Questions, Due April 11, 2012

Honestly, I feel that all the theorems that we need to know for the final are the most important. :) But written below is a theorem that I feel is important, but I am not exactly sure why. I can tell that if I understand this theorem better than a lot of other things will make much more sense to me, like quotient rings and groups for example. Anything dealing with those I feel is just very difficult for me for some reason, I do not know why.

• Theorem: If R is a commutative ring with identity and I is an ideal of R, then R/I is an integral domain if and only if I is a prime ideal. 

The general topics of the different kinds of rings and groups I think would be good topics to know. 

Any past homework question relating to A(n) is something that I need to understand how to do because I am not even sure what A(n) is. How do I even go about finding it? 

If there is one thing that this course has taught me I think it would be the importance of being exact, precise, and disciplined. There is great power that comes from exactness, and I think I am just starting to understand it, because it is a hard thing to learn how to always do. Also I have learned better how to problem solve and look at problem from the inside out, step by step, instead of the whole mountain at once. And of course this class has taught me patience. Patience in myself, my work and in those around me.  

Sections 8.4-8.5, Due April 5, 2012

Difficult:

As I read section 8.4, I had difficulty distinguishing between C and C(a). I know that C(a) is the centralizer of a. But then they used C in place of C(a) and then they used it as the representation of the conjugacy class and I got a little confused. Also, with how intricate all of the details are becoming about all the theorems and what we can and cannot say about any given group, it is difficult for me to really understand the why behind all of the theorems, especially those in 8.5, because to me many of them seem somewhat trivial. It seems random, even though I know it is not. I know that there are a lot of good reasons why someone discovered these theorems but, like I said, a couple of more examples would be quite help.

Reflective:

It is a sad thought, but I think I am just now starting to really appreciate abstract algebra better. It really is a fine, and complicated art. What is so funny about it is that there are times when the book seems to be making things so very simple and easy. And then all of a sudden it comes to a theorem and its proof and all simplicity gets thrown out the window at times. I just hope that I can study enough so that I can look at the final from the simplest view possible rather than trying to cram everything in and only make it unnecessarily complicated for myself.

8.3-8.4 Sections, Due April 3, 2012

Difficult:

I understand what a Sylow group is, the difficult part is understanding how it can be used and all of the different proofs about it. Any proof or theorem involving the group "K" for some reason to me is confusing. I do not see it as plainly as it seems like it is supposed to be seen from the theorems. Theorem 8.17 is particularly confusing to me.

Reflective:

I am really looking forward to the day in this class when we will stop moving forward. I know that that may sound foolish , but I honestly only just want to stop and give myself time to understand what we have already learned. Just when I think that I am about to understand things, we are introduced to a brand new kind of way to organize letters and groups. It can be very frustrating.

Section 8.2, Due April 1, 2012

Difficult:

I do not completely understand the concept of G(p), therefore it was difficult for me to understand the proof of Lemma 8.4. The paragraph at the top of page 255 is also confusing to me. I do not understand exactly what a p-group is or an element of masimal order. Also, even though the book said that I should be able to follow the logic of the proof of lemma 8.6, it was difficult for me to follow. I still do not understand it.

Reflective:

What we are now learning about groups has gotten to be very detailed that it is difficult for me to follow most ideas and concepts. I do like groups better than rings for some reason. I think it is because I think that they are more visual. A cyclic group, for example, is a group that I can visualize very well. So, hopefully as I do problems relating to this section I can better visualize what is happening.

Section 8.1, Due March 29, 2012

Difficult:

This whole section was a little difficult for me. I read through it seeming to somewhat understand what they were talking about but I really didn't. I do not really know what they mean by the product of two groups. I do not know what it means to multiply two groups together. The proof of theorem 8.1 was also difficult to follow.

