1. Which topics and theorems do you think are the most important out of those we have studied?
It seems to me, and this probably isn't a surprise at all, but I think the big ideas here are: primes. Both the number of primes, and whether a number is prime or not. So, it seems that if I can figure out if a number is prime or not, and how many primes are less than it (or relatively prime) or to be able to prove there are infinite primes, I should be in okay shape.
2. What kinds of questions do you expect to see on the exam?
Again, I expect to see questions really similar to those questions we have seen in homework. Assuming that the final is slightly weighted more towards the material we've covered since the second midterm, I should expect to use different algorithms to show that a number is either prime or composite. I also expect some type of cryptography, as well as some elliptic curve stuff.
3. What do you need to work on understanding better before the exam? Come up with a mathematical question you would like to see answered or a problem you would like to see worked out.
Well, I would really like to see number 1 of the last homework assignment worked out. I do not understand the p-1 algorithm at all, and I'm nervous about that.
I also need to work on remembering the names and steps of each primality test. They are all a jumbled mess in my head.
Tuesday, December 6, 2011
Sunday, December 4, 2011
Section 6.3, Due on December 5, 2011
1. What was the most difficult part of the reading for you?
Well, again, there were many things that were difficult. And, admittedly, I'm pretty tired, so I may have missed something. But, specifically I have a question about one thing. I felt like I understood "B-Power Smooth" from the first part of this section... But where I got confused was trying to tell if numbers were B-Power Smooth later on. I mean, from what I understand of the definition of B-Power smooth, it seems like everything is B-Power Smooth to some B... So why is it that in the later parts of this section they'd say that a number "Isn't B-Power Smooth"? Again, I probably just read over what they're saying there, but that's something that confused me.
2. What was the most interesting part of the reading for you?
I know this is going to sound a little lame (I can't help it... I didn't fully understand the reading... so sometimes I have to make stuff up to be interesting) and though I really don't understand this part, I think it's interesting that they can use these elliptic curves to factor big numbers. Seriously, after class I was feeling pretty good and exited about this elliptic curve business, so I'm excited to see what light you'll shed on that subject in class.
Well, again, there were many things that were difficult. And, admittedly, I'm pretty tired, so I may have missed something. But, specifically I have a question about one thing. I felt like I understood "B-Power Smooth" from the first part of this section... But where I got confused was trying to tell if numbers were B-Power Smooth later on. I mean, from what I understand of the definition of B-Power smooth, it seems like everything is B-Power Smooth to some B... So why is it that in the later parts of this section they'd say that a number "Isn't B-Power Smooth"? Again, I probably just read over what they're saying there, but that's something that confused me.
2. What was the most interesting part of the reading for you?
I know this is going to sound a little lame (I can't help it... I didn't fully understand the reading... so sometimes I have to make stuff up to be interesting) and though I really don't understand this part, I think it's interesting that they can use these elliptic curves to factor big numbers. Seriously, after class I was feeling pretty good and exited about this elliptic curve business, so I'm excited to see what light you'll shed on that subject in class.
Thursday, December 1, 2011
Section 6.1-6.2, Due December 2, 2011
1. What was the most difficult part of the reading for you?
Um... Let's blame my confusion on the fact that this is a new book with a new style that feels like a new language being spoken. Yes. Let's blame it on that. I'm still pretty confused about what Elliptical Curves are... but beyond that, I'm confused about what in the world this "Sage" business is. I mean.... what in the world is that? It kind of reminded me of playing Zelda and "Sage" is that annoying helper that beeps and tells you what to do every step of the way... only in this book, since I don't even know what "Sage" is, it's not very helpful to me. But, ignoring the weird Sage business, I didn't understand the condition of -16(4a^3+27b^2) not equaling zero. Also, I didn't understand how figure 6.2 is an elliptic curve... It just looks like dots to me.
2. What was the most interesting part of the reading for you?
Well, I really didn't understand much of what I read... so there wasn't much. I guess that if I had to pick something that caught my eye it would be what the very first paragraph says: It talks about putting keys on stamps and making them short and how these curves help with encryptions... Wow.... I guess it's going to be cool when I understand it...
Um... Let's blame my confusion on the fact that this is a new book with a new style that feels like a new language being spoken. Yes. Let's blame it on that. I'm still pretty confused about what Elliptical Curves are... but beyond that, I'm confused about what in the world this "Sage" business is. I mean.... what in the world is that? It kind of reminded me of playing Zelda and "Sage" is that annoying helper that beeps and tells you what to do every step of the way... only in this book, since I don't even know what "Sage" is, it's not very helpful to me. But, ignoring the weird Sage business, I didn't understand the condition of -16(4a^3+27b^2) not equaling zero. Also, I didn't understand how figure 6.2 is an elliptic curve... It just looks like dots to me.
2. What was the most interesting part of the reading for you?
Well, I really didn't understand much of what I read... so there wasn't much. I guess that if I had to pick something that caught my eye it would be what the very first paragraph says: It talks about putting keys on stamps and making them short and how these curves help with encryptions... Wow.... I guess it's going to be cool when I understand it...
Tuesday, November 29, 2011
Section 5.4.2, Due on November 30, 2011
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.
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.
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.
Tuesday, November 8, 2011
Section 4.2, pgs 144-the end, Due November 9, 2011
1. What was the most difficult part of the reading for you
One of the (many) things that I still don't understand from this (never ending) section is the stuff behind/around/about the constants "A" and now "B". I mean, I understand that they are being used to approximate some information, and that we can throw them around these inequality statements, but what confuses me is following what they are, where they come from, and why they matter. I mean, it just seems that so far they've only been able to give really poor statements about things that we already knew... So... why?
2. What was the most interesting part of the reading for you?
I guess that Bertrand's Theorem was probably the most interesting statement to me. I didn't follow the proof as well as I'd like (it deals with ideas I'm still not totally comfortable with) but just as a statement of n<p<2n, that seems pretty strong and very interesting. I hope to learn more about that, because it really does seem pretty cool.
One of the (many) things that I still don't understand from this (never ending) section is the stuff behind/around/about the constants "A" and now "B". I mean, I understand that they are being used to approximate some information, and that we can throw them around these inequality statements, but what confuses me is following what they are, where they come from, and why they matter. I mean, it just seems that so far they've only been able to give really poor statements about things that we already knew... So... why?
2. What was the most interesting part of the reading for you?
I guess that Bertrand's Theorem was probably the most interesting statement to me. I didn't follow the proof as well as I'd like (it deals with ideas I'm still not totally comfortable with) but just as a statement of n<p<2n, that seems pretty strong and very interesting. I hope to learn more about that, because it really does seem pretty cool.
Sunday, November 6, 2011
Section 4.2 pgs 138-144, Due November 7, 2011
1. What was the most difficult part of the reading for you?
Well, first, I must say that while I didn't follow everything in today's reading, it felt worlds better than reading the end of chapter 3. So... hooray. In terms of difficulty, I'll mention a few short things. Do you know that feeling you get when you're listening to somebody (usually a fast talking girl) tell a really long story that has a lot of characters that you're unfamiliar with? At first you really try to keep track of where everybody is in the story so that you can respond appropriately to the punch line? Well, that head-spinning feeling (at first you are okay, but somewhere in the middle you completely lost track but don't want to say anything because you don't want to hurt her feelings) is kind of what I felt tonight. I felt like the proof of Chebychev's estimate was like trying to listen to that girl tell a story. It was a little too long and introduce a few too many new ideas for me to stay caught up. But, as I said, it doesn't feel hopeless. I'm guessing that just a simple explanation/verbalization of some of those "greatest integer" things will be very helpful. Also, I struggled with that "O" business.
2. What was the most interesting part of the reading for you?
(By the way, I'm sorry again for my test blunder... It was a long weekend and I wasn't thinking clearly. But, I did spend most of my Saturday and Sunday preparing for this coming test, so hopefully things'll start looking up) What I found most interesting in this reading was something that you mentioned in class. Mostly, the probability of these large numbers being prime. It reminded me of that Birthday Paradox (I'm sure you've heard of) and how, though (using the book's example) .005% is not a very high percentage, it seems high in context of looking at an 86 digit number and asking if it's prime or not. I mean, 86 digits is a HUGE number, so to have that percent chance of picking a prime seems pretty remarkable. I would have thought that primes were much more sparse than that.
