 32, when we're talking about ADFGX ciphers, and in the last paragraph it says that you label the columns on the matrix with the keyword and "put the result of the initial step into another matrix" Now I investigated what I thought the previous step was, but I still didn't really get it, I understand everything else, but just not that part... anyway. When you are doing an ADFGX cipher and put the rest of the letters in a 5x5 matrix, do you put the rest of the letters in any particular order? I guess I just didn't understand that part very well. I'm also glad that we don't have to worry about table 2.4 :)
2. These sections were all really cool! I loved learning about matrices again, and using them to encrypt and decrypt. I thought the Sherlock Holmes section was really fun to read and learn about! I was sad that that man Cubitt died though, that was sad. The Playfair cipher was really cool too, it was very interesting to learn about, and can't wait to see more examples. Block ciphers were really neat too! The more we learn and the more complex they get, the more nervous I get, cause I know you probably will give us some sort of ciphertext to crack, so I gotta make sure I understand it! :) Learning about Binary numbers was fun too! These were a lot of sections, but really interesting! :)

Sec 2.3, due Sept. 14th

1. The most difficult part of this section for me was on page 21, when it gives an explanation of why the procedure given earlier finds the key length. That just kinda got me a little confused, because I felt like I understood everything up until then. The other thing that was a little difficult was the second method to finding the key. Probably just because I was comfortable with the first method, and I didn't really want to pay attention and learn the second method even though it says that it's more efficient and accurate. So I'll probably just need to read through that a few more times, but I was content with finding the key using the first method.
2. I think that Vigenere Ciphers are really cool and interesting! It's so cool how they use vectors and different shift amounts and keys and stuff. This book keeps coming up with new ways to encrypt messages and it's so cool, especially when it uses math. I just am really interested in this stuff. I enjoy reading, and I can't wait to learn more!

Sec. 2.1-2.2, 2.4, Due Sept 11th

1. The most difficult thing for me was just working out the modular arithmetic to crack all the ciphers. It wasn't hard to understand, I mean I understand it, but it just took some remembering and a little bit of arithmetic to solve them. Very interesting though! They keep coming up with stuff that I never would've thought of! The other thing that I would've liked to have seen an example of was #4 on pg 16. So maybe we can do an example of that tomorrow or something :)
2. I thought all 3 of these sections were really cool! I love learning this stuff! It's like I actually enjoy reading this book.. crazy huh? :) I thought the shift ciphers were clever, and the affine ciphers were cool as well, just took a little more busy work with numbers. It was fun writing out the alphabet like it said to do, and then count the numbers and fill in the blanks for alpha and beta, and just work it all out. I also like the substitution cipher. That's what we've been dealing with mostly in class so far, and I like them a lot. I always do the frequency count, as well as if there are spaces, look at the smaller words and start from there. Using that chart and eliminating possibilites was cool. I liked that we were given the charts this time, cause I think it might take a little while to make those ourselves, but if you really needed to crack a code, it's not that bad! They were really fun chapters to read, and it was cool to see how math was related to the cryptography! (Now when some kid asks what modular arithmetic is good for in your next 371 class, you can tell him some cool stuff!)

Guest Speaker, due Sept. 11th

1. The most difficult thing for me to understand is why I didn't know about this stuff earlier! :) I think that was one of the coolest things I've ever learned about! At some times it was diificult to imagine how they came up with some of the things they did, they were so creative! Like George Q Cannon referring back to previous letters and the names in those letters! Genius! I just think it is so awesome, and I would really love to learn more about it! Another thing that was hard to think about was adults learning the deseret alphabet. I guess it might come more easily than I think, but either way, that alphabet was sweet looking!
2. OK, as stated before, learning that stuff was Saaaweeet!!! I loved it!!! Good call on bringing her in to lecture Dr. Jenkins! I have a new motivation and desire to learn this stuff! I loved learning all the different ways that the church members used ciphers and codes! I guess I should've thought that they needed to earlier, but I never thought of it. I can't wait to tell my husband about the crazy code names they used in the D&C and see if he knew that. (I like knowing things about the scriptures that he doesn't, cause he always knows everything!:)) I thought it was really cool/cute how the Kane's wrote letters using a cipher. I know it was probably important stuff and not cute romantic stuff, but I like to think that sometimes it was :) and it makes me want to make up a secret cipher for me and my husband and write cool letters! I never realized why Parley P. Pratt was killed, all because that stupid 1st husband of his wife killed him, that stinks! I wish that they could've got away and pulled everything off. And the last thing, (that I can think of) that I thought was cool, was the Larrabee's Cipher! That would be really fun to do! Make up some code word and then write it all out! I think this stuff is so fun and cool to learn about! Thanks for letting us do that!