Reflective:

I liked the example starting at the end of page 245. It helped to be able to look at the tables and visually see why the two groups were isomorphic to each other. I am not anticipating how this new section will complicate our homework. I think at this point I am ready to only focus on what we have learned to prepare for the final. Though I am glad that we did not have to learn about a brand new entity. I like working in groups. If we stay in groups then that will be a good thing.

Section 7.10, March 27, 2012

Difficult:

I do not really understand the concept of alternating groups. It is difficult for me to understand what they mean without doing a couple of examples. Reading through the proofs I think I understand what the theorems mean and why they are true. But I still do not think I have grasped the concept of alternating groups.

Reflective:

I think mathematics is this never ending way to group numbers together and name them something. Anything that has a pattern it seems like you can have a different name for it. I would even venture to say the there is an infinite number of patterns that you can find using numbers and therefore mathematics is a kind of infinite subject. :)

Section 7.9, Due March 25, 2012

Difficult:

I understood most about cycle notation and the product of permutations, etc. But it is a little difficult for me sometimes to see what the product between two permutations will look like. Especially when there are more than two permutations to combine into one. It was also difficult for me to follow the proof of Lemma 7.49. I am sure there is an easy way of explaining it to someone, but the proof was difficult to follow.

Reflective:

I like the idea of cycle notation. I know that it will make it easier for me to write permutations. But I also know that I can potentially get very confused and start mixing up all the numbers. This will call for some serious careful calculations when I am doing my homework. It is sections like these that make me see mathematics as more of a history of ideas; one day someone was thinking about simpler ways to write permutations and then BOOM! he thought of cycle notation.

Section 7.8, March 22 2012

Difficult:

This section was a little more confusing than past sections. A couple of concepts were more difficult for me to grasp. I do not know what is meant by the fact that the kernel measures how far the homomorphism f is from being injective. That does not make any sense to me. I do not understand the concept of "how far" when dealing with numbers in abstract algebra.

Reflective:

I know that a lot of what we are learning about groups is supposed to connect with what we have already learned about rings. But I am having a difficult time making that connection. It is a wonderful thing that they can connect in such logical ways, but that connection is hard to make. I think part of it has to do with all the new names and notation. But other than that this new material is great!

Make-up Blog! Edward B. Burger, "History of Numbers"

I absolutely loved this Lecture! There is no other way to say. I enjoyed Dr. Burger and his enthusiasm for numbers and mathematics. He was very entertaining and gave a fabulous presentation about numbers.

I understand the disclaimer he gave at the beginning of the lecture stating that it is probable that at some of the information and stories are mostly true. But even then, I couldn't help but believe what he was presenting! I found it fascinating that it is very possible for literature, language, science and other subjects to stem from simply people learning to count. It made complete sense to me how the ancient people may have counted and how that lead from impressions in clay, and more detailed drawings, to writing and the development of our numbers today. I also found it fascinating that the Latin word for pebble is calculi. It makes so much sense!

As the lecture progressed, I found it more difficult to follow him. For some reason I did not quite make the connection between numbers and space. I think I may have missed some of what he said. But for most of the lecture I was glued to what he was saying about the possible future of numbers. I enjoyed it so much that I am convinced of the importance of the history of mathematics. As much as time and curriculum will allow, I am going to make sure that I add some history to my mathematics classes when I head off to teach.

Section 7.7, March 19, 2012

Difficult:

The most difficult part for me in this section was keeping up with the notation. Quotient rings were not really my favorite subject before this section and quotient groups are just as difficult for me to follow. It is difficult for me to conceptualize what exactly does G/N mean or what Na means. Overall, I was able to follow the reading fairly well, but I still do not understand exactly what I am dealing with.