Well, first, I must say that while I didn't follow everything in today's reading, it felt worlds better than reading the end of chapter 3. So... hooray. In terms of difficulty, I'll mention a few short things. Do you know that feeling you get when you're listening to somebody (usually a fast talking girl) tell a really long story that has a lot of characters that you're unfamiliar with? At first you really try to keep track of where everybody is in the story so that you can respond appropriately to the punch line? Well, that head-spinning feeling (at first you are okay, but somewhere in the middle you completely lost track but don't want to say anything because you don't want to hurt her feelings) is kind of what I felt tonight. I felt like the proof of Chebychev's estimate was like trying to listen to that girl tell a story. It was a little too long and introduce a few too many new ideas for me to stay caught up. But, as I said, it doesn't feel hopeless. I'm guessing that just a simple explanation/verbalization of some of those "greatest integer" things will be very helpful. Also, I struggled with that "O" business.
2. What was the most interesting part of the reading for you?
(By the way, I'm sorry again for my test blunder... It was a long weekend and I wasn't thinking clearly. But, I did spend most of my Saturday and Sunday preparing for this coming test, so hopefully things'll start looking up) What I found most interesting in this reading was something that you mentioned in class. Mostly, the probability of these large numbers being prime. It reminded me of that Birthday Paradox (I'm sure you've heard of) and how, though (using the book's example) .005% is not a very high percentage, it seems high in context of looking at an 86 digit number and asking if it's prime or not. I mean, 86 digits is a HUGE number, so to have that percent chance of picking a prime seems pretty remarkable. I would have thought that primes were much more sparse than that.
Thursday, November 3, 2011
Midterm 2 Study Prep
1. Which topics and theorems do you think are the most important out of those we have studied?
Well, looking back at my notes, it seems like the biggest theme here is: the Infinitude of Primes. It seems to me that there has been one proof after the other how many primes there are. So, I think that any theorems relating to that are going to be the most important.
2. What kinds of questions do you expect to see on the exam?
Like I said in the first part, I'm guessing that we will be expected to proof that there are an infinite number of primes of various forms. Hopefully, we'll get lots of questions about continuous fractions -- I like those. :) Also, perhaps we'll need to be able to calculate certain Mersenne numbers, or Fermat numbers or whatever.
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.
Well, I've got to say, with very few exceptions, I started getting desperately lost around quadratic reciprocity. I'm thinking that part of that is that I'm missing some real basic understandings somewhere early on, so I feel like I need to return to some of the basics before really delving into the understanding of these sections. But that's what this weekend is for. In terms of a question I'd like to see answered, I guess if you're going to be including anything about characters, I'd like to see the type of question that would be, and how you'd go about answering it. That is, without a doubt, my weak spot for this section. I feel like we just did one theorem after another with out any problems really being solved (I admit, the homework was so whelming to me that I didn't finish any of those assignments). I'd like to see a question relating to those that is solvable (not necessarily a proof).
4.Are there topics you are especially interested in studying during the rest of the semester? What are they?
As I've mentioned before, I'm really just trying to survive and not drown in number theory. I'm interested in any topic that won't make me feel like a complete idiot. Help me Bro. Jenkins. You're my only hope.
Well, looking back at my notes, it seems like the biggest theme here is: the Infinitude of Primes. It seems to me that there has been one proof after the other how many primes there are. So, I think that any theorems relating to that are going to be the most important.
2. What kinds of questions do you expect to see on the exam?
Like I said in the first part, I'm guessing that we will be expected to proof that there are an infinite number of primes of various forms. Hopefully, we'll get lots of questions about continuous fractions -- I like those. :) Also, perhaps we'll need to be able to calculate certain Mersenne numbers, or Fermat numbers or whatever.
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.
Well, I've got to say, with very few exceptions, I started getting desperately lost around quadratic reciprocity. I'm thinking that part of that is that I'm missing some real basic understandings somewhere early on, so I feel like I need to return to some of the basics before really delving into the understanding of these sections. But that's what this weekend is for. In terms of a question I'd like to see answered, I guess if you're going to be including anything about characters, I'd like to see the type of question that would be, and how you'd go about answering it. That is, without a doubt, my weak spot for this section. I feel like we just did one theorem after another with out any problems really being solved (I admit, the homework was so whelming to me that I didn't finish any of those assignments). I'd like to see a question relating to those that is solvable (not necessarily a proof).
4.Are there topics you are especially interested in studying during the rest of the semester? What are they?
As I've mentioned before, I'm really just trying to survive and not drown in number theory. I'm interested in any topic that won't make me feel like a complete idiot. Help me Bro. Jenkins. You're my only hope.
Tuesday, November 1, 2011
Section 3.3 pg 115-end, Due November 2, 2011
1. What was the most difficult part of the reading for you?
OMG, please, Bro. Jenkins, for the love, can we leave this character malarkey behind us forever? I feel so lost and sad and lost. I'm sure that this section (all of 3.3) is very interesting for people who know whatever it is talking about, but I am not one of those people. I do not understand what is happening. Well, I suppose that (after two weeks) I'm almost kind of comfortable with what a character is, but that's pretty much the limit of that. I do not understand L-series, or any of these theorems. It is making me feel so stupid.
2. What was the most interesting part of the reading for you?
I think it's interesting that we're still reading about these crazy characters. I mean, really. Looking at these proofs and formulas just seem so contrived and crazy. I'm mostly terrified that this concept is going to ruin me, and this class, and my future career, and my life. So, it's interesting that something this silly can be so de-motivating.
OMG, please, Bro. Jenkins, for the love, can we leave this character malarkey behind us forever? I feel so lost and sad and lost. I'm sure that this section (all of 3.3) is very interesting for people who know whatever it is talking about, but I am not one of those people. I do not understand what is happening. Well, I suppose that (after two weeks) I'm almost kind of comfortable with what a character is, but that's pretty much the limit of that. I do not understand L-series, or any of these theorems. It is making me feel so stupid.
2. What was the most interesting part of the reading for you?
I think it's interesting that we're still reading about these crazy characters. I mean, really. Looking at these proofs and formulas just seem so contrived and crazy. I'm mostly terrified that this concept is going to ruin me, and this class, and my future career, and my life. So, it's interesting that something this silly can be so de-motivating.
Sunday, October 30, 2011
Section 3.3 pg 110-115, Due October 31, 2011
1. What was the most difficult part of the reading for you?
Well, unfortunately, since I still don't understand this character malarkey, the beginning was the most difficult for me again. Seriously, what in the world are these L-series things? I'm lost beyond lost. I'm mostly praying that these character things are just here for this short visit, then they'll leave me alone for the rest of my life, because reading this section feels like I'm reading in a different language.
2. What was the most interesting part of the reading for you?
Okay, so, if I stop complaining for a minute and just accept the gibberish that I've read at the beginning of the section, I actually found myself following the Lemmas pretty easily. Again, I had to just accept the L-series and character stuff as they've described them, but then I was able to follow (using my 113 knowledge from 6 years ago) Lemmas 3.3.5-3.3.7 without too much trauma. So, I guess that's interesting... to me...
Well, unfortunately, since I still don't understand this character malarkey, the beginning was the most difficult for me again. Seriously, what in the world are these L-series things? I'm lost beyond lost. I'm mostly praying that these character things are just here for this short visit, then they'll leave me alone for the rest of my life, because reading this section feels like I'm reading in a different language.
2. What was the most interesting part of the reading for you?
Okay, so, if I stop complaining for a minute and just accept the gibberish that I've read at the beginning of the section, I actually found myself following the Lemmas pretty easily. Again, I had to just accept the L-series and character stuff as they've described them, but then I was able to follow (using my 113 knowledge from 6 years ago) Lemmas 3.3.5-3.3.7 without too much trauma. So, I guess that's interesting... to me...
