1. What I found difficult about this section was probably the bold rule at the bottom of page 84. It just seems confusing, I think I know what it means, like the number of the degree of f*g is less than or equal to the degree of both of them added, but I'm not sure. That was what I found most confusing.
2. I really like how we just keep building on what we've learned already. For example we are reintroduced to the Division Algorithm in this section. The theorem has changed a litttle, but it still has the same basics concepts. That helps me ot learn it if I 've already seen something like it before.
Friday, January 30, 2009
Tuesday, January 27, 2009
Questions, Due January 27th
- Which topics and theorems to you think are the most important out of those we have studied?
- What kinds of questions do you expect to see on the exam?
Sunday, January 25, 2009
Questions, due January 26th
- How long have you spent on the homework assignments?
- Did lecture and the reading prepare you for them?
- What have you liked or disliked about the class thus far?
- What contributes most to your learning?
- What do you think would help you learn more effectively or make the class better for you?
Thursday, January 22, 2009
3.3, due January 22
1. Ok, I think I kinda get this stuff. I've learned about functions being isomorphic before, so I kind of understood that a little bit; however, maybe it was a different definition because I don't remember the 3 rules that it must satisfy in order to be isomorphic. But anyway, on p. 75, in the paragraph before the first example it talks about how it is also important to show that something is not isomorphic. Then it says to do this you must show that there is no possible function from one to the other satisfying the 3 conditions. I guess I just didn't understand the way this was worded. In order to show that something is not isomorphic, don't you just have to show that one of the conditions fail? Anyway, I think I'll just need to practice with these to really get them down, but I'm pretty sure I understand the general idea.
2. Well I think it is cool how other math classes relate to each other. If what I learned in one of my math classes last year about isomorphism was the same as what I'm learning now, then it's so good, cause I've done some of it before. I also like that if something is isomorphic it is also homomorphic, that'll save some time if we're ever asked to show both. Well, I hope that I understand everything, I'll just need practice, like always! :)
2. Well I think it is cool how other math classes relate to each other. If what I learned in one of my math classes last year about isomorphism was the same as what I'm learning now, then it's so good, cause I've done some of it before. I also like that if something is isomorphic it is also homomorphic, that'll save some time if we're ever asked to show both. Well, I hope that I understand everything, I'll just need practice, like always! :)
Tuesday, January 20, 2009
3.2, due January 20th
1. I'm pretty sure that I understood most of the material covered in this section; however, a few of the examples had me confused about the previous definitions. One of the examples that for some reason I didn't understand, was the example right after the definition of a multiplicative inverse. It talks about Z10, and I understand everything up to when it talks about the inverse of 7, and that it is equal to 3, and vice versa. Is it saying that 1/7 in Z10 =3? Because I guess I just don't understand that, but I'm sure I will after an easily explained example by you, and then I'll feel stupid :) That was mostly the thing I didn't understand very well in this section. As for the new theorems and things, I'll just have to study them, and make sure I truly understand them really well.
2. I really like how each section continues to build on the previous one. I know that is probably what they're supposed to do, but it really helps me to understand the new material, when we continue to use the other stuff that I just learned. It's also good that we keep working with these axioms: addition, multiplication, and now adding on subtraction. So, so far I enjoy everything, I hope to continue to understand and like the things I'm learning, but it has been very interesting and it has helped me to learn the material so much better when I read the sections like this!
2. I really like how each section continues to build on the previous one. I know that is probably what they're supposed to do, but it really helps me to understand the new material, when we continue to use the other stuff that I just learned. It's also good that we keep working with these axioms: addition, multiplication, and now adding on subtraction. So, so far I enjoy everything, I hope to continue to understand and like the things I'm learning, but it has been very interesting and it has helped me to learn the material so much better when I read the sections like this!
Thursday, January 15, 2009
3.1, due January 15th
1. This section definitely had a lot of information to cover; however, I think I understood most of it, especially since a lot of it dealt with the addition and multiplication axioms that we having been working with in the other sections, and even in my other math class. There were a few difficult parts for me though. Like the 5th example on p 43, I don't understand that, but then again, I seem to have a hard time with switching from something I'm so used to and understand, like numbers, to something new and vague, like variables. Anyway, that was one thing that I didn't quite get, but I'm sure if I just read it some more I will understand it. Other than that, I think I understand the rest, but there is a lot of information, and with new notation and new definitions to add to my vocabulary, it should be quite interesting, and I hope to be able to grasp the concepts that I need to.