Reflective:

I have noticed that this class basically just builds on itself over and over again like a snowball. Especially when you have already learned what a congruence class is, a quotient ring is, what a subring is, ect. Now we are learning about everything all over again with groups. It is wonderfull. Just wonderful. :)

Section 7.4, Due March 9, 2012

Difficult to understand:

At this point most of abstract algebra is what you would call "difficult" to me. In fact, the difficult thing about it is trying to really narrow it down to what is difficult. :) I comprehended most of the section, but I know that I really do not understand it yet because I know that I will be confused as soon as I start the homework problems. I think what is really difficult for me right now is to visualize how all of the groups and numbers relate to one another. I was confused about what an automorphism is because I do not think it was explained very well. Is it just an isomorphism from G to G?

Interesting:

Abstract is definitely getting to abstract for me at this point. Right now it seems like they are just throwing around letters and making up groups and connections and relations. The kind of math that I really appreciate is the math that relates more with the physical world rather than the imaginary, patterned world.

Questions in Prep for Exam

What do you think are the most important topics and theorems?
I think that the second theorem that we need to be able to prove on the exam is very important to know. This is because you can gather a lot of information about a problem and how to prove it by knowing the implications of this theorem.
I also think that the different group definitions are important to know. Knowing the definitions is a great tool on the test even if you did not memorize all the different types of examples of the groups, you can still find them if you know the definitions.

What kinds of questions do you expect to see on the exam? 
I expect to see questions about the theorems that we are being asked to memorize. I expect to see questions about definitions of important concepts. I expect to see questions asking to prove something that was on the homework. However, I expect the test to be reflective of our homework and excluding those problems that were the most difficult on the homework.

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


I need to review exactly what must be done on the test to prove that something is a (insert defintion). I need to go over the how to prove this, material for the test. Also, if possible, in class could you give us the exact numbers of all the theorems that we will have to prove, or should know. It helps me and other students better when we know the actual theorem number rather than what it is about.
Also, please do the sample problem, 5 in class. Thank you so much!!!

Section 7.3, Due March 4, 2012 (see below for a make-up blog post)

Difficult:

I understood about three quarters of this section, so I did understand most of it, but it was a little longer than usual and my brain somewhat stopped working at about the end of page 185. One thing that I found difficult was the proof of theorem 7.10 on page 182. It was a little confusing to me why they only needed to prove that e was in H. I think I may understand why, but it would have been nice to have a little more of an explanation after the proof or something. I also don't really grasp the understanding of cyclic groups. So the first example on pg. 185 was confusing to me. In general, I think I could easily understand all of the material in this chapter, I just need a little bit more time and experience with it in my homework.

Reflective:

I think I have discovered from reading this book that one of the key underlying features in math is patterns. Patterns make up everything in math. Just when you think that they have talked about every different kind of arrangement of numbers, the sprouts another one. That is what I feel about this section. Math really is amazing. I know that I have said that before a lot on these blogs, but it really is true. It is astonishing to me how many different patterns and kinds of "groups" of numbers there are in this world.

MAKE UP BLOG POST-Guest Speaker on Sep. 28, 2012 "Puzzles"

There were a couple of things that I enjoyed about the Guest Speaker on Tuesday, Sep. 28. (Sorry, I completely forgot his name). I really enjoyed the last puzzle he did with the triangles and the zeros and the ones. It made a lot of sense that that is how a computer would make different patterns.

Something that confused me was the one pattern that he put on the overhead but then told us that he was not going to tell us how to finish it. He said that he would just let us finish it. That was confusing to me because then he ended up moving the puzzle off the overhead. I did not even see it long enough to finish the puzzle so it was somewhat pointless. It was neat that this man has discovered a lot of ways to find patterns, but I found myself thinking at the end. So what? What does this mean for us? That was all that I thought the presentation lacked.

The rest of section 7.1, Due Feb. 28, 2012

Difficult:

I do not know enough about groups yet to really define was is most difficult about them that I have learned so far. I know that once I start doing problems, certain difficulties will arise and then I find myself saying, "Goodness, the most difficult thing about groups is (this)!" But until then everything is kind of smashed into a ball of knowledge in my head. I guess you can say the most difficult thing about this section was the whole section. :) I mean I understood everything that I read, but don't think I will honestly understand what I have read until I do some homework problems.