Sec 3.2, 3.3, Due Sept 4th

1. The part that was a little more difficult for me to remember and learn again was the Division and fractions with congruences. I understand it, it just requires a little bit of busy work to do the extended EA, and plug stuff in, and find out what is the multiplicative inverse. So it all makes sense pretty much, it just took me a little while to remember and get it down. Also, the section about what if d > 1, it all makes since, but I just think that I'd like to see more examples. So yeah, mostly the division and fractions with congruence, I just need to practice a few examples to really get it down.
2. I really liked that we covered this stuff in 371, it helped me to be able to read it and remember the things that I had learned and go back and look at my homework and make sure that I really know the stuff. It took me a couple examples to remember the extended Euclidean Algorithm, but I remember it. I like all the Congruences and Modular arithmetic, I think that stuff is fun and interesting.

Sec. 1.1-1.2, 3.1, due Sept 2nd

1. The most difficult part of this reading assignment was just getting used to the language used in cryptography and trying to wrap my brain around it's concepts. For example, when I read about Public key communication, I was kind of confused trying to imagine what they were saying in a real life example, but when they gave us a nonmathematical example, it immediately made sense!
It also took me awhile to understand how they tried to explain the other way that you can find the gcd of two numbers. I don't know if it was just the wording of that paragraph (which is was I think) or what, but it took me a little while and I had to look at the examples. I think I understand it, it probably doesn't matter now, but I think I got it down. I just like the way we did it; using the Euclidean algorithm.
2. This stuff is soooo cool to learn about!! I actually enjoyed reading! :) I was wanting to know what a birthday attack was (cause it sounded fun, even though I'm sure it's not as exciting as it sounds). I thought that the one-time pad was really cool to learn about, and would love to learn more. I just didn't know what crazy stuff they had in cryptography, but I've always been fascinated and interested. I also thought it was really interesting to read about all the ways that we're kept safe online with our credit card numbers, digital signatures, and the section about games was pretty sweet too! I can't wait to learn about these things.

Questions, Due September 2

• What is your year in school and major?

I’m a senior this year, and I’m a math major.

• Which post-calculus math courses have you taken? (Use names or BYU course numbers.)

I have taken Math 113, 190, 343, 334, 214, 362, 371, and 315.

• Why are you taking this class? (Be specific.)

I’m taking this class because it looks like a fun class, I’m very interested in the subject of cryptography, and it is also for my major, and I’ve had you before Dr. Jenkins, and although very hard, you’re still a great and nice teacher J

• Do you have experience with Maple, Mathematica, SAGE, or another computer algebra system? Programming experience? How comfortable are you with using one of these programs to complete homework assignments?

I have no experience with these programs, but I’m eager to learn and hope that I can understand everything and be ok. I have no programming experience either, but I’m comfortable with using these things to do homework, as long as I can get help when I need it and be ok

• 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?

One professor that I really looked up to was Dr Dorff. He was very organized. He came to calss everyday prepared with the material we were covering that day, and he didn't go off track. He also made class fun and enjoyable, which I think is a necessity because it makes students want to come to class and learn. Another professor I had who I loved, but was not a very good teacher did not have any kind of schedule, we didn't know what homework we would have assigned until the day we learned that material, we didn't know when the tests would be, we didn't really know anything. He would teach the material, but one question from the class could get him off subject for the rest of the class period. It was not a very helpful class, and unfortunately for me it was one I really needed to understand.

• Write something interesting or unique about yourself.

I’m going to the BYU vs. OU game this weekend, and I’m really excited about that… but I guess that isn’t that unique…um, I have a freckle on the palm of my hand, that’s pretty unique I think.

• If you are unable to come to my scheduled office hours, what times would work for you? I can come to office hours this semester!! Yea!! Except on Wednesdays, then the mornings would work best.

Last Blog Ever!! Until Next Fall :)

Ok, so I went to Brian Conrey's lecture last tuesday on Riemann's Hypothesis. It was very interesting and it was fun. A few things that I learned were that Gauss's Guess was that the number(primes < x)~ x/ln(x), and that was also called the prime number theorem, and RH was that Gauss's conjecture is accurate to 1/2 the number of digits of n. He also found that there was a set of numbers intimately connected with the primes. These are the first 9 zeros. Also, the key to understanding the primes is to understand the zeta function. Whis I can't type out, because I don't know the right keys, but I know it. I also found out that my 315 teacher Dr. Li discovered that RH is true iff lambda is greater than or equal to zero. It was a fun and interesting lecture.