Thursday, October 27, 2011
Section 3.6 Due October 28, 2011
1. What was the most difficult part of the reading for you?
First of all, let me say that this class is just a rollercoaster. I mean, continued fractions felt like a breeze, then came Dirichlet characters which have dropped me back into the pit of h-e-double hockey sticks, and now we have this section, which wasn't half bad. So... okay. But, in terms of what was difficult for me, something that is common for me (especially approaching the a midterm) is that everything seems to bleed together. It isn't until I start writing up my study guide for the test that I'm able to really go back, section by section, definition by definition, and remember/distinguish things. This was my problem with this section. Things were a little mushy with the several different arithmetic functions proven to be multiplicative. Truthfully, I hardly remembered any of those functions, but they seem like a good guideline for getting ready for the upcoming test. The other thing that was difficult for me (since my brain already felt mushy) was the Mobius inversion formula. I really struggled to follow this one. Period. It was pretty darn complicated.
2. What was the most interesting part of the reading for you?
I found the Mobius function, and the proof that it is multiplicative, to be pretty interesting. And, believe it or not, I think I understood everything that was said in those two half pages. I almost felt like I might survive this semester without having to take this class again next semester (please, pass me). But then, just when I was feeling good/strong/smart, the Mobius inversion formula came along and ruined everything. I guess what I found to be so interesting about these pages was the way in which th proof of Theorem 3.6.3 really helped me understand exactly what the multiplicitivity stuff was trying to say. (I mostly understood it, but because I had forgotten about the arithmetic functions it was referring to, having the function and the multiplicitivity side by side was nice.) And that's how it felt for me.
First of all, let me say that this class is just a rollercoaster. I mean, continued fractions felt like a breeze, then came Dirichlet characters which have dropped me back into the pit of h-e-double hockey sticks, and now we have this section, which wasn't half bad. So... okay. But, in terms of what was difficult for me, something that is common for me (especially approaching the a midterm) is that everything seems to bleed together. It isn't until I start writing up my study guide for the test that I'm able to really go back, section by section, definition by definition, and remember/distinguish things. This was my problem with this section. Things were a little mushy with the several different arithmetic functions proven to be multiplicative. Truthfully, I hardly remembered any of those functions, but they seem like a good guideline for getting ready for the upcoming test. The other thing that was difficult for me (since my brain already felt mushy) was the Mobius inversion formula. I really struggled to follow this one. Period. It was pretty darn complicated.
2. What was the most interesting part of the reading for you?
I found the Mobius function, and the proof that it is multiplicative, to be pretty interesting. And, believe it or not, I think I understood everything that was said in those two half pages. I almost felt like I might survive this semester without having to take this class again next semester (please, pass me). But then, just when I was feeling good/strong/smart, the Mobius inversion formula came along and ruined everything. I guess what I found to be so interesting about these pages was the way in which th proof of Theorem 3.6.3 really helped me understand exactly what the multiplicitivity stuff was trying to say. (I mostly understood it, but because I had forgotten about the arithmetic functions it was referring to, having the function and the multiplicitivity side by side was nice.) And that's how it felt for me.
Tuesday, October 25, 2011
Section 3.3 - Pg 110, Due October 26, 2011
1. What was the most difficult part of the reading for you?
Geez louize. I should have known. Yesterday was such a nice/easy day. I understood the section and the homework was a breeze. I should have known something crappy was coming. I struggled with this reading from the beginning. I'm not sure why that is, but my guess is that it's because something completely new to me is being introduced, and it has a weird name. I mean "character"? Really? What does that even mean? To me, it's just a symbol. Obviously it's denoted by a symbol here, but I'm really struggling to understand exactly what it does. From the definition, it is a function (okay...) that maps integers to complex numbers. But, if it's a function, how does it belong to a modular residue class? I'm probably not reading that right, but that's how I'm reading the definition. That's where I get lost. Ignoring that, I can follow the rest of the definition of this function....
2. What was the most interesting part of the reading for you?
Um... good question. Mostly I feel confused, and that's not interesting at all, since it's so common these days. I guess it's interesting because these 'characters' ([disgruntled] whatever) follow so many of the rules and theorems we've established over the last several years of math. Like, x(1)><0, x(a1a2)=x(a1)x(a2) and so on. I mean, since I haven't quite figured out what a character is, it's not that "interesting" but it gives me hope that I might be able to catch up on this idea after a good day in class.
Geez louize. I should have known. Yesterday was such a nice/easy day. I understood the section and the homework was a breeze. I should have known something crappy was coming. I struggled with this reading from the beginning. I'm not sure why that is, but my guess is that it's because something completely new to me is being introduced, and it has a weird name. I mean "character"? Really? What does that even mean? To me, it's just a symbol. Obviously it's denoted by a symbol here, but I'm really struggling to understand exactly what it does. From the definition, it is a function (okay...) that maps integers to complex numbers. But, if it's a function, how does it belong to a modular residue class? I'm probably not reading that right, but that's how I'm reading the definition. That's where I get lost. Ignoring that, I can follow the rest of the definition of this function....
2. What was the most interesting part of the reading for you?
Um... good question. Mostly I feel confused, and that's not interesting at all, since it's so common these days. I guess it's interesting because these 'characters' ([disgruntled] whatever) follow so many of the rules and theorems we've established over the last several years of math. Like, x(1)><0, x(a1a2)=x(a1)x(a2) and so on. I mean, since I haven't quite figured out what a character is, it's not that "interesting" but it gives me hope that I might be able to catch up on this idea after a good day in class.
Monday, October 24, 2011
Section 3.2.5 Due on October 24, 2011
1. What was the most difficult part of the reading for you?
Well, this was a pretty short reading (thanks, by the way) so it embarrasses me to say that I struggled to understand Theorem 3.2.5.2 (including Lemma 3.2.5.1 (together, these make up more than half of the section). I guess, for starters, what are [NZM] AND [P]? I'm guessing these are like... appendices? Other books? I really just don't know what in the world these are. But, to get points for this amazing blog, let me attempt to pinpoint where exactly I got lost. (also, I get lost on where the proof for the theorem and the proof for the lemma end....). Really, I'm confused about which proof goes with which theorem. Like, on the top of page 104 it begins a proof.... and it says "Proof (the sequence of primes is infinite)", so is that starting a proof of its own theorem? Is it proving something specifically mentioned/named above? And, I guess I got lost somewhere around the 10th line. I'm not sure how (maybe it's from something earlier that I'm forgetting) they made this leap about q^2+1 needing to be a power of two. I realize that's only the surface of my confusion, but hey, it's a start.
2. What was the most interesting part of the reading for you?
I thought that looking at this crazy fraction thing as being periodic in nature was kind of interesting. I mean, I was sad that it just lists a special case, rather than a proof (as far as I can see), but that it makes sense that if a_0,a_1,....a_n has some sort of periodic pattern that it could mean something (that I also don't understand.) I guess you can be excited that I'll be in class eager to learn what the heck is being taught here, because I am just not following the connections that they are trying to make. Shocker.
Well, this was a pretty short reading (thanks, by the way) so it embarrasses me to say that I struggled to understand Theorem 3.2.5.2 (including Lemma 3.2.5.1 (together, these make up more than half of the section). I guess, for starters, what are [NZM] AND [P]? I'm guessing these are like... appendices? Other books? I really just don't know what in the world these are. But, to get points for this amazing blog, let me attempt to pinpoint where exactly I got lost. (also, I get lost on where the proof for the theorem and the proof for the lemma end....). Really, I'm confused about which proof goes with which theorem. Like, on the top of page 104 it begins a proof.... and it says "Proof (the sequence of primes is infinite)", so is that starting a proof of its own theorem? Is it proving something specifically mentioned/named above? And, I guess I got lost somewhere around the 10th line. I'm not sure how (maybe it's from something earlier that I'm forgetting) they made this leap about q^2+1 needing to be a power of two. I realize that's only the surface of my confusion, but hey, it's a start.
2. What was the most interesting part of the reading for you?
I thought that looking at this crazy fraction thing as being periodic in nature was kind of interesting. I mean, I was sad that it just lists a special case, rather than a proof (as far as I can see), but that it makes sense that if a_0,a_1,....a_n has some sort of periodic pattern that it could mean something (that I also don't understand.) I guess you can be excited that I'll be in class eager to learn what the heck is being taught here, because I am just not following the connections that they are trying to make. Shocker.