Reflective:

It is amazing to me how many different ways we can find patterns in mathematics. I really enjoyed looking at the shape example with the square and the different ways to move the square. It was a great way to introduce the idea of dihedral groups. I am fairly enjoying this section and I hope to grasp its ideas better than I did with the rings.

Section 7.1, First Part, Due Feb. 27, 2012

Difficult:

The main thing that I found to be difficult with this section was understanding the difference between a group and a ring. At first, when I was reading the definition of a group it seemed to me that it was similar to a ring. But then I realized the bigger specification that a group holds for most of the ring axioms only with ONE operation. Whereas, a ring has different axioms involving a few different operations.

Reflective:

I enjoy compositions of permutations. At first they are a little tricky and I was a little confused trying to follow them in the reading. But once you see the pattern it is interesting to find inverses of certain arrays. I am sure that is what I will be doing in the homework. :)

Section 6.1-6.2, Due Feb. 21, 2012

Difficult:

Overall I think I understood most of the ideas behind this section. The difficulty for me is trying to become comfortable enough with this material to be able to complete problems on my own. For instance, the example on the top of page 141 was somewhat confusing to me. With most of the theorems and examples that I read I start out somewhat intimidated and unsure of how I would go about proving it. I am still wrestling with the definitions of rings, fields, ideals, etc. in my head trying to get myself more comfortable in thinking about them in abstract ways. But, almost always, as soon as I start reading the solution to an example or a proof I always think, "oh Duh! Of course that is how you would do it!" Which is very frustrating because then that means that I am so close to being able to think about these things on my own. I just hope that I grasp everything before the next test.

Reflective:

Math never ceases to astonish me! I just love how simple everything is explained in this book! Even though this material is still very difficult, it is quite comforting knowing that there is always a logical and simple way of approaching each problem. It helps give me a model for how I should go about proving my homework problems and problems on the test. :)

Section 5.3, Due Feb. 14, 2012

Difficult:

Almost everytime I read a new section in this book it seems like the book presents things in such simple ways that I should be able to understand it. And while reading it, I feel like I comprehend what I am reading, but I don't understand it. I know what the book is saying, but I don't understand what it entails. The difficulty in these readings is trying to really understand the new concepts. But it seems that understanding only comes after expereicne with the new concept and trying problems on my own. If I can try to come to understand the concepts as I am reading than that would minimize the amount of times that I need someone elses help on the homework and I will be able to do the homework problems on my own.

Reflective:

It is interesting to note about past mathmeticians and what their views were of math. Especially understand now what they did not understand then. I find it fascinateing that abstract algebra can be used to define the complex numbers and proof of their existence. Though I do not fully understand how or why that works, it makes me smile thinking that it does make sense and that mathmeticians would not doubt the logic if they had known it then.

Section 5.2, Due February 12, 2012

Difficult:

It is difficult for me to fully grasp and understand how the the field F[x] modulo p(x) can act just like the Integers modulo n. It seems to make sense when it is explained in terms of proofs and generic letters representing numbers, but when I start to think of actual polynomials, the connection and the understanding starts to fall apart. I guess the reason for this confusion is that I always saw polynomials as these random sequences of numbers and variables that I needed to solve. I never really saw any kind of significance to their patterns.

Reflective:
Like, I have said before it is amazing how you can expand one simple idea into another realm of combinations. The whole congruence modulo has been expanded from the integers now into the field F[x]. Like, I have said before, it seems to make sense in the book. But it will take a little time and experience before I can become completely comfortable with understanding how everything works.