Ok, something that I would like to go over today would be anything from this last section of learning that we've been going over. Maybe 8.3 #14 again, that was rushed when I learned it, but if that won't be on the test then that's fine :)

8.5, due April 10th

1. Um... well I thought I understood most of this section, but maybe I didn't. I'll choose the one that I guess I understood the least...Ok well in theorem 8.4 I didn't remember what a Quaternion was, so maybe that might be nice to know, I suppose I could go look it up and probably will, but yeah I thought that I understood most because they were basically telling us what was isomorphic to what. Hmm, we'll see in class today!
2. Ok, so I started reading this section and it was so cool! They all of a sudden have all these shortcuts and theorems about stuff! This would've been nice to have known during some of the homework!! But it was so cool, I started reading and BOOM, there was a shortcut, I need to read ahead more often!! Oh, and Hahahaha, Corollary 8.31, thanks... that was our number 23 in our homework last time!! sheesh! I also like that it gave us a nice long list of what groups can be isomorphic to, that's very nice!

8.4, due April 8th

1. I think that theorem 8.25 was kind of confusing, it's basically the same as theorem 8.21 I think, but it was just a little tricky to me to think of the proof for theorem 8.25, who knows, I'll just read it some more.
2. I thought this was a neat section, and I felt like I remembered a lot of stuff that was in this section from other sections, and it was cool to learn about it in a different way!

8.3, due April 6th

1. I felt like I really understood this section, but if I had to choose something confusing and difficult for me to understand, it would probably be corollary 8.18. I always feel like I understand the theorems and stuff, but then I start the homework problems and I get lost, but we'll see what happens this time.
2 I really thought this section was cool. It was fun to learn about the Sylow theorems and it seemed like I understood the stuff! Plus the section was short and that is always a plus :)

8.2, due April 3rd

1. Wow, You were right! This is like the longest section on earth! :) There were a few confusing theorems such as lemma 8.6 and thm 8.10, they seemed the most difficult for me, but I'm sure you'll explain them well enough in class!
2. Although this section was long, it was pretty interesting. It's funny that there is a fundamental theorem of finite abelian groups. There seems to be a fundamental theorem for almost anything! And there were so many, I mean sooo many theorems and lemmas in this section, it was crazy!! But good :)

8.1, due April 1st

1. I don't really understand what they mean when they say that Gi is NOT a subgroup of the direct product G1 x G2 x...x Gn.... So yeah, that's kind of confusing to me. Also, the proof of Thm 8.1 is kinda really long and a little confusing. I'm sorry, it's just a rough day!
2. I do think it is all quite interesting however! Especially the things I think I understand, like the bolded words on p 245, and the other theorems. Yea for learning abou Group Theory!

7.10, due MArch 30th

1. Well, this was a pretty short section, but if I had to choose one of the more confusing things it would actually probably be Thm 7.52. So is it for any n as long as n is not equal to 4? that that s true for? And why not 4? Anyway, that was a little confusing.
2. This section was very interesting just like the ones before it. I like learning this new stuff and although it'll probably take a little while for me to get it down, I really like it.

7.9, due March 27

1. This section was pretty interesting, but I mostly had a hard time understanding the Alternating Groups and Lemma 7.49, those were what I had the most trouble with understanding.
2. This section was very interesting! It was like the first time that most everything was new to me and that we haven't previously gone over, so I'm excited!

Questions, Due March 25th

• What do you need to work on understanding better before the exam?

I need to work on a few things before the exam. I just want to go through every section and make sure that I understand everything in it and the examples. I guess one thing that I really need to focus on is section 9.4 since that's the section I didn't do homework for, and I probably need to learn that and really have that down as well.

• 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 Wednesday.

I would really like to see some "examples" problems. Like you know the 1st problem on the test is always for us to give examples, I would just like a lot of examples of the different kinds of groups you can have and stuff like that. I would also like any hard problems that might be on the test to be solved, and yeah :)

7.8, due March 23rd

1. The most difficult part of the section for me was the 3rd Isomorphism theorem and thm 7.44. I know that we learned the 3rd Iso Thm before for rings, but I think that it is just a little confusing, along with some parts of theorem 7.44. So I'm looking forward to class today so that I can understand these things and do well on the test :)
2. I liked this section because I could understand a lot of it, probably since we've gone over stuff just like it before, but for rings. I'm pretty sure that I like groups a lot better than rings.

7.7, due March 20

1. The thing that was most difficult for me to understand in this section was the last theorem, theorem 7.38. I understand what it is saying, I just kinda forgot what Z(G) meant, I know I will probably go look it up, I think it means the center, but I will have to double check. Also, will we have to find the center of the group in order to use this proof? It's not just given to us I don't think, right?
2. I kinda really liked this section because it mostly made sense, and it seemed like we could use a lot of the theorems as shortcuts without having to prove some big long thing.

7.6, due March 18

1. This section was very interesting, but there were a couple things that I didn't quite understand. The first thing is the bold sentence at the top pf page 212. After reading all the examples on the previous page, it did seem like when they say Na=aN implied that na=an for every n in N, but I guess that's not true. I read the other sentence below that one, but I don't like that it changed on me all of a sudden :) The other thing that was a little confusing was theorem 7.34. There are a lot of things that are equivalent to each other there, but I don't quite understand exactly what some of them are saying.
2. This section was interesting because we learned about Normal subgroups, and it's just funny to me as if we hadn't already been learning about normal groups, I guess that they're all abnormal before this secction. I also like that it has a lot of similarities to 7.5 and a lot of the other sections in the book.