Wednesday, October 19, 2011
Section 3.2.2 Due on October 19, 2011
1. What was the most difficult part of the reading for you?
This time, I will not blame the book. I think it's because of the late hour or because it used a bunch of other proofs from earlier in the section that we haven't discussed in class yet, but I had a hard time following Theorem 3.2.2.2 (Fermat's two square theorem), which makes me nervous because it has a name, so it's probably important. I think I just got confused following the logic on the top of page 92 where everything seems to meld together.
2. What was the most interesting part of the reading for you?
Again, maybe it's the late hour, but I really kind of enjoyed reading Lemma 3.2.2.1. I'm not sure if that's just because I could actually follow it (a treat for me these days) or what it was exactly.... maybe I just felt impressed with the way in which a bunch of theorems we talked about (what seems like forever ago) earlier really came into play in a nice and cohesive way during this proof. I don't think I could ever replicate it (so don't ask me to) but I could actually follow it. Three pats on the back for me.
This time, I will not blame the book. I think it's because of the late hour or because it used a bunch of other proofs from earlier in the section that we haven't discussed in class yet, but I had a hard time following Theorem 3.2.2.2 (Fermat's two square theorem), which makes me nervous because it has a name, so it's probably important. I think I just got confused following the logic on the top of page 92 where everything seems to meld together.
2. What was the most interesting part of the reading for you?
Again, maybe it's the late hour, but I really kind of enjoyed reading Lemma 3.2.2.1. I'm not sure if that's just because I could actually follow it (a treat for me these days) or what it was exactly.... maybe I just felt impressed with the way in which a bunch of theorems we talked about (what seems like forever ago) earlier really came into play in a nice and cohesive way during this proof. I don't think I could ever replicate it (so don't ask me to) but I could actually follow it. Three pats on the back for me.
Monday, October 17, 2011
Section 3.2-3.2.1 Due October 17
1. What was the most difficult part of the reading for you?
I had an okay time following the Pythagorean triples proof, which I'll discuss later, but I must say that I did not have such an okay time following the proof about the equation of x^4+y^4=z^2. It started off simple enough, but then I got lost in somewhere around page 89...
2. What was the most interesting part of the reading for you?
I remember doing a proof for Pythagorean triples a few years ago in "History of Math" that seemed more straightforward and easier to understand than his.... I cannot remember what it is, but believe you me, I am motivated to find my notes from that class, since I think it will help me remember/understand this proof a little better. Like I said before, there is something about this book that makes it so difficult for me to follow proofs (even if I've experienced them before).
I had an okay time following the Pythagorean triples proof, which I'll discuss later, but I must say that I did not have such an okay time following the proof about the equation of x^4+y^4=z^2. It started off simple enough, but then I got lost in somewhere around page 89...
2. What was the most interesting part of the reading for you?
I remember doing a proof for Pythagorean triples a few years ago in "History of Math" that seemed more straightforward and easier to understand than his.... I cannot remember what it is, but believe you me, I am motivated to find my notes from that class, since I think it will help me remember/understand this proof a little better. Like I said before, there is something about this book that makes it so difficult for me to follow proofs (even if I've experienced them before).
Tuesday, October 11, 2011
Section 3.1.4b Due on October 12, 2011
1. What was the most difficult part of the reading for you?
Well, I'm not sure if this is the MOST difficult part, but something that seems really basic and is probably important that I didn't understand was really close to the beginning of the reading. So, on page 72, at the beginning of the proof of the Binet formula, it begins by stating x^2-x-1=0, which we know about the golden ratio from deriving it. BUT, right after that, it says "It follows that..." and gives two equations that supposedly "follow" from what was said above, and I do not get it. Where did these come from? HOw did they come from what was said above? It is frustrating for me because I don't understand how these came to be, and I feel like they're pretty important to the rest of what is being proven. Boo.
2. What was the most interesting part of the reading for you?
I guess that for me the most interesting part of the reading was Corollary 3.1.4.1 where we look at the limit of one Fibonacci number over the previous one, as the limit goes to infinity, and how that equals the golden ratio. Also, I thought that the form in which the golden ratio is written (1+1/1+1/....) was pretty interesting.
Well, I'm not sure if this is the MOST difficult part, but something that seems really basic and is probably important that I didn't understand was really close to the beginning of the reading. So, on page 72, at the beginning of the proof of the Binet formula, it begins by stating x^2-x-1=0, which we know about the golden ratio from deriving it. BUT, right after that, it says "It follows that..." and gives two equations that supposedly "follow" from what was said above, and I do not get it. Where did these come from? HOw did they come from what was said above? It is frustrating for me because I don't understand how these came to be, and I feel like they're pretty important to the rest of what is being proven. Boo.
2. What was the most interesting part of the reading for you?
I guess that for me the most interesting part of the reading was Corollary 3.1.4.1 where we look at the limit of one Fibonacci number over the previous one, as the limit goes to infinity, and how that equals the golden ratio. Also, I thought that the form in which the golden ratio is written (1+1/1+1/....) was pretty interesting.
Thursday, October 6, 2011
Section 3.1.3 Due on October 7, 2011
1. What was the most difficult part of the reading for you?
I'm not sure that there was anything terribly 'difficult' about the reading, but what is making me nervous is the thought of keeping these different types of numbers and formulas memorized and separated in my mind. I mean, maybe it'll get better with time, especially if we discuss their differences in class, but for now I couldn't really tell you the difference between Mersenne numbers or Fermat Numbers. I know that I understand how perfect numbers from the other two, but remembering that crazy formula (when compared with the other two) makes me antsy.
2. What was the most interesting part of the reading for you?
Um... it was interesting to me that there are Mersenne/Fermat Numbers and Primes. I also thought that finding the GCD of two Mersenne numbers was interesting. Also, I'm interested (because I don't feel that the book really gave any insight in this section) in what the Fermat and Mersenne numbers have to do with anything. I mean, they even said in the book that they don't know if there are infinite primes in these sequences... so why are we even talking about them? Obviously there will be an answer now... but there isn't one now, and that makes me sad.
I'm not sure that there was anything terribly 'difficult' about the reading, but what is making me nervous is the thought of keeping these different types of numbers and formulas memorized and separated in my mind. I mean, maybe it'll get better with time, especially if we discuss their differences in class, but for now I couldn't really tell you the difference between Mersenne numbers or Fermat Numbers. I know that I understand how perfect numbers from the other two, but remembering that crazy formula (when compared with the other two) makes me antsy.
2. What was the most interesting part of the reading for you?
Um... it was interesting to me that there are Mersenne/Fermat Numbers and Primes. I also thought that finding the GCD of two Mersenne numbers was interesting. Also, I'm interested (because I don't feel that the book really gave any insight in this section) in what the Fermat and Mersenne numbers have to do with anything. I mean, they even said in the book that they don't know if there are infinite primes in these sequences... so why are we even talking about them? Obviously there will be an answer now... but there isn't one now, and that makes me sad.
Tuesday, October 4, 2011
Section 3.1.2 Due on October 5, 2011
1. What was the most difficult part of the reading for you?
I had a rough week last week, but I have taken the test, and I'm re-committed to this section.
Now, having said that, this section really lost me.... again. Is it me? Is it this book? I've mentioned before how grateful I am that I didn't have to buy a book, but I read these proofs and I hardly understand anything. Seriously. What is my problem.
But, let me see if I can get specific. That might help. Perhaps my first problem is totally my fault. I'm not sure that I remember the exact meaning behind "Diverges" or "Converges." Because, I remember I remember that Sum(1/n) as n goes to infinity converges... but doesn't 1/n diverge? I just don't remember what this stuff means. Both go close to zero, so why does one converge and one diverge? I know this is probably elementary (It's been a few years since I've taken a class that talks about this) but this is one of my big hang ups. (Also, my teacher sucked... so I learned tests and procedures, but I don't know meaning behind them.)
I guess that was the most difficult thing for me. Since both of these big proofs listed here seem to rely on those definitions, I felt lost from the begining.
