1. What was the most difficult part of the reading for you
Well, the reading was short, so I'll make this short. I kind of got lost reading about the RSA Algorithm. I just got lost in the math of it all... with choosing the primes and the e and the... everything. Mostly I felt confused about that, but that could be because I'm just kind of tired....
2. What was the most interesting part of the reading for you?
The most interesting part of the reading for me was reading about the one-way function/authentication stuff. I mostly thought that was interesting because I was trying to figure out how two functions could be public knowledge, and you'd still be able to encrypt/decrypt something. Then, on top of that, to add the "Authentication" seemed kind of genius to me.
Tuesday, November 29, 2011
Saturday, November 26, 2011
Section 5.4-5.4.1, Due on November 28, 2011
1. What was the hardest part of the reading for you?
I felt like this reading was very straight forward. If I had to pick a "hardest thing" it would probably be the trying to remember the linear algebra stuff with matrices. It was just kind of a trip to remember determinants and inverses and all of that kind of stuff. I know it's lame, and not much to go on, but I really didn't have any problem with this reading.... so that was a good thing, I guess.
2. What was the most interesting part of the reading for you?
Well, I'm sure that in the world today we've moved beyond using the simple encryption codes discussed in this section. However, I am kind of a war-movie junkie, and I was incredibly interested to see the roots of coding and to see how messages we most likely coded during early wars. So I think that was cool to read about.
I felt like this reading was very straight forward. If I had to pick a "hardest thing" it would probably be the trying to remember the linear algebra stuff with matrices. It was just kind of a trip to remember determinants and inverses and all of that kind of stuff. I know it's lame, and not much to go on, but I really didn't have any problem with this reading.... so that was a good thing, I guess.
2. What was the most interesting part of the reading for you?
Well, I'm sure that in the world today we've moved beyond using the simple encryption codes discussed in this section. However, I am kind of a war-movie junkie, and I was incredibly interested to see the roots of coding and to see how messages we most likely coded during early wars. So I think that was cool to read about.
Monday, November 21, 2011
Section 5.3.2, Due on November 22, 2011
1. What was the most difficult part of the reading for you?
Um... I think this will be easy enough. The proof of Theorem 5.3.3.2 (Lucas-Lehmer Test) was the most difficult part of the reading for me. That thing was SO LONG!!!! (... to me...) I'm sure it makes sense to someone somewhere... but for me it just looks like a confusing mess.
2. What was the most interesting part of the reading for you?
I guess, as we've been in these last sections, the things that are most interesting to me are the things that are so modern. I feel like there is some exponential correlation between the year these things were discovered and how difficult they are to comprehend. But, not only that, but I think that it is interesting to view the field of mathematics these days. For example, take a look at the Mersene primes. It almost seems that to be an accomplished mathematician these days, you need to have some sort of computer programing experience. It almost feels like all "Paper and pencil" discoveries are over (obviously, any sort of new proof must be written by someone, and that can't really be done with a computer) and the implementation of new mathematical discoveries (like new Mersene primes) are done by computer programs. We have only to run the programs and wait for the next big discovery. That, to me, is so interesting.
Um... I think this will be easy enough. The proof of Theorem 5.3.3.2 (Lucas-Lehmer Test) was the most difficult part of the reading for me. That thing was SO LONG!!!! (... to me...) I'm sure it makes sense to someone somewhere... but for me it just looks like a confusing mess.
2. What was the most interesting part of the reading for you?
I guess, as we've been in these last sections, the things that are most interesting to me are the things that are so modern. I feel like there is some exponential correlation between the year these things were discovered and how difficult they are to comprehend. But, not only that, but I think that it is interesting to view the field of mathematics these days. For example, take a look at the Mersene primes. It almost seems that to be an accomplished mathematician these days, you need to have some sort of computer programing experience. It almost feels like all "Paper and pencil" discoveries are over (obviously, any sort of new proof must be written by someone, and that can't really be done with a computer) and the implementation of new mathematical discoveries (like new Mersene primes) are done by computer programs. We have only to run the programs and wait for the next big discovery. That, to me, is so interesting.
Sunday, November 20, 2011
Section 5.3.1, Due November 21, 2011
1. What was the most difficult part of the reading for you?
Well.... Hm... That's a tricky question. I feel like there was so much information packed into this section that I'd struggle to recall most of it. I got the basics for the base stuff and maybe the Carmichael (?) stuff, but after that, as I was reading, I felt like the section was just rambling off information I wasn't ready to handle. Even during the Carmichael stuff, the whole time I was reading it, I thought "Can you just give me an example of what you are talking about?!?" ...Then the did, and I still didn't feel that much clarification from their example. So, I guess that though I didn't grasp the second test they discussed at all, I most struggled with the Carmichael stuff.