7.5, due March 13

1. Ok, for some reason I thought this section was pretty understandable. The theorems weren't very difficult to understand, and I thought that they were pretty straight forward. One question I do have is about thm 7.29 and 7.30; I was wondering why 7.29 said just "every group" whereas 7.30 says "every group G" is there a difference there since they named the group or no? Just curious.
2. I really like the rest of this section because it was the first time that I kinda felt like I understood a lot of it and thought that it was pretty straight forward. I also think that these theorems are pretty cool and very convenient.

7.5, due March 13

1. The most difficult part for me in this section was Thm 7.25 For some reason it just didn't click for me and I need help understanding what it all means.
2. I of course like that we have dealt with congruence class 3 times now, and I hope that with my prior understanding that I can really understand what we're learning now with groups. I also like learning the new things in the section, even though I don't understand everything right away, I hope to better understand them after class tomorrow.

7.4, due March 11th

1. This section also contained a lot of new info even though we've gone over homo and isomorphisms before, there is a lot more to take in. There are a lot of new Thms and def. that I need to read a lot, and try to understand, but I think the most confusing one for me is Cayley's Thm, and since it's a "big name" theorem, I reckon I better know and understand it! So I'll be looking for to going over that in class!
2. Well clearly this section is helpful because we've gone over isomorphisms and homomorphisms time and time again, so if I dind't have the down before, I should surely have them down after going over them for the third or so time. Honestly, I kinda like iso- and homomorphisms, they make sense and they're pretty straight forward. The rest of the stuff is pretty interesting too, I just have to make sure that I understand them! :)

7.3, due March 9th

1. This section was pretty long if I do say so myself. Very interesting though! there were a few difficult parts for me to understand, including the center of a group and theorem 7.17. It's just a lot of new information to take in, and I just probably need to read it a few times through to really understand everything, and to try and retain all the info.
2. I thought this was a very interesting section, a lot of new definitons and theorems that we haven't seen before (like I mean we haven't seen stuff like that really before) SO I do think it is very interesting, I just need to read it again and again and make sure that I understand it!

7.2, due March 6th

1. Ok I really liked this section up to about Theorem 7.8, and then it got a little difficult for me to understand. So that and the corollary on page 178 is what I'll need to be listening especially to in class, so that I can understand it better.
2. I like that we finally have an inverse, yea! I know that sometimes we've written it before, but now I can write it with no problem! I also like that we've learned a lot of this stuff before, and that we're giving more properties to groups.

7.1, due March 4

1. Ok, there are a few difficult things about the rest of this section for me. The definitions on page 167 are a little hard for me to understand. On page 169, I'm confused when it says that "Under multiplication, a nonzero ring is NEVER a group," and then it says that certain subsets of a ring (which are still rings right, or no?) may be groups under multiplication.... I guess I just don't really understand that. Theorem 7.2 is actually a little confusing too, sheesh I'm just having a hard time tonight I guess! I think what I'm having a hard time with is that with groups we talk about the set of all things, right? Like in this theorem, it's the set of all units, not just one. I remember you talking about this on Monday, about how a subset or something is not just a part of the set, but it includes the whole thing, I can't remember exactly what we were talking about, I'll have to ask you. And ok, what's up with all the notation on page 170? I mean diamonds, really? Must we bring in more new terms?? Goodness gracious! I'm going to have to really get this down! I hope it's ok that I see you tomorrow most likely :)
2. I think a lot of this stuff is very interesting! I like learning this new material, but I get some of it, because some of it is similar to what we've learned already. Anyway, I think it is cool and interesting, and hope that I can understand all of it soon!

7.1, due March 2

1. The last example on page 163, that continues onto page 164 was kind of confusing to me when I read it, so I think I'll need a little help understanding that example better.
2. I like that a group has a lot of the same properties as a ring, and so it hopefully won't be too hard to remember what you need to test to see if something is a group or not. I also like permutations, I feel like I understand what those are and how to find them.

9.4, due February 27

1. This section wasn't so bad, I did get a little confused, however, on Lemma 9.29. I guess maybe the notation threw me off a bit, or maybe I just need to read it a few more times to understand it better. ALso, theorem 9.31 was a little confusing for me. I idn't really understand what it meant by F is a field of quotients, and then there is just a lot in that theorem to take in. ANyway, I'll just read them more and more and try to understand them.
2. I like how we're sticking with some of the same notation, like on the top of page 321, the equivalence class of (a,b) is a/b, kinda ilke the congruence classes of functions. Then other than that I like this section, because most of it I felt I understood, and that's always good!