2. What was the most interesting part of the reading for you?
I thought that it was interesting that primes are denser than the sequence of squares. Thinking about it, it's obvious, but I hadn't thought of comparing the two before. But those squares sure do get large rather quickly, while the primes don't "get large" as much as they get more spacy. So, I thought that was interesting, even though that fact relies on the "Converges/Diverges" dilemma I mentioned above.
I had a rough week last week, but I have taken the test, and I'm re-committed to this section.
Now, having said that, this section really lost me.... again. Is it me? Is it this book? I've mentioned before how grateful I am that I didn't have to buy a book, but I read these proofs and I hardly understand anything. Seriously. What is my problem.
But, let me see if I can get specific. That might help. Perhaps my first problem is totally my fault. I'm not sure that I remember the exact meaning behind "Diverges" or "Converges." Because, I remember I remember that Sum(1/n) as n goes to infinity converges... but doesn't 1/n diverge? I just don't remember what this stuff means. Both go close to zero, so why does one converge and one diverge? I know this is probably elementary (It's been a few years since I've taken a class that talks about this) but this is one of my big hang ups. (Also, my teacher sucked... so I learned tests and procedures, but I don't know meaning behind them.)
I guess that was the most difficult thing for me. Since both of these big proofs listed here seem to rely on those definitions, I felt lost from the begining.
2. What was the most interesting part of the reading for you?
I thought that it was interesting that primes are denser than the sequence of squares. Thinking about it, it's obvious, but I hadn't thought of comparing the two before. But those squares sure do get large rather quickly, while the primes don't "get large" as much as they get more spacy. So, I thought that was interesting, even though that fact relies on the "Converges/Diverges" dilemma I mentioned above.
Thursday, September 29, 2011
Test 1 Review Due September 29, 2011
1. Which topics and theorems do you think are the most important out of those we have studied?
It seems to me that The Fundamental Theorem of Arithmetic will be important (I mean, it does have the word "Fundamental" in it. Also the Phi Function, Chinese Remainder Theorem, and Quadratic Reciprocity all seem to be big ideas that were built upon other smaller ideas we've discussed.
2. What kinds of questions do you expect to see on the exam?
I expect us to have to solve a system of congruences (using the chinese remainder theorem) as well as finding if a number is a quadratic residue mod whatever using that mess. Also, I'm guessing there will be some questions about rings and probably a proof or two about primes.
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.
As is pretty obvious, my frustration over the homework that was due Monday seemed to put a damper on what I thought had been pretty good progress. I've pretty much given up for this week (with every intention to pick myself up at the start of next week...) But, I am still really confused about the whole Quadratic Reciprocity thing. I thought I understood how to flip and solve and yadda yadda at the end of class, but then I started to do the homework and got confused and frustrated. I'm mostly confused because from the theorems in that chapter (and with the jacobi stuff) it seemed that your numbers had to be, at the very least, odd. Then you were saying something about using the chinese therorem to break things up and whatever.... I revisited the chinese theorem, and I was still pretty confused. So, I need to understand that stuff better, and I'd like to see an example done, like the one in the homework, where the numbers weren't necessarily prime, and one of them was even -- so you had to use the CRT. After that it'll just be up to me to decide how much I'll be watching conference, and how much I'll be studying... sigh... what a spiritual dilemma....
It seems to me that The Fundamental Theorem of Arithmetic will be important (I mean, it does have the word "Fundamental" in it. Also the Phi Function, Chinese Remainder Theorem, and Quadratic Reciprocity all seem to be big ideas that were built upon other smaller ideas we've discussed.
2. What kinds of questions do you expect to see on the exam?
I expect us to have to solve a system of congruences (using the chinese remainder theorem) as well as finding if a number is a quadratic residue mod whatever using that mess. Also, I'm guessing there will be some questions about rings and probably a proof or two about primes.
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.
As is pretty obvious, my frustration over the homework that was due Monday seemed to put a damper on what I thought had been pretty good progress. I've pretty much given up for this week (with every intention to pick myself up at the start of next week...) But, I am still really confused about the whole Quadratic Reciprocity thing. I thought I understood how to flip and solve and yadda yadda at the end of class, but then I started to do the homework and got confused and frustrated. I'm mostly confused because from the theorems in that chapter (and with the jacobi stuff) it seemed that your numbers had to be, at the very least, odd. Then you were saying something about using the chinese therorem to break things up and whatever.... I revisited the chinese theorem, and I was still pretty confused. So, I need to understand that stuff better, and I'd like to see an example done, like the one in the homework, where the numbers weren't necessarily prime, and one of them was even -- so you had to use the CRT. After that it'll just be up to me to decide how much I'll be watching conference, and how much I'll be studying... sigh... what a spiritual dilemma....
Tuesday, September 27, 2011
Section 3.1.1 Due on September 28, 2011
1. What was the most difficult part of the reading for you?
I.... hmm... I am kind of confused by some of the different proofs that explain the infinite number of primes. I'm aware (it makes sense to me) that a prime cannot divide p1p2p3...pk+1, but I'm not sure how that is proven. I know that that isn't the most important part of those proofs, but it is something that has me caught up and distracts me. Aside from that, I struggled to follow the factorial proofs... I guess that's all I have to say about that.
2. What was the most interesting part of the reading for you?
I thought it was interesting that you could prove something about the number of primes using polynomials. I didn't follow the proof very well, but it seems interesting -- and complicated. On the other hand, the proof that made the most sense to me was the one that used the Euler phi function.
I.... hmm... I am kind of confused by some of the different proofs that explain the infinite number of primes. I'm aware (it makes sense to me) that a prime cannot divide p1p2p3...pk+1, but I'm not sure how that is proven. I know that that isn't the most important part of those proofs, but it is something that has me caught up and distracts me. Aside from that, I struggled to follow the factorial proofs... I guess that's all I have to say about that.
2. What was the most interesting part of the reading for you?
I thought it was interesting that you could prove something about the number of primes using polynomials. I didn't follow the proof very well, but it seems interesting -- and complicated. On the other hand, the proof that made the most sense to me was the one that used the Euler phi function.
Thursday, September 22, 2011
Section 2.6 Due on September 23, 2011
1. What was the most difficult part of the reading for you?
Oh gub. I don't want to sound like a moron. I'm serious when I say that I read these sections 2 or 3 times before blogging about them (always after class, usually that night, then the next night before class). I'm not sure why things don't really make sense to me while reading them... but this section really really confused me again. (The last section really confused me too, but after class it made more sense to me, so hopefully the same will be said for this one too.) But here, my problem begins at the roots of the section. The lemma (2.6.1) really doesn't make sense to me. Not even after reading the proof. There's just to many if/then/if and only if's for me to follow the logic of what is being said. Unfortunately, it goes down from there.
2. What was the most interesting part of the reading for you?
Well, I guess I'm going to have to take a hit on this because I didn't think anything was interesting because I didn't understand anything in it... Oh well. Cest La Vie! I hope you are having the most amazing trip of your life.
Oh gub. I don't want to sound like a moron. I'm serious when I say that I read these sections 2 or 3 times before blogging about them (always after class, usually that night, then the next night before class). I'm not sure why things don't really make sense to me while reading them... but this section really really confused me again. (The last section really confused me too, but after class it made more sense to me, so hopefully the same will be said for this one too.) But here, my problem begins at the roots of the section. The lemma (2.6.1) really doesn't make sense to me. Not even after reading the proof. There's just to many if/then/if and only if's for me to follow the logic of what is being said. Unfortunately, it goes down from there.
2. What was the most interesting part of the reading for you?
Well, I guess I'm going to have to take a hit on this because I didn't think anything was interesting because I didn't understand anything in it... Oh well. Cest La Vie! I hope you are having the most amazing trip of your life.
Tuesday, September 20, 2011
Section 2.5.2 Due on September 21, 2011
1. What was the most difficult part of the reading for you?
Okay... I've now read this section 3 times (all on different parts of the day) and I can honestly say that I struggled through most of it, which is embarrassing because it doesn't seem like it should be too difficult. I guess that most of my confusion is coming from when to do what or whatever. I'm kind of confused by how many solutions you get when (mostly Theorem 2.5.2.3 and really that whole page kind of confused me.) Also, this quadratic residue and quadratic nonresidue malarky didn't make much sense to me.