2. The thing I liked about this section was that we're dealing with matrices. I really like matrices, and I hope that I continue to like them after this class :) (jk). I also like the fact that we continued to work with the addition and multiplication axioms, it is helping me understand it in both of my math classes. Anyway, I've never learned about rings before, I think, and I'm excited to learn about them and hope I can understand everything I need to know!
2. The thing I liked about this section was that we're dealing with matrices. I really like matrices, and I hope that I continue to like them after this class :) (jk). I also like the fact that we continued to work with the addition and multiplication axioms, it is helping me understand it in both of my math classes. Anyway, I've never learned about rings before, I think, and I'm excited to learn about them and hope I can understand everything I need to know!
Wednesday, January 14, 2009
2.3, due January 13th
1. This section was actually kind of confusing for me. I'm sure if I read it more, (which I probably will), that I would begin to understand it better. The first thing that I didn't understand was Theorem 2.8 where it says that if p>1 is an integer, then the following things must be true. The fist thing is that p is prime. I don't understand why p has to be prime, for any p>1. Maybe I'm just reading it wrong, but I don't really understand that part. The rest of it, I think I understand, but I was just a little confused on that.
2. This section is actually pretty helpful, because it builds on every thing we've learned so far, and so it's not too hard to understand. I'm hoping that once I understand the few things I was confused about, that I should be able to understand everything pretty well so far. I really enjoy learning about these sections, because to me they're quite interesting! Also, please forgive me for doing this early in the morning before class! I was up late doing homework, and I fell asleep doing my homework. I promise it won't happen again! :)
2. This section is actually pretty helpful, because it builds on every thing we've learned so far, and so it's not too hard to understand. I'm hoping that once I understand the few things I was confused about, that I should be able to understand everything pretty well so far. I really enjoy learning about these sections, because to me they're quite interesting! Also, please forgive me for doing this early in the morning before class! I was up late doing homework, and I fell asleep doing my homework. I promise it won't happen again! :)
Sunday, January 11, 2009
2.2, due on January 11th
1. The most difficult part of this section for me was probably the transition from writing the congruence classes with brackets around them to writing them without brackets. Simply because I feel like I'll get confused if I'm using real integers and congruence classes at the same time, but maybe you go back to the brackets if you are to avoid confusion. The other thing I found confusing was the Warning at the end of the chapter which said that exponents are ordinary integers-- not elements of Zn. I guess what I don't understand is what they're saying. I understand that 2^4 does not equal 2^1, but that 4=1 in Z3, but I guess I just don't get why they gave us an example of this. Are they just saying that the 4 in 2^4 is just an integer, not a congruence class? Cause that makes sense, I'd never think of it differently, that maybe why I'm confused on why they gave an example of that. Anyway, everything else seemed to be fine, just the transition and the warning.
2. The cool thing that I like about this section, is that theorem 2.6 and 2.7 will help me remember what I'm learning in my 315 class, because in that class we're learning about the ordered sets and the addition and multiplication axioms that apply to them. They're basically the same rules, and so that is really nice because I'll be learning them in 2 different classes, and hopefully be able to remember it better. Overall, I thought this was a very good section, I like learning about Modular arithmetic and congruence classes.
2. The cool thing that I like about this section, is that theorem 2.6 and 2.7 will help me remember what I'm learning in my 315 class, because in that class we're learning about the ordered sets and the addition and multiplication axioms that apply to them. They're basically the same rules, and so that is really nice because I'll be learning them in 2 different classes, and hopefully be able to remember it better. Overall, I thought this was a very good section, I like learning about Modular arithmetic and congruence classes.