Questions, Due February 25th

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

I think most of the topics that we have studied will be important for the test, and the general message of most the theorems, especially the ones given to us in class to study.

• What do you need to work on understanding better before the exam?

There are a few things that I need to brush up on and work on understanding before the exam. Mostly some of the theorems and the examples so that I can know what I should be looking for and doing for the test.

• 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 Wednesday.

Haha, how about problems 2, 6, 10, 13, and 15 from section 6.3... just kidding, unless you want to. :) I'll probably be up to your office anyway for help. Besides the ones I said already, I can't really think of one off the top of m head, but I'll be sure to have one for class.

6.3, due Feb 22

1. Ok, the most difficult part of this section for me was the theorems about something being maximal. I understand the definition of maximal, but then I just think I'm getting a little confused with the theorems. Like Thm 6.15, so I understand that if M is an ideal in a comm. ring R with identity, then M is maximal if R/M is a field. So going on to corollary 6.16, in a comm ring R with identity, evey maximal ideal is prime. So does that mean that whenever R/M is a field (along with the other condition) that M is always a maximal ideal, and it's prime?
2. I like that I've seen things in this section before, such as the definition of prime on p154, that is the same as the one we had in chapter 2 I think, so that's nice. It has been a pretty interesting section too, inda fun to read about.

6.2, due Feb 20th

1. The most difficult thing for me in this section was still probably the notation, just getting used to how everything is written, and telling myself that they're really not adding in a coset, and stuff like that. A few of the theorems were a little confusing at first , but I think I might understand them a bit. Theorem 6.2 is a little difficult for me to completely grasp, but I"m sure I should get it after class today.
2. I like that we're talking about homomorphisms and isomorphisms again, I understand things when they talk about that. I just still like how they continue to build on previous sections and add new knowledge to each section. I liked the definitions we learned in this section. I think I understand them, but we'll see in class today.

6.2, due February 18th

1. Ok, the book called it out on this one. Page 146, the definitions of addition and multiplication of cosets in R/I. I guess it might be one of those things that you just have to make yourself learn without understanding it completely. Like when the teacher says, "That's just how it is..." I understand it is the definition and everything, but I want to add the I's together and get 2 I's and multiply the other multiplication rule out... I guess it might be something that I just have to memorize and learn without really completely understanding. Along with that, I don't like that there are 3 entirely different meanings to the plus sign; plus is plus people! Anyway, I'm sure you'll explain it tomorrow and I'll get it!
2. I like how we've gone over all this stuff before except that now we're using ideals and hopefully I'll get used to that and understand it. I'll try to not read too far ahead, except for that I'm curious... So I will, I just won't tell you about it until Thursday night. :)

6.1, due February 17th

1. Well I guess that the most difficult part of this section for me was the definition of ideal. I know that this is what the entire section is on, and I think I understand what it means, but I'm not positive. Is it basically saying that it is a commutative subring of R except that the different elements, a,r, are from the 2 different rings I and R? I'm just a little hazy on it, but I think I will understand it if I go through it a few more times.
2. I really liked this section even though I didn't quite understand the first definition, because it is basically stuff that we've already gone over except with different rings. So hopefully after I understand exactly what an ideal is, it will all click even more!

5.3, due February 12th

1. The most difficult thing in this chapter for me was the definition of an extension field. And then that wasn't good that I didn't understand that definition because it was used in the rest of the theorems after that. So after class when we go over what it is, I'm sure I'll understand it a lot better and then be able to understand the rest of the other theorems more clearly.
2. The cool thing about this section is that it matches section 2.3, except for that we're dealing with functions. So hopefully with the prior knowledge of that previous section, I will be able to understand this section a little better

5.2, due February 11... My Birthday!!!!

1. The most difficult thing for me in this section is about the same thing as last section, I'm having a hard time getting used to the way we denote the congruence classes modulo p(x). Every time I read a theorem or a proof, I feel like I understand it until I see that symbol and my mind automatically tells me that we're dividing p(x). I know it's something that I just need to get used to and stop whining about, but it's giving me a hard time!
2. Like the other sections we've been discussing, I really like how we build on the previous information, and particularly on chapter 2 in this chapter. It boosts my confidence to read something that I've already done in the integers, and it helps me to think that I can understand it and do it with functions!

5.1, due February 9th

1. Luckily, this section seemed to be ok, since we've already had these theorems and corollaries in chapter 2. One thing that I don't quite understand why we do, and that I'll have to get used to is the way we denote the congruences classes modulo p(x) on p 122. I don't get why we denote it like that cause to me it looks like we're dividing the function by p(x). Anyway, that's what I don't really understand and am going to have t get used to
2. I really like how this is mostly like chapter 2, except that we're dealing with functions now, but it helps because I've already done stuff like this, so hopefully it won't be too bad.