Questions, Due January 27--but cleared with Dr. Jenkins to turn in late :)

-How long have you spent on the homework assignments? Did Lecture and the reading prepare you for them?
I usually spend about an hour and a half on the homework. Unfortunately, this is not because I am really smart and consistent enough that that is all the time I need, it is simply that that is the all the time I have to spend on my homework every MWF. I should be starting the homework before the day that it is due, and I plan to do that from now on, but that is what I have been doing up to now. And that is why many of my assignments have been turned in incomplete. :)
Lectures and readings do help prepare for the homework, but not near as much as they could. I find that the lectures and the readings are very similar. As a student I go through both of them because I have to; i.e. I read the book because I need to blog, and I go to class because I want to do well in the class. But I often find myself and my classmates just focusing on copying down all of the lecture notes rather than trying to understand them better. In fact, there are times when it feels as though it would be against the flow of lecture to ask questions and really try to understand the material better. Does that make sense? This doesn't happen all of the time; questions are not unwelcome in class by any means. It just seems like the lecture should explore more discussion and discussion from the students rather than a repeat of the theorems that we just read, only now we are listening to them and frantically copying them down. :) I hope this helps.

-What has contributed most to your learning in this class thus far?
Honestly, working out the problems with my peers and having them decipher the book and give it to me in a lay person terms. That is how it is with almost all math classes at BYU it seems. The professor requires reading, regurgitates everything from the book onto the blackboard, answers a couple of questions from those daring enough to interrupt the flow of lecture, and then gives us the homework assignment to do where we have to completely re-invent how to solve problems so that we can make it through the homework and the midterms. :) Like I said before, honestly, if it weren't for the math lab and my friends, I would not have made it through my assignments in this class. I think it is great that we have the math lab, and I think study groups are awesome but I think that the professors should help the students prepare more to have the confidence needed to do the problems by themselves.

-What do you think would help you learn more effectively or make the class better for you? 
I have obviously given you feedback above, so I will give myself some goals seeing as I obviously play a big part in my education as well. My goals are as follows:
-1. At least try all of the problems before the day that they are due.
-2. Try to understand the readings and the lectures more by paying better attention and taking notes as I read.
-3. Write down questions that I come across so that I can ask them in class, seeing as other students might have the same questions.

Section 4.4, Due February 5, 2012

Difficult:

The difficulty of this section started at the very beginning. For some reason the very first paragraph was confusing to me. Ironically, understood mostly everything else from that point on. It took me a second, but I soon quickly understood what they meant by a polynomial function when I started to think of it as the same polynomial functions that I have been dealing with since I was in junior high. From there I came to understand the distinction between the intermediate x and the variable x. I also understood the concepts of roots, seeing as it is not a novel concept in math. As soon as they began to discuss these polynomial functions in terms of fields, it became more difficult. Fortunately, I was able to understand fairly well at first but it gradually got more difficult towards the end of the section. In particular I did not fully understand the proof of Corollary 4.16. Consequently, Corollaries 4.17 and 4.18 were not completely clear as well. But other than that, I pretty much understood the overall picture that this section was trying to depict.

Reflective:

I find it very interesting and almost humorous that they found the need to really make sure that we understood the difference between the intermediate x and the variable x, seeing as the intermediate x deals with polynomials in the polynomial ring R[x] and the variable x deals with polynomials in the ring R. Oh my goodness! Heave forbid we get them confused! I guess I understand the need for a distinction, because they are different, it just seemed like something obvious to a math major. But, nevertheless, as is expected in a Math major, I appreciate the attention to detail and the extreme thoroughness. :)  

Section 4.3, Due February 3, 2012

Difficult:

This section required that I have a good understanding of fields and integral domains. But unfortunately I am having a difficult time understanding exactly what those are and what can happen in them and what cannot. So that made it difficult for me to understand most of this section. I do not completely understand all of the definitions that were given. I guess this is where this class starts to get more ABSTRACT wich is difficult for me to connect with because there is no physical visual aspect of it.

Reflective:

Once I started to try to understand the material better it began to make better sense to me. I find it interesting how everything is connected to each other through different proofs and theorems. I also find it helpful how everything is very clear cut in this book. The book explains things very well and and clearly. You would think I would understand it better, but it is still difficult for me to connect to.