2. What was the most interesting part of the reading for you?
I guess that when we were discussing Quadratic Reciprocity and Jacobi Symbols forever ago (which, truthfully, I'm still struggling to fully understand) I felt like the Jacobi Symbol stuff was so far away and that we'd never reach that section. And, in turn, that was my personal excuse as to why I didn't fully understand it. However, here we are, now reading about the Jacobi Symbols and I am still a little fuzzy about them. I guess that excuse has died down. So, hopefully, if I'm not too busy playing the new Zelda game today, I'll revisit Quadratic Reciprocity and Jacobi Symbols, and hope that helps me out a little bit.
Well.... Hm... That's a tricky question. I feel like there was so much information packed into this section that I'd struggle to recall most of it. I got the basics for the base stuff and maybe the Carmichael (?) stuff, but after that, as I was reading, I felt like the section was just rambling off information I wasn't ready to handle. Even during the Carmichael stuff, the whole time I was reading it, I thought "Can you just give me an example of what you are talking about?!?" ...Then the did, and I still didn't feel that much clarification from their example. So, I guess that though I didn't grasp the second test they discussed at all, I most struggled with the Carmichael stuff.
2. What was the most interesting part of the reading for you?
I guess that when we were discussing Quadratic Reciprocity and Jacobi Symbols forever ago (which, truthfully, I'm still struggling to fully understand) I felt like the Jacobi Symbol stuff was so far away and that we'd never reach that section. And, in turn, that was my personal excuse as to why I didn't fully understand it. However, here we are, now reading about the Jacobi Symbols and I am still a little fuzzy about them. I guess that excuse has died down. So, hopefully, if I'm not too busy playing the new Zelda game today, I'll revisit Quadratic Reciprocity and Jacobi Symbols, and hope that helps me out a little bit.
Wednesday, November 16, 2011
Section 5.3, Due November 18, 2011
1. What was the most difficult part of the reading for you?
I'm sure that you'd expect that I'd get lost at some point... so I'll just say when. I started getting lost during Theorem 5.3.3 (Mostly, I got confused about part (2). But, I'm assuming it's because I need to review that malarky.
After that, I got completely totally completely lost as they started bringing up the AKS algorithm. I mean.... what? It was so so so oh so confusing for me. I'm guessing (hoping) it's because it's so new and stuff. I mean... wow.
2. What was the most interesting part of the reading for you?
Though the part where I got lost made me want to cry, it also fascinated me that something that seems pretty important in the mathematical world has been proven post-2000. Not only that, but it even made it into this crazy book. So, I think that's cool and I want to know how much money that they made for deriving this algorithm.
I'm sure that you'd expect that I'd get lost at some point... so I'll just say when. I started getting lost during Theorem 5.3.3 (Mostly, I got confused about part (2). But, I'm assuming it's because I need to review that malarky.
After that, I got completely totally completely lost as they started bringing up the AKS algorithm. I mean.... what? It was so so so oh so confusing for me. I'm guessing (hoping) it's because it's so new and stuff. I mean... wow.
2. What was the most interesting part of the reading for you?
Though the part where I got lost made me want to cry, it also fascinated me that something that seems pretty important in the mathematical world has been proven post-2000. Not only that, but it even made it into this crazy book. So, I think that's cool and I want to know how much money that they made for deriving this algorithm.
Tuesday, November 15, 2011
Section 5.1-5.2 pg 202, Due November 16, 2011
1. What was the most difficult part of the reading for you?
Well, it must be time to start a new chapter. This reading wasn't too bad. In fact, and don't tell anybody, it was almost kind of enjoyable. However, I did get a little lost in the Proof of theorem 5.2.1. I mostly think that's just because I'm struggling with the floor function of that proof. I think I just need it verbalized to me. Then, I don't really remember what a kernel is (I remember learning about it, and I think it has something to do with mapping things to zero), so I didn't quite follow the "Square-free kernel of m" stuff.
2. What was the most interesting part of the reading for you?
Well, like I said, I found this reading kind of enjoyable. I think that's just because I had already learned about this technique (the Sieve stuff) in my "History of Math" class a few years ago. So, sometimes when I've tone this homework and I wasn't near a computer to google prime numbers, I'd use this technique to figure out if a number is prime or not. So... That's what I found interesting about it.
Well, it must be time to start a new chapter. This reading wasn't too bad. In fact, and don't tell anybody, it was almost kind of enjoyable. However, I did get a little lost in the Proof of theorem 5.2.1. I mostly think that's just because I'm struggling with the floor function of that proof. I think I just need it verbalized to me. Then, I don't really remember what a kernel is (I remember learning about it, and I think it has something to do with mapping things to zero), so I didn't quite follow the "Square-free kernel of m" stuff.