2. What was the most interesting part of the reading for you?
I thought that the fact that you can still use (sometimes) the quadratic formula was pretty interesting. But... when can I use it? The theorem says when p is an odd prime (so, not 2? Isn't that when we normally use the quadratic formula?). In the second line of page 45, is there a typo? I mean, what's an inverse of Z7? What does that even mean?
Okay... I've now read this section 3 times (all on different parts of the day) and I can honestly say that I struggled through most of it, which is embarrassing because it doesn't seem like it should be too difficult. I guess that most of my confusion is coming from when to do what or whatever. I'm kind of confused by how many solutions you get when (mostly Theorem 2.5.2.3 and really that whole page kind of confused me.) Also, this quadratic residue and quadratic nonresidue malarky didn't make much sense to me.
2. What was the most interesting part of the reading for you?
I thought that the fact that you can still use (sometimes) the quadratic formula was pretty interesting. But... when can I use it? The theorem says when p is an odd prime (so, not 2? Isn't that when we normally use the quadratic formula?). In the second line of page 45, is there a typo? I mean, what's an inverse of Z7? What does that even mean?
Sunday, September 18, 2011
Section 2.5.1 Due on September 19, 2011
1. What was the most difficult part of the reading for you?
Well, they say that Chinese is one of the hardest languages to learn... I've gotta say that if the language is anything like the Chinese remainder theorem, I'd agree. I'm not exactly sure what it's trying to say and I certainly couldn't follow the proof. As best as I could tell, it was like solving a set of equations where, if we were in the integers, you'd line up your equations and subtract, or solve for one x and plug it into another, etc. But, I must say that I was pretty lost when it came to the example they provided. It just looked like a mess to me.
2. What was the most interesting part of the reading for you?
I guess that for me, the most interesting part of the reading was solving for x mod Zn when n wasn't prime and (a,m)=d (as described in the book). It made sense to me that there would be more than one solution . I guess that I would have just written out a table or something to solve these problems, but obviously that isn't really rational all of the time. But their method was helpful in reminding me of the nature of Zn when n is composite.
Well, they say that Chinese is one of the hardest languages to learn... I've gotta say that if the language is anything like the Chinese remainder theorem, I'd agree. I'm not exactly sure what it's trying to say and I certainly couldn't follow the proof. As best as I could tell, it was like solving a set of equations where, if we were in the integers, you'd line up your equations and subtract, or solve for one x and plug it into another, etc. But, I must say that I was pretty lost when it came to the example they provided. It just looked like a mess to me.
2. What was the most interesting part of the reading for you?
I guess that for me, the most interesting part of the reading was solving for x mod Zn when n wasn't prime and (a,m)=d (as described in the book). It made sense to me that there would be more than one solution . I guess that I would have just written out a table or something to solve these problems, but obviously that isn't really rational all of the time. But their method was helpful in reminding me of the nature of Zn when n is composite.
Wednesday, September 14, 2011
Section 2.4.5 Due on September 16, 2011
1. What was the most difficult part of the material for you?
First of all, I'm glad that that example in 2.4.4 really was wrong, because I was ready to throw up. I also found this section easier to follow than some of the others. I think that part of that is because a lot of the things discussed are almost "restating" things that we've already covered. However, I did kind of struggle with Theorem 2.4.5.1. If I were to state it in my own words, I might say "If G is a finite cyclic group of order n, any number that divides n, there exists subgroups of that order." So, I'm pretty sure that is what the theory is saying, but following the proof (since I always struggle with contradiction proofs) kind of lost me.
2. What was the most interesting part of the material?
I really wish that we could make a big chart of the phi function's functionalities. Like, numbers that divide n (in Zn, or whatever) can tell you the different sizes of subgroups, or a number d such that (d,n)=1 will be a generator of that group, or something... It just seems like there are so many similar things for things dealing with the phi function that I know I should probably make a chart or list them out or something so I can compare and contrast all of these theorems that are bleeding together for me.
First of all, I'm glad that that example in 2.4.4 really was wrong, because I was ready to throw up. I also found this section easier to follow than some of the others. I think that part of that is because a lot of the things discussed are almost "restating" things that we've already covered. However, I did kind of struggle with Theorem 2.4.5.1. If I were to state it in my own words, I might say "If G is a finite cyclic group of order n, any number that divides n, there exists subgroups of that order." So, I'm pretty sure that is what the theory is saying, but following the proof (since I always struggle with contradiction proofs) kind of lost me.
2. What was the most interesting part of the material?
I really wish that we could make a big chart of the phi function's functionalities. Like, numbers that divide n (in Zn, or whatever) can tell you the different sizes of subgroups, or a number d such that (d,n)=1 will be a generator of that group, or something... It just seems like there are so many similar things for things dealing with the phi function that I know I should probably make a chart or list them out or something so I can compare and contrast all of these theorems that are bleeding together for me.
Tuesday, September 13, 2011
Section 2.4.4 Due on September 14, 2011
1. What was the most difficult part of the material for you?
Wow. No joke, I'm struggling with a couple of things in this chapter. As I was reading it, and things were getting jumbled together, I kept thinking "Geez Loueez, I wish they'd just give an example or two." Then, they gave two examples. I definitely followed the first one, but the second, holy cow. Is it just me? or are there some issues with 2.4.4.2? I mean, in that table it has a 1 beneath the x. Shouldn't that be an x(bar)? Also, why does the number 1 have order 4? Shouldn't 1 have order 1? And 2 has order 2? Doesn't 2x2=4? Not 8 or 15? (I wasn't sure which it should equal in this case. In fact, I'm kind of confused about this group of units from a non prime n for mod n. Does that make sense? I really remember (and almost enjoy) cyclic groups, and I remember orders of groups and elements, but this chapter lost me.
2. What was the most interesting part of the material?
Hmmmm... this is a tough on because I really struggled with this chapter. The entire time I was reading it I was kind of wondering if we'd be talking about that thing we did in Abstract Algebra last year. I don't remember exactly what it was.... but with these cyclic groups we divided them into subgroups where those subgroups were all of equal order and I think it had something to do with associates. Crap. What was that called? I don't even remember. Anyway, I just kept thinking about that as I was reading page 31 that listed so many theorems.
Wow. No joke, I'm struggling with a couple of things in this chapter. As I was reading it, and things were getting jumbled together, I kept thinking "Geez Loueez, I wish they'd just give an example or two." Then, they gave two examples. I definitely followed the first one, but the second, holy cow. Is it just me? or are there some issues with 2.4.4.2? I mean, in that table it has a 1 beneath the x. Shouldn't that be an x(bar)? Also, why does the number 1 have order 4? Shouldn't 1 have order 1? And 2 has order 2? Doesn't 2x2=4? Not 8 or 15? (I wasn't sure which it should equal in this case. In fact, I'm kind of confused about this group of units from a non prime n for mod n. Does that make sense? I really remember (and almost enjoy) cyclic groups, and I remember orders of groups and elements, but this chapter lost me.
2. What was the most interesting part of the material?
Hmmmm... this is a tough on because I really struggled with this chapter. The entire time I was reading it I was kind of wondering if we'd be talking about that thing we did in Abstract Algebra last year. I don't remember exactly what it was.... but with these cyclic groups we divided them into subgroups where those subgroups were all of equal order and I think it had something to do with associates. Crap. What was that called? I don't even remember. Anyway, I just kept thinking about that as I was reading page 31 that listed so many theorems.
Sunday, September 11, 2011
Section 2.4.3
1. What was the most difficult part of the material for you?
I'm confused about a couple of things. First of all, I'm not exactly sure what a "Reduced residue system" is... I've read the definition several times, and I still haven't quite figured it out. I guess I'm confused by the last line in that definition.
The other thing that I don't quite understand is that big pi/n looking thing that first shows up on theorem 2.4.3.1.
2. What was the most interesting part of the material?
I think that we talked about this in abstract algebra, but I feel like we used a different name, or notation, or formula, or something. Maybe I should double check my notes. But, I find the Euler phi function pretty interesting. I'm not exactly sure why it's useful yet, but I'm sure we'll find out before too long since the name of this book is "Number Theory: an Introduction via the distribution of primes."
