How long have you spent on the HW assignments? Did the lecture/reading prepare you for it?
I usually spend about 1.5-2.5 hours on each assignment. The lecture is usually more helpful than the reading. I'll be honest, the blogging is a bit annoying, BUT, it is forcing me to read before the lecture, so it is a very smart strategy on your part. I guess overall I really appreciate it. I think the reading can be somewhat v--like I don't know what questions to have--and I find myself going back and reading it again when I'm working on the problems. I think this is just how mathematics is--it's hard to know what's going on until you are DOING the work.
What has contributed most to your learning in this class thus far?
The most important aspect of my learning has been doing the problems. It's thinking over them, struggling with them, sleeping on them and then asking for help from classmates that helps the most. I don't want to make the assignments sound harder than they are. But, usually there are one or two problems on an assignment that are a bit tricky and take some extra time.
What do you think would help you learn more effectively or make the class better for you?
Maybe reading a bit slower would make doing the problems a bit easier. It's difficult because I have so much to do that I always feel pressured to get the assignments/reading done as fast as possible, but this stifles learning. I feel that I learn best if I'm not rushed and am a bit more relaxed. Maybe I could achieve this by blocking out a little more time so I'm not so pressed. I think the lectures are going great. Not trying to brown-nose, but you (Dr. Jenkins) are definitely one of the better lecturers I've had in this department, which I'm really grateful for. I wouldn't change anything about the lectures.
Thursday, January 27, 2011
Tuesday, January 25, 2011
3.3 due on January 26
What was most difficult?
The most confusing thing for me was on the first example, the addition and multiplication tables are a bit confusing. Namely, why is it arranged 0,6,2,8,4? Is there a special reason or is the author just showing that it doesn't matter which order we make the table? It threw me off.
Reflection
I find myself wondering, "what is the point of this?" What is this leading up to/why do we care about this? Is this "useful" or is this just a mathematician's playground to make up rules for the sake of doing it?
The most confusing thing for me was on the first example, the addition and multiplication tables are a bit confusing. Namely, why is it arranged 0,6,2,8,4? Is there a special reason or is the author just showing that it doesn't matter which order we make the table? It threw me off.
Reflection
I find myself wondering, "what is the point of this?" What is this leading up to/why do we care about this? Is this "useful" or is this just a mathematician's playground to make up rules for the sake of doing it?
Saturday, January 22, 2011
3.2, due on January 24
What was most difficult?
The most difficult thing about this section was some of the new vocabulary: unit, and zero divisor. For unit, it just seems like a strange name. We have an element a that is a unit if some other number is it's reciprocal? That's sort of the intuitive definition I'm getting. And for zero divisor, we have a nonzero a where this is also a nonzero b such that their product is 0. That's not too difficult. It's still all unclear where this is leading.
Reflection
All I can say is I can't wait for Monday's lecture, to see this explained. It's usually easier to understand when you (Dr. Jenkins) explain it.
The most difficult thing about this section was some of the new vocabulary: unit, and zero divisor. For unit, it just seems like a strange name. We have an element a that is a unit if some other number is it's reciprocal? That's sort of the intuitive definition I'm getting. And for zero divisor, we have a nonzero a where this is also a nonzero b such that their product is 0. That's not too difficult. It's still all unclear where this is leading.
Reflection
All I can say is I can't wait for Monday's lecture, to see this explained. It's usually easier to understand when you (Dr. Jenkins) explain it.
Tuesday, January 18, 2011
3.1 (through page 48), due on January 19.
What was most difficult for you?
In all honesty, this wasn't difficult. I've never seen rings before, but it was very clearly defined in the text. I've had enough other math classes, that the idea of constructing sets to meet certain properties(such as those of rings or fields) isn't anything new to me. The examples were very clear, and it became obvious to me before I read the example on real matrices that they would be considered rings as well. I don't know if this is a satisfactory answer, but nothing was difficult. The "most difficult" part of the text would equally be any part.
Reflection
I'm eager to see what we will do with rings, and why they exist. What is their role in mathematics? As an applied math person, I'm always interested in the utility of different branches of mathematics, and I believe (or want to believe) that in their own way, each part is useful. Therefore, I'm very curious to learn more about rings and their place in Algebra and mathematics in general.
In all honesty, this wasn't difficult. I've never seen rings before, but it was very clearly defined in the text. I've had enough other math classes, that the idea of constructing sets to meet certain properties(such as those of rings or fields) isn't anything new to me. The examples were very clear, and it became obvious to me before I read the example on real matrices that they would be considered rings as well. I don't know if this is a satisfactory answer, but nothing was difficult. The "most difficult" part of the text would equally be any part.
Reflection
I'm eager to see what we will do with rings, and why they exist. What is their role in mathematics? As an applied math person, I'm always interested in the utility of different branches of mathematics, and I believe (or want to believe) that in their own way, each part is useful. Therefore, I'm very curious to learn more about rings and their place in Algebra and mathematics in general.