4.5 & 4.6, due February 5th

1. First of all, anything with a name that looks like Einstein's name in it already turns me away from even trying to understand it! After last semester in Physical Science and the whole theory of relativity thing, I'm done with Einstein, or anything that looks like his name, even if it is Eisenstein. But honestly, that is probably what I don't understand in these two sections, it's confusing to me. But I'll keep reading it and looking at the examples until I figure it out!
2. I like learning new things, and these sections were pretty interesting! The irreducibility just keeps going and going! It's traveling into the rationals, reals, and now the complex numbers! Good stuff! I like how each section builds on the former, because it helps you learn and understand a little better.

4.4, due February 4th

1. I think I understood most of this section (of course I always think that until I start to do the homework :) ) but one thing I had a question about was on page 103 where it proves corollary 4.17 and then goes onto say how the converse is not always true except for degrees 2 & 3, I was wondering if those were the only 2 degrees for which the converse is true?
2. I really liked this section, because I feel like I know what we're talking about for the most part, roots! I knew how to find roots, and hopefully I still know how to find them. :) Anyway, I this section has been very interesting, and I'm eager to see how interesting I'll find the homework to be.... But I like that I'm understanding the remainder and factor theorems, along with most of the corollaries. I'll just have to see how the homework treats me, and what I can learn in class.

4.2 & 4.3, due February 2nd

1. For section 4.2, on part that I wasn't sure about was the bold sentence underneath the first example on page 90, where it talked about if f(x) divides g(x), then cf(x) also divides g(x) for each nonzero c contained in f. I was just wondering what c is. Is it any just any integer multiplied by f(x) like a coefficient, or does if have it have to be in f(x)? That was just a little confusing to me.
For section 4.3, at first I wasn't getting what they meant exactly by irreducible until I looked at the asterisk at the bottom of page 95, and then I realized that it's just another name for "prime," but that when using polynomials, we say irreducible, so that made a lot more sense. I think I just need to see some more examples to really understand everything in these 2 sections.
2. In section 4.2, I like how we are talking about the gcd again, except this time we're using functions, hopefully I will be able to understand it a little better since we've worked with the gcd before, same with the definition of relatively prime.
In section 4.2, I also like how we've dealt with things like this before, but now we're just using functions, I think I just need to see a few examples to understand these things better.

4.1, due January 29th

1. What I found difficult about this section was probably the bold rule at the bottom of page 84. It just seems confusing, I think I know what it means, like the number of the degree of f*g is less than or equal to the degree of both of them added, but I'm not sure. That was what I found most confusing.
2. I really like how we just keep building on what we've learned already. For example we are reintroduced to the Division Algorithm in this section. The theorem has changed a litttle, but it still has the same basics concepts. That helps me ot learn it if I 've already seen something like it before.

Questions, Due January 27th

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

I think the most important topics and theorems I'll need to study are the ones that we've really focused on, or mentioned that they were very important. Such as the Big name theorems, and other topics that we had a lot of homework problems over. I will probably study the big name theorems and their proofs, as well as other topics that we spent a lot of time on, and I'll probably go over my homework assignments and make sure I understand as much as I can!

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

I expect to see all type A problems on the exam, in fact maybe even just the question, "What is your name?" will be good enough! :) 100% for everyone!! Ok, well back to reality here, I think that there will be maybe one or two type A questions, the majority will be type B, and then a couple type C. Maybe even some proving of the big name theorems, and I'm hoping a lot of problems like we had in the homework! :) But I guess we will wait and see!

Questions, due January 26th

• How long have you spent on the homework assignments?
  

So far I've spent anywhere from an hour to probably 2.5 hours on the homework.

• Did lecture and the reading prepare you for them?

Of course the reading and lecture prepared me for them, they're always VERY helpful!

• What have you liked or disliked about the class thus far?
  

I like the having to read part, even though I almost forget every other night, but it really does help me understand the material a lot faster. I dislike it when I don't understand something.

• What contributes most to your learning?

Reading and the lectures, along with doing the homework, so I guess everything :)

• What do you think would help you learn more effectively or make the class better for you?

Just continue to do the readings and I love as many examples of homework and proofs as I can get, they help me understand the different way I can do things and the different problems I'll encounter.