I'm confused about a couple of things. First of all, I'm not exactly sure what a "Reduced residue system" is... I've read the definition several times, and I still haven't quite figured it out. I guess I'm confused by the last line in that definition.
The other thing that I don't quite understand is that big pi/n looking thing that first shows up on theorem 2.4.3.1.
2. What was the most interesting part of the material?
I think that we talked about this in abstract algebra, but I feel like we used a different name, or notation, or formula, or something. Maybe I should double check my notes. But, I find the Euler phi function pretty interesting. I'm not exactly sure why it's useful yet, but I'm sure we'll find out before too long since the name of this book is "Number Theory: an Introduction via the distribution of primes."
Wednesday, September 7, 2011
Section 2.4.2
1. What was the most difficult part of the material for you?
It's a small paragraph, and maybe I just need a review on quotient rings and such, but the paragraph that starts "This theorem is actually a special case..." on page 24 kind of lost me. Maybe it isn't so important right now, since I followed everything else in this section, but that was the most difficult part of the reading for me.
2. What was the most interesting part of the material?
Initially I was going to say that Wilson's Theorem (2.4.2.3, pg. 26) was the most difficult part of the reading. But, as I was re-reading it in preparation for this blog, one sentence at a time, I thought the logic was really fascinating. I'm glad it wasn't assigned as a homework problem, since I don't think I would have ever thought about proving it in that way, but it really helped me revisit modular arithmetic in a way I hadn't thought of yet this semester.
It's a small paragraph, and maybe I just need a review on quotient rings and such, but the paragraph that starts "This theorem is actually a special case..." on page 24 kind of lost me. Maybe it isn't so important right now, since I followed everything else in this section, but that was the most difficult part of the reading for me.
2. What was the most interesting part of the material?
Initially I was going to say that Wilson's Theorem (2.4.2.3, pg. 26) was the most difficult part of the reading. But, as I was re-reading it in preparation for this blog, one sentence at a time, I thought the logic was really fascinating. I'm glad it wasn't assigned as a homework problem, since I don't think I would have ever thought about proving it in that way, but it really helped me revisit modular arithmetic in a way I hadn't thought of yet this semester.
Monday, September 5, 2011
Pg. 21-2.4.1
1. What was the most difficult part of the material for you?
I have a pretty good grasp on associates and units and such (I think.) Like, I understand that in Integers, 6, -6 are associates because 1,-1 are units.... But I am struggling with the UFD (Unique Factorization Domain) So, let me get this straight, if D is an integral domain, then if ab=0 either a=0 or b=0. Okay, so for d in D, either d=0, d is a unit (1,-1 for integers), or d has a factorization into primes (okay, that's that fundamental theorem of whatever.) But what I don't understand are the theorems that follow. Like, the Euclidean domain, or Gaussian integers. So, for the Euclidean domain, it says that if there is some function N: D\{0} to N+{0}, (or, a function that maps, in the example of integers I'm using, all integers except for 0, to the natural numbers plus zero) For each a,b in D where a=0 (would b be zero? I mean, it seems to me like the domain can't be zero since it's D\{0}), there exist q,r also in D such that b=aq+r and either r=0 or r doesn't equal zero, and N(r)<N(a). So, I'm confused as to when there is and isn't a zero here. I'm also confused at what it's saying at the end: N(r)<N(a). Also, if I'm understanding this correctly, it just sounds like the euclidean algorithm to me. Like, if we start with some d in D, we could take the absolute value of it, and that's our function mapping it to N. We could even say that D(0)=N(0)=0. So, then is the N(r)<N(a) just saying 0<=r<a?
I guess I'm mostly confused at what this is saying, and if it's any different than the division algorithm.
2. What was the most interesting part of the material?
This reading was pretty short, so I'm not sure what was "interesting" to me. Maybe I can get away with saying that I don't remember the term "Residue" being used in 371. Is a complete residue system just the same as saying all of the classes that are congruent to one another? Like, in modulo 3, [0], [3], [6], [9].... all of those is a complete residue system? No, wait, I just re-read it, and it seems like a "complete residue system" for mod 3 would be [0], [1], and [2]. Right? That's how I understand it. Isn't changing books just so annoying? It's like... such a change of vocabulary and definitions, and whatever. (I know it's not your fault, and I'm glad I didn't have to buy a book, I just wish all authors used the same brain.)
I have a pretty good grasp on associates and units and such (I think.) Like, I understand that in Integers, 6, -6 are associates because 1,-1 are units.... But I am struggling with the UFD (Unique Factorization Domain) So, let me get this straight, if D is an integral domain, then if ab=0 either a=0 or b=0. Okay, so for d in D, either d=0, d is a unit (1,-1 for integers), or d has a factorization into primes (okay, that's that fundamental theorem of whatever.) But what I don't understand are the theorems that follow. Like, the Euclidean domain, or Gaussian integers. So, for the Euclidean domain, it says that if there is some function N: D\{0} to N+{0}, (or, a function that maps, in the example of integers I'm using, all integers except for 0, to the natural numbers plus zero) For each a,b in D where a=0 (would b be zero? I mean, it seems to me like the domain can't be zero since it's D\{0}), there exist q,r also in D such that b=aq+r and either r=0 or r doesn't equal zero, and N(r)<N(a). So, I'm confused as to when there is and isn't a zero here. I'm also confused at what it's saying at the end: N(r)<N(a). Also, if I'm understanding this correctly, it just sounds like the euclidean algorithm to me. Like, if we start with some d in D, we could take the absolute value of it, and that's our function mapping it to N. We could even say that D(0)=N(0)=0. So, then is the N(r)<N(a) just saying 0<=r<a?
I guess I'm mostly confused at what this is saying, and if it's any different than the division algorithm.
2. What was the most interesting part of the material?
This reading was pretty short, so I'm not sure what was "interesting" to me. Maybe I can get away with saying that I don't remember the term "Residue" being used in 371. Is a complete residue system just the same as saying all of the classes that are congruent to one another? Like, in modulo 3, [0], [3], [6], [9].... all of those is a complete residue system? No, wait, I just re-read it, and it seems like a "complete residue system" for mod 3 would be [0], [1], and [2]. Right? That's how I understand it. Isn't changing books just so annoying? It's like... such a change of vocabulary and definitions, and whatever. (I know it's not your fault, and I'm glad I didn't have to buy a book, I just wish all authors used the same brain.)
Thursday, September 1, 2011
Section 2.3
1. What was the most difficult part of the material for you?
Oh man. I knew this day would come, but I didn't expect it so soon. I struggled with this in Abstract algebra, and here we are again... And I'm still struggling... Hopefully after class tomorrow, I'll understand it better... But enough of the "..." What I'm really struggling are the two proofs about how there is an infinite number of primes. I understand breaking numbers down into primes, and how they are unique, but the fact that they are infinite still hurts my head.
2. What was the most interesting part of the material?
Though I thought 2.3.4 was kind of confusingly stated, it was through trying to understand what it was saying that I actually understood this theorem better. I remember we talked about this last semester too, and I kind of understood it, but I know that I get it better now. Also, I really like this way of finding GCD and LCM. At least, I like it much more than the Euclidean Algorithm.
Oh man. I knew this day would come, but I didn't expect it so soon. I struggled with this in Abstract algebra, and here we are again... And I'm still struggling... Hopefully after class tomorrow, I'll understand it better... But enough of the "..." What I'm really struggling are the two proofs about how there is an infinite number of primes. I understand breaking numbers down into primes, and how they are unique, but the fact that they are infinite still hurts my head.
2. What was the most interesting part of the material?
Though I thought 2.3.4 was kind of confusingly stated, it was through trying to understand what it was saying that I actually understood this theorem better. I remember we talked about this last semester too, and I kind of understood it, but I know that I get it better now. Also, I really like this way of finding GCD and LCM. At least, I like it much more than the Euclidean Algorithm.