Thursday, January 13, 2011
2.3, due on January 14
What was difficult?
I'm struggling with the difference between corollary 2.9 and 2.10. We were told in the previous section that when it is understood we are working in Zn that we omit the brackets for the congruence classes. So, other than the fact that one of these has brackets and one doesn't, they seem to be concluding the same thing.AHHH...As I just wrote that I glanced again at the page and read again more carefully to see that for 2.10, n need not be prime...Got it.
Reflection
I was glad this section was short and that there wasn't much to read. I don't really have much to say about this topic in particular yet... I feel like I'd have more to say after doing the problems. I'm still just taking all of this (Abstract Algebra) in and seeing where it goes.
I'm struggling with the difference between corollary 2.9 and 2.10. We were told in the previous section that when it is understood we are working in Zn that we omit the brackets for the congruence classes. So, other than the fact that one of these has brackets and one doesn't, they seem to be concluding the same thing.AHHH...As I just wrote that I glanced again at the page and read again more carefully to see that for 2.10, n need not be prime...Got it.
Reflection
I was glad this section was short and that there wasn't much to read. I don't really have much to say about this topic in particular yet... I feel like I'd have more to say after doing the problems. I'm still just taking all of this (Abstract Algebra) in and seeing where it goes.
Tuesday, January 11, 2011
2.2, due on January 12
What was the most difficult part of the material for you?
The most difficult part is just wrapping my head around the idea of modular arithmetic. I guess the concept isn't really that difficult, but I'm not thrilled about the idea of having to remember more definitions for something that isn't very intuitive to me. Perhaps the new notation will be confusing. All in all, nothing is super difficult in the class yet. I'm sure it will get worse (or better, depending on your perspective) later. As for now, it's mostly just that the stuff is new.
Reflection
Theorem 2.7, or the different rules for the integers applied to Zn is pretty cool. It's just cool how in math, things can be generalized to work in different areas so many times--yet other times they can't.
The most difficult part is just wrapping my head around the idea of modular arithmetic. I guess the concept isn't really that difficult, but I'm not thrilled about the idea of having to remember more definitions for something that isn't very intuitive to me. Perhaps the new notation will be confusing. All in all, nothing is super difficult in the class yet. I'm sure it will get worse (or better, depending on your perspective) later. As for now, it's mostly just that the stuff is new.
Reflection
Theorem 2.7, or the different rules for the integers applied to Zn is pretty cool. It's just cool how in math, things can be generalized to work in different areas so many times--yet other times they can't.
Saturday, January 8, 2011
2.1, due on January 10
What was the most difficult part of the material for me?
The Most difficult part of the material is the main idea of the section, congruence classes. I'm sure it will be seen later, but I have no idea what these are used for, which makes it difficult to understand it right now. So to me right now, it is just an(vague)idea. I'm sure once we have the lecture it will be a bit more clear. It's hard to say what exactly is difficult about this, other than I'm wondering why we care about this.
Reflection
I'd say the most interesting thing about this is that it's just so different than what I'm used to dealing with (this whole class is). I remember discussing congruence classes and mod for a couple weeks in Math 190, but even then we just learned how to solve the problems given to us--we weren't exposed to anything done at a higher level with it. That reminds me, what is mod and why do we care about it? Basically, I don't have time to read ahead in the textbook because I need to stay caught up in other classes, but I'm actually a bit excited to see what will come. I'm used to working with partial differential equations, matrices, etc. Something like this is a whole other branch of math of which I know nothing, and this section reminded me of that.
The Most difficult part of the material is the main idea of the section, congruence classes. I'm sure it will be seen later, but I have no idea what these are used for, which makes it difficult to understand it right now. So to me right now, it is just an(vague)idea. I'm sure once we have the lecture it will be a bit more clear. It's hard to say what exactly is difficult about this, other than I'm wondering why we care about this.
Reflection
I'd say the most interesting thing about this is that it's just so different than what I'm used to dealing with (this whole class is). I remember discussing congruence classes and mod for a couple weeks in Math 190, but even then we just learned how to solve the problems given to us--we weren't exposed to anything done at a higher level with it. That reminds me, what is mod and why do we care about it? Basically, I don't have time to read ahead in the textbook because I need to stay caught up in other classes, but I'm actually a bit excited to see what will come. I'm used to working with partial differential equations, matrices, etc. Something like this is a whole other branch of math of which I know nothing, and this section reminded me of that.
Thursday, January 6, 2011
1.1-1.3, due on January 7
What was the most difficult part of the material?
This material isn't too difficult, as it's basically a review of Math 190 and some common sense stuff. I'd say though that the proof of Theorem 1.1 was kind of long, and as simple as it is, I probably wouldn't know how to come up with it on my own. But in all honesty, the topics covered in these first sections had easy to follow proofs and were topics that I'm already familiar with. I'm trying to think of this on a deeper level and I'm not sure I can.