3.3, due January 22

1. Ok, I think I kinda get this stuff. I've learned about functions being isomorphic before, so I kind of understood that a little bit; however, maybe it was a different definition because I don't remember the 3 rules that it must satisfy in order to be isomorphic. But anyway, on p. 75, in the paragraph before the first example it talks about how it is also important to show that something is not isomorphic. Then it says to do this you must show that there is no possible function from one to the other satisfying the 3 conditions. I guess I just didn't understand the way this was worded. In order to show that something is not isomorphic, don't you just have to show that one of the conditions fail? Anyway, I think I'll just need to practice with these to really get them down, but I'm pretty sure I understand the general idea.
2. Well I think it is cool how other math classes relate to each other. If what I learned in one of my math classes last year about isomorphism was the same as what I'm learning now, then it's so good, cause I've done some of it before. I also like that if something is isomorphic it is also homomorphic, that'll save some time if we're ever asked to show both. Well, I hope that I understand everything, I'll just need practice, like always! :)

3.2, due January 20th

1. I'm pretty sure that I understood most of the material covered in this section; however, a few of the examples had me confused about the previous definitions. One of the examples that for some reason I didn't understand, was the example right after the definition of a multiplicative inverse. It talks about Z10, and I understand everything up to when it talks about the inverse of 7, and that it is equal to 3, and vice versa. Is it saying that 1/7 in Z10 =3? Because I guess I just don't understand that, but I'm sure I will after an easily explained example by you, and then I'll feel stupid :) That was mostly the thing I didn't understand very well in this section. As for the new theorems and things, I'll just have to study them, and make sure I truly understand them really well.
2. I really like how each section continues to build on the previous one. I know that is probably what they're supposed to do, but it really helps me to understand the new material, when we continue to use the other stuff that I just learned. It's also good that we keep working with these axioms: addition, multiplication, and now adding on subtraction. So, so far I enjoy everything, I hope to continue to understand and like the things I'm learning, but it has been very interesting and it has helped me to learn the material so much better when I read the sections like this!

3.1, due January 15th

1. This section definitely had a lot of information to cover; however, I think I understood most of it, especially since a lot of it dealt with the addition and multiplication axioms that we having been working with in the other sections, and even in my other math class. There were a few difficult parts for me though. Like the 5th example on p 43, I don't understand that, but then again, I seem to have a hard time with switching from something I'm so used to and understand, like numbers, to something new and vague, like variables. Anyway, that was one thing that I didn't quite get, but I'm sure if I just read it some more I will understand it. Other than that, I think I understand the rest, but there is a lot of information, and with new notation and new definitions to add to my vocabulary, it should be quite interesting, and I hope to be able to grasp the concepts that I need to.
2. The thing I liked about this section was that we're dealing with matrices. I really like matrices, and I hope that I continue to like them after this class :) (jk). I also like the fact that we continued to work with the addition and multiplication axioms, it is helping me understand it in both of my math classes. Anyway, I've never learned about rings before, I think, and I'm excited to learn about them and hope I can understand everything I need to know!

2.3, due January 13th

1. This section was actually kind of confusing for me. I'm sure if I read it more, (which I probably will), that I would begin to understand it better. The first thing that I didn't understand was Theorem 2.8 where it says that if p>1 is an integer, then the following things must be true. The fist thing is that p is prime. I don't understand why p has to be prime, for any p>1. Maybe I'm just reading it wrong, but I don't really understand that part. The rest of it, I think I understand, but I was just a little confused on that.
2. This section is actually pretty helpful, because it builds on every thing we've learned so far, and so it's not too hard to understand. I'm hoping that once I understand the few things I was confused about, that I should be able to understand everything pretty well so far. I really enjoy learning about these sections, because to me they're quite interesting! Also, please forgive me for doing this early in the morning before class! I was up late doing homework, and I fell asleep doing my homework. I promise it won't happen again! :)

2.2, due on January 11th

1. The most difficult part of this section for me was probably the transition from writing the congruence classes with brackets around them to writing them without brackets. Simply because I feel like I'll get confused if I'm using real integers and congruence classes at the same time, but maybe you go back to the brackets if you are to avoid confusion. The other thing I found confusing was the Warning at the end of the chapter which said that exponents are ordinary integers-- not elements of Zn. I guess what I don't understand is what they're saying. I understand that 2^4 does not equal 2^1, but that 4=1 in Z3, but I guess I just don't get why they gave us an example of this. Are they just saying that the 4 in 2^4 is just an integer, not a congruence class? Cause that makes sense, I'd never think of it differently, that maybe why I'm confused on why they gave an example of that. Anyway, everything else seemed to be fine, just the transition and the warning.
2. The cool thing that I like about this section, is that theorem 2.6 and 2.7 will help me remember what I'm learning in my 315 class, because in that class we're learning about the ordered sets and the addition and multiplication axioms that apply to them. They're basically the same rules, and so that is really nice because I'll be learning them in 2 different classes, and hopefully be able to remember it better. Overall, I thought this was a very good section, I like learning about Modular arithmetic and congruence classes.