Monday, August 29, 2011
Sections 2.1 and 2.2
1. What was the most difficult part of the material for you?
I struggled to follow the proof of Lemma 2.1.3, which states "The inductive property is equivalent to the well-ordering property." I know we kind of touched on this in class, and I'm sure it's just because it is the first day of school and we're just using a book with new notations for things we did last semester for Abstract Algebra, but this kind of lost me. I think what confused me most, was the beginning of the proof. Like, I'm having a hard time understanding exactly what T and S are, then the proof by contradictions kind of lost me too... Maybe I'll reread it and try to draw it out tomorrow or something.
2. What was the most interesting part of the material?
I know this is probably pretty silly, (well, not to you, since this is your field) but I kind of like Rings and Groups. I remember them pretty well and did think about them over the summer. Not that I thought they'd leave forever, but I didn't think we'd be hitting them so early, and I'm glad we are. But, I'm nervous for Quotient things... oh man. Those were rough on me. But, and I'm not joking when I wrote this, I love modular congruence so much that the chapters in the books I wrote over the summer (the ones with the broken timelines) are numbered so that they are congruent mod 3. In other words, my chapters 0,3,6,9... are along the same timeline, and so are 1,4,7,10, and so are 2,5,8,11... Anyway, it's nerdy, but I thought you'd be proud.
I struggled to follow the proof of Lemma 2.1.3, which states "The inductive property is equivalent to the well-ordering property." I know we kind of touched on this in class, and I'm sure it's just because it is the first day of school and we're just using a book with new notations for things we did last semester for Abstract Algebra, but this kind of lost me. I think what confused me most, was the beginning of the proof. Like, I'm having a hard time understanding exactly what T and S are, then the proof by contradictions kind of lost me too... Maybe I'll reread it and try to draw it out tomorrow or something.
2. What was the most interesting part of the material?
I know this is probably pretty silly, (well, not to you, since this is your field) but I kind of like Rings and Groups. I remember them pretty well and did think about them over the summer. Not that I thought they'd leave forever, but I didn't think we'd be hitting them so early, and I'm glad we are. But, I'm nervous for Quotient things... oh man. Those were rough on me. But, and I'm not joking when I wrote this, I love modular congruence so much that the chapters in the books I wrote over the summer (the ones with the broken timelines) are numbered so that they are congruent mod 3. In other words, my chapters 0,3,6,9... are along the same timeline, and so are 1,4,7,10, and so are 2,5,8,11... Anyway, it's nerdy, but I thought you'd be proud.
An Introduction
- What is your year in school and major?
I'm an 8 year senior and I'm not even a doctor. Instead I'm still an undergraduate studying Math Education.
-Which post-calculus math courses have you taken?
Foundation Mathematics (290), Elementary Linear Algebra (313), Multivariable Calculus (314), Ordinary Differential Equations (334), Theory of Analysis (341) Abstract Algebra (371)
-Why are you in this class?
So I can graduate and finally get out of school!!!! Oh yeah, and change the lives of the kids who I'm sure are dying to know what I know about number theory...
-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?
Oh man, honestly it's hard to even tell them apart at this point. I don't feel like I've had any stellar math professors, but I did have an incredibly negative experience with one. For my Multivariable Calculus class I remember specifically that I worked my butt off that semester, studied any chance I got, did my homework and never missed a class period. I have never complained about any grading issue, and I don't even mind getting bad grades because it shows exactly what I need to improve on. However, on one test I studied particularly hard on I got a 0/30 points on a specific question because I copied 1 number down incorrectly at the very very very beginning of the problem. I did all of the steps correctly (it was a 3 part question that was 10 points for each part) and know that I knew what I was doing, I just happened to copy down "15" instead of "13" and got zeros on all 3 parts. I decided to talk to the professor (the first and only time I've ever done that in my 8 years here) to see if he could work with me since I thought zero points was a little extreme. He wouldn't even agree to set an appointment with me. He just looked at the test and said, "You got the answer wrong, and there's nothing I can do about it." That really ticked me off and I stopped caring the rest of the semester. Luckily I did well enough for the first half of the semester that my sour attitude didn't completely kill my grade by the end. Anyway, I felt the teacher didn't acknowledge my general efforts and didn't care about me as a person and that was poor teaching to me.
-Write something interesting about yourself
I'm not much of a reader, and I've always been a terrible writer (hence the math). However, over the last several years I have been pretty interested in zombies. Anyway, after an appendectomy last year, a zombie story popped into my head and I couldn't seem to shake it. So, I started writing a book. Well, the book turned into a trilogy, I finished writing the second one a couple of months ago, and I'm currently trying to outline the third one. Now I love writing and am excited to see if I can ever get anything published, even if I just do it as a self-publisher on Amazon.com or something... Anyway, if you're at all interested in zombies, let me know. Maybe I'll let you read a copy. The series is called Living Dead, and it's a mix of Lost (My favorite TV show) and The Walking Dead. It's a zombie survival story told with a broken timeline. Each book is focused on one specific character and chronicles their choices during the great zombie war. So, because each book bounces around in time, one scene is told in one book, and retold from a different point of view in another book. I think that's kind of fun.
-If you are unable to come to my scheduled office hours, what times would work for you?
I don't remember when your office hours are... but anytime after class.
P.S. I admit that, with a few exceptions, I just copied most of these questions/answers from my Abstract algebra blog.... I hope that isn't awkward. If any questions/answers have changed since last semester, I did change them here...
I'm an 8 year senior and I'm not even a doctor. Instead I'm still an undergraduate studying Math Education.
-Which post-calculus math courses have you taken?
Foundation Mathematics (290), Elementary Linear Algebra (313), Multivariable Calculus (314), Ordinary Differential Equations (334), Theory of Analysis (341) Abstract Algebra (371)
-Why are you in this class?
So I can graduate and finally get out of school!!!! Oh yeah, and change the lives of the kids who I'm sure are dying to know what I know about number theory...
-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?
Oh man, honestly it's hard to even tell them apart at this point. I don't feel like I've had any stellar math professors, but I did have an incredibly negative experience with one. For my Multivariable Calculus class I remember specifically that I worked my butt off that semester, studied any chance I got, did my homework and never missed a class period. I have never complained about any grading issue, and I don't even mind getting bad grades because it shows exactly what I need to improve on. However, on one test I studied particularly hard on I got a 0/30 points on a specific question because I copied 1 number down incorrectly at the very very very beginning of the problem. I did all of the steps correctly (it was a 3 part question that was 10 points for each part) and know that I knew what I was doing, I just happened to copy down "15" instead of "13" and got zeros on all 3 parts. I decided to talk to the professor (the first and only time I've ever done that in my 8 years here) to see if he could work with me since I thought zero points was a little extreme. He wouldn't even agree to set an appointment with me. He just looked at the test and said, "You got the answer wrong, and there's nothing I can do about it." That really ticked me off and I stopped caring the rest of the semester. Luckily I did well enough for the first half of the semester that my sour attitude didn't completely kill my grade by the end. Anyway, I felt the teacher didn't acknowledge my general efforts and didn't care about me as a person and that was poor teaching to me.
-Write something interesting about yourself
I'm not much of a reader, and I've always been a terrible writer (hence the math). However, over the last several years I have been pretty interested in zombies. Anyway, after an appendectomy last year, a zombie story popped into my head and I couldn't seem to shake it. So, I started writing a book. Well, the book turned into a trilogy, I finished writing the second one a couple of months ago, and I'm currently trying to outline the third one. Now I love writing and am excited to see if I can ever get anything published, even if I just do it as a self-publisher on Amazon.com or something... Anyway, if you're at all interested in zombies, let me know. Maybe I'll let you read a copy. The series is called Living Dead, and it's a mix of Lost (My favorite TV show) and The Walking Dead. It's a zombie survival story told with a broken timeline. Each book is focused on one specific character and chronicles their choices during the great zombie war. So, because each book bounces around in time, one scene is told in one book, and retold from a different point of view in another book. I think that's kind of fun.
-If you are unable to come to my scheduled office hours, what times would work for you?
I don't remember when your office hours are... but anytime after class.
P.S. I admit that, with a few exceptions, I just copied most of these questions/answers from my Abstract algebra blog.... I hope that isn't awkward. If any questions/answers have changed since last semester, I did change them here...
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