2. What was the most interesting part of the reading for you?
Well, like I said, I found this reading kind of enjoyable. I think that's just because I had already learned about this technique (the Sieve stuff) in my "History of Math" class a few years ago. So, sometimes when I've tone this homework and I wasn't near a computer to google prime numbers, I'd use this technique to figure out if a number is prime or not. So... That's what I found interesting about it.
Thursday, November 10, 2011
Midterm 2 Study Prep - For Real This Time
(First of all, I'd like to apologize again for doing this last week. Second of all, I'd like to really thank you for helping me yesterday via e-mail with those questions. You really helped a lot. The second I read your hint about number 4, I was so embarrassed because I knew exactly what to do... I think my brain is just fried because, believe it or not, I've been studying/preparing for this test all week. I've typed up a study guide from everything you listed on your study guide (don't worry, I know it's not exhaustive) but I thought that might be a good place to start. So... without much further ado, let's get started.)
1. Which topics and theorems do you think are the most important out of those we have studied?
It seems to me that the theme of this exam, as I said last week, would be prime numbers. Specifically, the infinitude of primes. It seems that everything we have done this section has come back around to proving that there are an infinite number of primes.
2. What kinds of questions do you expect to see on the exam?
You know, I really am not sure. Mostly I'm scared. Hopefully we'll see some very similar to the ones on the homework (at least, the questions on the homework assignments that I completed successfully... So just look up my grade and don't ask anything from any of the assignments where I have a zero.)
3. What do you need to work on understanding better before the exam? Come up with a mathematical question you would like to see answered or a problem you would like to see worked out in class on Friday.
Characters. Characters. Characters. I'm really praying that you don't put much emphasis on them. They are the bane of my existence. But, I'm guessing they'll be somewhere on the test. So, I really need to work on those. I'm still not sure that I understand EXACTLY what the Method of Infinite Descent is. I skimmed over the section that you recommended, but I probably need to READ it very closely and slowly. However, of everything listed on the study guide, I have been unable to find (I could probably figure it out, after some more studying) in the book, or in my notes, the proof of the second part of the Orthogonality Relations II. I'm just really nervous because it seems that that is one of the proofs that we need to be able to prove, and I don't want to mess this one up. Stupid characters.
4. Are there topics you are especially interested in studying during the rest of the semester? What are they?
I say this with no desire for offense at all. I doubt you'd take any, but I'll just warn you. But, when I was deciding to take this class, graph theory, or combinatorix (?) for my math ed major, I really really wanted to take combinatorix (?) because I'm so interested in that stuff. But, I was nervous that I wouldn't get in, and I wanted my last semester here (wahoo!!!) to be lighter than the rest. So I settled (I know, I'm so mean) for Number Theory. I know I could take combinatorix next semester, but that would require extra money and time I don't have. So I would love to see some more of that. But, I also know that isn't what this class is for. So, I'll try to get over it.
1. Which topics and theorems do you think are the most important out of those we have studied?
It seems to me that the theme of this exam, as I said last week, would be prime numbers. Specifically, the infinitude of primes. It seems that everything we have done this section has come back around to proving that there are an infinite number of primes.
2. What kinds of questions do you expect to see on the exam?
You know, I really am not sure. Mostly I'm scared. Hopefully we'll see some very similar to the ones on the homework (at least, the questions on the homework assignments that I completed successfully... So just look up my grade and don't ask anything from any of the assignments where I have a zero.)
3. What do you need to work on understanding better before the exam? Come up with a mathematical question you would like to see answered or a problem you would like to see worked out in class on Friday.
Characters. Characters. Characters. I'm really praying that you don't put much emphasis on them. They are the bane of my existence. But, I'm guessing they'll be somewhere on the test. So, I really need to work on those. I'm still not sure that I understand EXACTLY what the Method of Infinite Descent is. I skimmed over the section that you recommended, but I probably need to READ it very closely and slowly. However, of everything listed on the study guide, I have been unable to find (I could probably figure it out, after some more studying) in the book, or in my notes, the proof of the second part of the Orthogonality Relations II. I'm just really nervous because it seems that that is one of the proofs that we need to be able to prove, and I don't want to mess this one up. Stupid characters.
4. Are there topics you are especially interested in studying during the rest of the semester? What are they?
I say this with no desire for offense at all. I doubt you'd take any, but I'll just warn you. But, when I was deciding to take this class, graph theory, or combinatorix (?) for my math ed major, I really really wanted to take combinatorix (?) because I'm so interested in that stuff. But, I was nervous that I wouldn't get in, and I wanted my last semester here (wahoo!!!) to be lighter than the rest. So I settled (I know, I'm so mean) for Number Theory. I know I could take combinatorix next semester, but that would require extra money and time I don't have. So I would love to see some more of that. But, I also know that isn't what this class is for. So, I'll try to get over it.
Subscribe to:
Posts (Atom)