2.1, due on January 8th

1. The most difficult part of the material for me was corollary 2.4. I understand most everything up to that pretty well, but what does it mean by "disjoint"? Does it mean that the two congruence classes have nothing in common? So does the corollary say that two congruence classes mod n have to either have nothing in common or everything in common, meaning identical. I suppose if I thought about it enough I would understand it better. In fact simply asking the question to myself is helping me grasp a little better of an understanding. So, I think I mostly understand everything else, just corollary 2.4 and then sentence about it are a little fuzzy to me.
2. The most interesting thing to me is that when you have a congruence class mod 3, for example, there will be a lot of the classes that are equal. I missed that on a test last year without realizing that half of my congruence classes had the same numbers in it :) But now it makes a lot more sense to me, and I think that is pretty cool. I also think that the equivalence relations that the congruence classes can possess such as reflexive, symmetric, and transitive will be very helpful knowledge while dealing with this chapter. I know we used that information a lot in Math 190 to prove things, so I'm eager to see how much and in what ways we will use it again. Overall, I thought this section was very interesting and I learned a lot. I know I'll understand the things I didn't understand after tomorrow's lecture. I look forward to meeting you for the first time tomorrow!

1.1-1.3, due on January 7th

1. As I read sections 1.1-1.3, I felt like I understood most of the material. However, for some reason there is one sentence of a theorem that I don't quite understand. I've read it over and over again, but I guess my brain just isn't clicking. It's probably a really stupid question, but what does it mean in Theorem 1.3 when it says, "Furthermore, d is the smallest positive integer that can be written in the form au + bv." I understand that d is the GCD, but I don't get what it means when it says it is the smallest positive integer that can be written in that form. For example, if d is the GCD, then can there be a number greater than d that can be written in the form of that equation? If so, I don't understand that. Also, corresponding with that, since I guess there CAN BE a number other than the GCD that can be written in the form of that equation, then what is it? I bet these are all stupid questions and obvious, but I don't get it right now. Because right after that theorem it gives us a warning that the fact that d= au + bv does NOT imply that d=(a,b) (or in other words is the GCD), then what else can d be? If d is the greatest common divisor between any two numbers, then what number can be greater than d and also satisfy the linear combination equation? Anyway, Sorry if this is confusing, I'm confused. Maybe we can meet and I can better explain what I mean.
2. I found most everything in this chapter to be pretty interesting. I really liked the little short cuts we were taught to make things like finding the GCD a lot easier than finding all the divisors of each number, especially with some of the numbers we were given in the homework including (12378, 3054). That only took like 6 lines to find the GCD. I also found theorem 1.10 interesting. For some reason I had never thought of that before, or for a long while, that ever integer except 0 and +/- 1, is the product of primes. I don't know why I found that so cool but I did. Along with some other vocab words I added to my vocabulary, and a few theorems that I thought were pretty cool, this chapter was very interesting, and I know will help me in my career interests of being a teacher in that I can use these nifty shortcuts to save time and teach others. It was a great chapter to start with! I'm afraid though that there will be a lot more added to the first question as the semester progresses :)

Sec. 2 Introduction, due on January 7

What is your year in school and major? I am a Junior majoring in Mathematics

Which post-calculus math courses have you taken? I have taken Math 113, 190, 343, 334, 214, and 362.

Why are you taking this class? I am taking this class because it is a requirement for my major. I also have heard that it is a really good class and very interesting.

Tell me about the math professor or teacher you have had who was the most and/or least effective. The most effective math teachers I have had are very organized, with a set schedule, and they lecture about the material in the book that we have homework in, or that is on the test. The least effective teachers I have had are unorganized, no set schedule, go off on tangents, and do not lecture on useful material, which I feel is a waste of my time.

What did s/he do that worked so well/poorly? One professor that I really looked up to was Dr Dorff, he was very organized. He came to calss everyday prepared with the material we were covering that day, and he didn't go off track. He also made class fun and enjoyable, which I think is a necessity because it makes students want to come to class and learn. Another professor I had who I loved, but was not a very good teacher did not have any kind of schedule, we didn't know what homework we would have assigned until the day we learned that material, we didn't know when the tests would be, we didn't really know anything. He would teach the material, but one question from the class could get him off subject for the rest of the class period. It was not a very helpful class, and unfortunately for me it was one I really needed to understand.

Write something interesting or unique about yourself. I was born and raised in Broken Arrow, Oklahoma. I played volleyball for 5 years, even though I'm short, (I'm a good Libero). I love the outdoors, and I have a freckle on the palm of my right hand.

If you are unable to come to my scheduled office hours, what times would work for you? I am actually unable to come to the office hours, because I have a class immediately after this class. The best hours that would work for me would be either in the mornings on Tues and Thurs, like 8am, (I don't know if you'd want to come to school that early), or in the afternoons on Tuesday and Friday like around 4 or 5, which I don't think you'd want to stay that late. I'm sorry my schedule is so complicated. I work 25 hours a week, but I'm sure I could make some arrangments to make an appointment with you when I need to. Thanks!