Section 4.2, Due January 31, 2012

Reflective:

Like a couple of past readings I enjoyed this one because it was short and sweet. This section was very straightforward and very much like the last section. It is interesting to learn how the division algorithm and the G.C.D can also apply to polynomials. It also makes sense to me how they come to defining a unique G.C.D.

Difficult:

The most difficult part about this reading was understanding how these polynomials apply to a field and also the proof of theorem 4.5. I understood the first half of the proof, but after the first paragraph, the second paragraph was difficult for me to connect to the first. I understand how polynomials can be treated like integers, but it was just difficult to follow the rest of proof 4.5.

Section 4.1 Due January 26, 2012

Difficult:

It was difficult for me to follow the proof on the last two pages. For example I am not sure why they multiplied by a_(n) b_(m)^(-1) x(n-m). It did not make sense to me. I understand long division using polynomials, and I understand how the division algorithm applies to F[x]. But that was all as far as those couple of pages. The rest of the section I understood very well. It is difficult for me to visualize rings and fields and how they relate to this material, but I still understood most of it. Everything was very straightforward for this section. But probably the most difficult part, like I said earlier, was the Division Algorithm in F[x].

Reflective:

I have never thought of x being not any particular number but just being treated like a number. The analogy using pi help a lot with that explanation. It was very interesting in this section to try to understand the connection that R and R[x] have in polynomials. It was also interesting to note that the ring R is a sub-ring of the polynomial ring R[x] and yet, if R is an integral domain, then so is R[x]. Usually it seems like it would be the other way around on the latter statement.

Section 3.3, Due on January 23, 2012

Difficult:

As usual with these sections I understand most of the first half of the section and then the last half is the most difficult part. I had difficulty understanding all of theorem 3.12 and it's following proof. I was able to understand what a homomorphism is and I feel like I was able to read through the proofs and understand the picture. But it is difficult for me to get a deeper understanding of it so that I can feel more confident.

Reflective:

In general it is interesting to me how math can define one thing and relate it on so many levels to the rest of mathematics. It really helps me to see why they call math a language; because it is so intricate and unique in its patters and how these pattern's connect to the rest of the language.

Section 3.2 Due January 19, 2012

Difficult:
I followed the first half of the section well, but as it got more complicated it became more difficult to understand. Plus I am still having troubles understanding exactly what a ring is. What is most difficult to me at this point is keep track of the terminology. I do not remember what it means for a ring to be an integral domain. But for the most part I am able to follow the proofs and understand the overall idea of what is happening. Also, a big difficulty is connecting what is being taught now with the axioms. There are many times when the book references an axiom and I do not know what it is talking about. I need to make sure I memorize them.

Reflective:
I find it fascinating that there is the whole other domain it seems that works almost just like the integers, but in a different way. As I was reading through the proofs it made more sense to my why a ring could behave like the integers. It also continues to fascinate me that everything stays so consistent. Math is one, if not the most consistent fields of study that exists I think. I enjoying reading material when it finally makes complete mathematical sense in my head. Some of these proofs were like that.

Section 3.1, Due January 17, 2012

Difficult:
I think I understand the overall idea of rings, but I am still having difficulty completely understanding how to prove that something is a ring. Particularly axiom 4 and 5 of the definition. I understand the concept that there needs to be a solution to a+0=a=0. But the subtext in the text book throws me off. I do not completely understand that.

Reflective:
I like the overall concept of abstract algebra. From the book I liked the sentence that said that "By 'abstracting' the common core of essential features, we can develop a general theory that includes as special cases Z, Z (sub n) and other familiar systems. I like the idea of simply relating systems by what they have in common to make the process more simple. I am excited to learn more in abstract algebra, I just hope that it doesn't get too abstract. :)

Section 2.2, Due January 11, 2012

Difficult Parts:

Most of this section was very strait forward for me and a simply review of what I have already learned in Math 290. But the most difficult part about this material has always been understanding that other equivalence classes are the same as other equivalence classes and so on.