Thursday, January 8, 2009
2.1, due on January 8th
1. The most difficult part of the material for me was corollary 2.4. I understand most everything up to that pretty well, but what does it mean by "disjoint"? Does it mean that the two congruence classes have nothing in common? So does the corollary say that two congruence classes mod n have to either have nothing in common or everything in common, meaning identical. I suppose if I thought about it enough I would understand it better. In fact simply asking the question to myself is helping me grasp a little better of an understanding. So, I think I mostly understand everything else, just corollary 2.4 and then sentence about it are a little fuzzy to me.
2. The most interesting thing to me is that when you have a congruence class mod 3, for example, there will be a lot of the classes that are equal. I missed that on a test last year without realizing that half of my congruence classes had the same numbers in it :) But now it makes a lot more sense to me, and I think that is pretty cool. I also think that the equivalence relations that the congruence classes can possess such as reflexive, symmetric, and transitive will be very helpful knowledge while dealing with this chapter. I know we used that information a lot in Math 190 to prove things, so I'm eager to see how much and in what ways we will use it again. Overall, I thought this section was very interesting and I learned a lot. I know I'll understand the things I didn't understand after tomorrow's lecture. I look forward to meeting you for the first time tomorrow!
2. The most interesting thing to me is that when you have a congruence class mod 3, for example, there will be a lot of the classes that are equal. I missed that on a test last year without realizing that half of my congruence classes had the same numbers in it :) But now it makes a lot more sense to me, and I think that is pretty cool. I also think that the equivalence relations that the congruence classes can possess such as reflexive, symmetric, and transitive will be very helpful knowledge while dealing with this chapter. I know we used that information a lot in Math 190 to prove things, so I'm eager to see how much and in what ways we will use it again. Overall, I thought this section was very interesting and I learned a lot. I know I'll understand the things I didn't understand after tomorrow's lecture. I look forward to meeting you for the first time tomorrow!
Tuesday, January 6, 2009
1.1-1.3, due on January 7th
1. As I read sections 1.1-1.3, I felt like I understood most of the material. However, for some reason there is one sentence of a theorem that I don't quite understand. I've read it over and over again, but I guess my brain just isn't clicking. It's probably a really stupid question, but what does it mean in Theorem 1.3 when it says, "Furthermore, d is the smallest positive integer that can be written in the form au + bv." I understand that d is the GCD, but I don't get what it means when it says it is the smallest positive integer that can be written in that form. For example, if d is the GCD, then can there be a number greater than d that can be written in the form of that equation? If so, I don't understand that. Also, corresponding with that, since I guess there CAN BE a number other than the GCD that can be written in the form of that equation, then what is it? I bet these are all stupid questions and obvious, but I don't get it right now. Because right after that theorem it gives us a warning that the fact that d= au + bv does NOT imply that d=(a,b) (or in other words is the GCD), then what else can d be? If d is the greatest common divisor between any two numbers, then what number can be greater than d and also satisfy the linear combination equation? Anyway, Sorry if this is confusing, I'm confused. Maybe we can meet and I can better explain what I mean.
2. I found most everything in this chapter to be pretty interesting. I really liked the little short cuts we were taught to make things like finding the GCD a lot easier than finding all the divisors of each number, especially with some of the numbers we were given in the homework including (12378, 3054). That only took like 6 lines to find the GCD. I also found theorem 1.10 interesting. For some reason I had never thought of that before, or for a long while, that ever integer except 0 and +/- 1, is the product of primes. I don't know why I found that so cool but I did. Along with some other vocab words I added to my vocabulary, and a few theorems that I thought were pretty cool, this chapter was very interesting, and I know will help me in my career interests of being a teacher in that I can use these nifty shortcuts to save time and teach others. It was a great chapter to start with! I'm afraid though that there will be a lot more added to the first question as the semester progresses :)
2. I found most everything in this chapter to be pretty interesting. I really liked the little short cuts we were taught to make things like finding the GCD a lot easier than finding all the divisors of each number, especially with some of the numbers we were given in the homework including (12378, 3054). That only took like 6 lines to find the GCD. I also found theorem 1.10 interesting. For some reason I had never thought of that before, or for a long while, that ever integer except 0 and +/- 1, is the product of primes. I don't know why I found that so cool but I did. Along with some other vocab words I added to my vocabulary, and a few theorems that I thought were pretty cool, this chapter was very interesting, and I know will help me in my career interests of being a teacher in that I can use these nifty shortcuts to save time and teach others. It was a great chapter to start with! I'm afraid though that there will be a lot more added to the first question as the semester progresses :)
Friday, January 2, 2009
Sec. 2 Introduction, due on January 7
What is your year in school and major? I am a Junior majoring in Mathematics
Which post-calculus math courses have you taken? I have taken Math 113, 190, 343, 334, 214, and 362.