Write something reflective
The most interesting part of the reading was the proof of Theorem 1.10. It was just a cute, clever proof by contradiction. I also enjoyed Theorem 1.3 because the talking of linear combinations reminded me of linear algebra, a subject I really enjoy.
This material isn't too difficult, as it's basically a review of Math 190 and some common sense stuff. I'd say though that the proof of Theorem 1.1 was kind of long, and as simple as it is, I probably wouldn't know how to come up with it on my own. But in all honesty, the topics covered in these first sections had easy to follow proofs and were topics that I'm already familiar with. I'm trying to think of this on a deeper level and I'm not sure I can.
Write something reflective
The most interesting part of the reading was the proof of Theorem 1.10. It was just a cute, clever proof by contradiction. I also enjoyed Theorem 1.3 because the talking of linear combinations reminded me of linear algebra, a subject I really enjoy.
Wednesday, January 5, 2011
Introduction, due on January 7
Answers to questions from the syllabus:
Q: What is your year in school and major?
A: I am a senior and my major is mathematics.
Q: Which post-calculus math courses have you taken?
A: I have taken Math 334, 341, 570, 521, 447, and Math 352.
Q: Why are you taking this class?
A: I am taking this class because it is required for the mathematics major.
Q: 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?
A: Dr. Barrett is the most effective I've had thus far. I had him for Math 570, a class I really loved. He was effective because his lecture notes were very well organized, he wrote clearly on the board at a comfortable pace, and worked very hard to help students have their questions answered. He's also a very kind and funny man, which helped me feel at ease about approaching him and discussing the course with him. Another way he was really effective was in his tests. I feel like the questions he put on exams were very well correlated to what we learned--no surprises. Yet, the questions were challenging enough that they required complete mastery of the material. Also, given the nature of the course and all the cool theorems and results associated with matrices, some of my most joyful moments in math were when I'd figure out how to prove or disprove something I'd been working on for hours, and the result or proof of how to do it was beautiful and clever. I guess I'm saying that he chose test questions that were actually interesting...something that I feel most people would want to know the answer to and be delighted as to why it is true or not. This is in contrast to teachers who've asked questions that are enormously beyond the scope of what was discussed in homework or previous preparation for the exam. I won't name names, but a really good professor who I think writes terrible tests did just that--he'd ask students to reach (I felt) too far. That sounds like I'm just complaining about hard tests...I'm not, because I have aced some of them, but objectively, I felt like I could prepare as best I could from homework and study sessions, etc. and then only hope that I'd figure out the result he wanted that was beyond the scope of the learning outcomes. I resented this. Other teachers have been ineffective by not being polite, talking in a monotone voice, or showing a lack of interest in the course or their students.
Q: Write something interesting or unique about yourself.
A: I am a pretty good drummer. I'm not in a band, but I love rock music and really enjoy playing.
Q: If you are unable to come to my scheduled office hours, what times would work for you?
A: I actually can't make office hours because I have a class then. A time that would work would be between 10 and 2 on Tuesday, or 9 am MWF.
Q: What is your year in school and major?
A: I am a senior and my major is mathematics.
Q: Which post-calculus math courses have you taken?
A: I have taken Math 334, 341, 570, 521, 447, and Math 352.
Q: Why are you taking this class?
A: I am taking this class because it is required for the mathematics major.
Q: 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?
A: Dr. Barrett is the most effective I've had thus far. I had him for Math 570, a class I really loved. He was effective because his lecture notes were very well organized, he wrote clearly on the board at a comfortable pace, and worked very hard to help students have their questions answered. He's also a very kind and funny man, which helped me feel at ease about approaching him and discussing the course with him. Another way he was really effective was in his tests. I feel like the questions he put on exams were very well correlated to what we learned--no surprises. Yet, the questions were challenging enough that they required complete mastery of the material. Also, given the nature of the course and all the cool theorems and results associated with matrices, some of my most joyful moments in math were when I'd figure out how to prove or disprove something I'd been working on for hours, and the result or proof of how to do it was beautiful and clever. I guess I'm saying that he chose test questions that were actually interesting...something that I feel most people would want to know the answer to and be delighted as to why it is true or not. This is in contrast to teachers who've asked questions that are enormously beyond the scope of what was discussed in homework or previous preparation for the exam. I won't name names, but a really good professor who I think writes terrible tests did just that--he'd ask students to reach (I felt) too far. That sounds like I'm just complaining about hard tests...I'm not, because I have aced some of them, but objectively, I felt like I could prepare as best I could from homework and study sessions, etc. and then only hope that I'd figure out the result he wanted that was beyond the scope of the learning outcomes. I resented this. Other teachers have been ineffective by not being polite, talking in a monotone voice, or showing a lack of interest in the course or their students.
Q: Write something interesting or unique about yourself.
A: I am a pretty good drummer. I'm not in a band, but I love rock music and really enjoy playing.
Q: If you are unable to come to my scheduled office hours, what times would work for you?
A: I actually can't make office hours because I have a class then. A time that would work would be between 10 and 2 on Tuesday, or 9 am MWF.
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