Reflective:

Surprisingly, the part that I found to be the most difficult to understand was also the part that I think is most interesting about this section. They way the classes work together with regular algebra and the fact that there are only n-1 distinct equivalence classes, fascinates me.

Section 2.1, Due on January 8, 2012

Difficult:
Overall, not much was difficult for me in this section. But if I had to label one part as being the most difficult it was when they made the connection between congruence and the Division Algorithm. Specifically, Corollary 2.5 was more difficult for me to grasp. Especially part (1). The statement that if any integer is divided by n, the congruence class of that integer and its remainder will be equal.  This was difficult for me because the part of the Corollary seemed to simple, basic and general. I found myself thinking, "How is that possible for ANY integer?" But then as I read the proof, it made more obvious sense to me.

Reflective:
I enjoyed reading this section. The way that the book represented equality really stuck out to me. Their definitions of reflexive, symmetric and transitive, though familiar to me were presented in a slightly more simplistic way then I remember. I think I had always associated those three characteristics with equivalence relations and not just with basic numbers. As I read through the definitions carefully, it made deeper sense to me this time than it had before.

Sections 1.1-1.3, Due on January 5, 2012

1. Difficult

I find it most difficult with material likes this to focus on the overall idea that is being presented in the text and proofs. I get so caught up and easily confused by the letters, equations and words that many times it seems to go in one ear and out the other. I know that right now most of what we are learning is mostly review, but even with material where I know the answers and I have already understood the overall concept I still get caught up on the details and it is difficult for me to completely judge in my head what the book is actually trying to say.
It is also difficult for me to completely see or judge why or how a proof actually proves something. Often times when I read a theorem, especially when it is overly simple, I think, oh that is such a basic fact, how on earth could you prove it? And then the books proof's strategy is a process or something that I wouldn't have even thought to come up with for the answer.

2. Reflective

I really enjoy reading about simple basic facts and why they are true. Of course sometimes I loose focus because the topic gets a little deeper than I would prefer, but most of the time it is great! It gives me a sense of security about some basic math facts that I know to be true. It is also fascinating to how all of the parts are related to one another. For example, it did not occur to me that the gcd of two numbers can obviously be written as a linear combination of the two numbers. I think I always new that, but I never really acknowledged it until know. Now that makes me curious, because I know that we used linear combinations all the time in Math 313. So I am interested to see how this course uses this information and what we have learned in Math 313 to relate it to abstract algebra.

Introduction, Due on January 5, 2012

Hello! This is Abbylynn Payne, and I am taking Abstract Algebra, Math 371 at Brigham Young University from Dr. Jenkins this winter semester 2012. This blog is part of an assignment for that class. It will include, for the most part, posts describing each section of our textbook. Here is a brief introduction of myself as Dr. Jenkins has required:

-I am a Senior at BYU and my major is Math Education.
-After calculus I have taken Math 290 and Math 313.
-I am taking this class because it is a requirement for my major, and because I enjoy math. Specifically, algebra was one of my favorite courses in school, so I am excited to expand my learning of algebra by taking abstract algebra.
-Last semester I had two Math professors who I thought were some of the most effective teachers I have ever had. In my opinion, they were most effective because they were both VERY organized, and one of them   was VERY good at explaining things. The reason he was particularly effective was because he REALLY simplified what he said and HOW he said it. Some teachers get excited and talk quickly and in a complicated way, but this professor spoke very slowly and clearly. That helped him to be the best math teacher I have every had.
-Something interesting about me is that I was on the BYU Ballroom Dance Team for three years at BYU and now I have been given the wonderful opportunity to teach ballroom at Pleasant Grove Junior High, part time.
-One time that works really well for me to get help with homework is MWF from 1-2pm.