Why are you taking this class? I am taking this class because it is a requirement for my major. I also have heard that it is a really good class and very interesting.
Tell me about the math professor or teacher you have had who was the most and/or least effective. The most effective math teachers I have had are very organized, with a set schedule, and they lecture about the material in the book that we have homework in, or that is on the test. The least effective teachers I have had are unorganized, no set schedule, go off on tangents, and do not lecture on useful material, which I feel is a waste of my time.
What did s/he do that worked so well/poorly? One professor that I really looked up to was Dr Dorff, he was very organized. He came to calss everyday prepared with the material we were covering that day, and he didn't go off track. He also made class fun and enjoyable, which I think is a necessity because it makes students want to come to class and learn. Another professor I had who I loved, but was not a very good teacher did not have any kind of schedule, we didn't know what homework we would have assigned until the day we learned that material, we didn't know when the tests would be, we didn't really know anything. He would teach the material, but one question from the class could get him off subject for the rest of the class period. It was not a very helpful class, and unfortunately for me it was one I really needed to understand.
Write something interesting or unique about yourself. I was born and raised in Broken Arrow, Oklahoma. I played volleyball for 5 years, even though I'm short, (I'm a good Libero). I love the outdoors, and I have a freckle on the palm of my right hand.
If you are unable to come to my scheduled office hours, what times would work for you? I am actually unable to come to the office hours, because I have a class immediately after this class. The best hours that would work for me would be either in the mornings on Tues and Thurs, like 8am, (I don't know if you'd want to come to school that early), or in the afternoons on Tuesday and Friday like around 4 or 5, which I don't think you'd want to stay that late. I'm sorry my schedule is so complicated. I work 25 hours a week, but I'm sure I could make some arrangments to make an appointment with you when I need to. Thanks!
Which post-calculus math courses have you taken? I have taken Math 113, 190, 343, 334, 214, and 362.
Why are you taking this class? I am taking this class because it is a requirement for my major. I also have heard that it is a really good class and very interesting.
Tell me about the math professor or teacher you have had who was the most and/or least effective. The most effective math teachers I have had are very organized, with a set schedule, and they lecture about the material in the book that we have homework in, or that is on the test. The least effective teachers I have had are unorganized, no set schedule, go off on tangents, and do not lecture on useful material, which I feel is a waste of my time.
What did s/he do that worked so well/poorly? One professor that I really looked up to was Dr Dorff, he was very organized. He came to calss everyday prepared with the material we were covering that day, and he didn't go off track. He also made class fun and enjoyable, which I think is a necessity because it makes students want to come to class and learn. Another professor I had who I loved, but was not a very good teacher did not have any kind of schedule, we didn't know what homework we would have assigned until the day we learned that material, we didn't know when the tests would be, we didn't really know anything. He would teach the material, but one question from the class could get him off subject for the rest of the class period. It was not a very helpful class, and unfortunately for me it was one I really needed to understand.
Write something interesting or unique about yourself. I was born and raised in Broken Arrow, Oklahoma. I played volleyball for 5 years, even though I'm short, (I'm a good Libero). I love the outdoors, and I have a freckle on the palm of my right hand.
If you are unable to come to my scheduled office hours, what times would work for you? I am actually unable to come to the office hours, because I have a class immediately after this class. The best hours that would work for me would be either in the mornings on Tues and Thurs, like 8am, (I don't know if you'd want to come to school that early), or in the afternoons on Tuesday and Friday like around 4 or 5, which I don't think you'd want to stay that late. I'm sorry my schedule is so complicated. I work 25 hours a week, but I'm sure I could make some arrangments to make an appointment with you when I need to. Thanks!
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