Is Re-taking Abstract Algebra Necessary for a Strong Foundation in Mathematics?

[The_ArtofScience]

I really feel dissapointed in myself that I didn't perform as well as I wanted last semester. I took Modern Algebra I and Geometry. The Geometry class covered Euclidean and non-Euclidean geometries. I bombed the final but earned an overall of a B+ because of a 90-something percentile homework grades and better midterm scores.

The real issue for me last semester was Algebra. I could not get passed the materials and know what to do when I was asked to write a proof. The instructor never collected our homework so we were mostly left in the dark for feedback. I managed to earn passing scores on the midterms, although on that final I had a miserable 55%, so my final grade was a B-. I later talked to the instructor and he told me that 17 people had Fs and that I was one of the few with a higher passing grade. Looking back at this semester, I have to say that I did not learn much from Algebra. The lectures were very fast paced and sometimes completely disorganized. What I mean by disorganized is that the instructor would jump around, sometimes using a result that was never proven in class or from his pamphlet of a book. We had to remind him several times that a result that he was using was not obvious, so I ended up feeling more confused than I should've. I'm thinking about re-taking this class but from a different instructor. I'm just not sure if it's absolutely essential. At my university, a person with a passing grade (a C or above) has to pay $330 per unit if s/he decides on a re-take. This is a huge decision that I am making because if I'm absolutely sure on the re-take I'll be borrowing an extra $990. I do want to understand group and ring theory at a basic level, but I'm just not sure that it's a wise decision.

For the record, my concentration in math is teaching and I've already fulfilled the abstract algebra requirement. I still feel that I would be cheating myself by not learning the subject. I really don't feel like I should even consider teaching if I'm not competent in a core math subject since I'll be a bad role model.

 

[Poopsilon]

If you are not going to graduate school don't retake it that is too much money. There are a number of quality abstract algebra books on the market and someone who is studying education should hopefully know enough about how learning and knowledge acquisition works to pick up a good one and teach this material to themselves, especially since you have prior exposure to it.

For a solid but ultimately introductory treatment I would work recommend Hungerford's Introduction to Abstract Algebra. Its unorthodox in that it treats rings before groups, with a bit of number theory in the beginning to wet your appetite, but ultimately it is pedagogically sound and it went down quite smoothly all things considered.

 

[The_ArtofScience]

The only issue with self-studying is how am I going to know that my work is correct without some feedback from a grader? I appreciate your advice though. I just don't see it being very practical in my case.

 

[Skrew]

The only issue with self-studying is how am I going to know that my work is correct without some feedback from a grader? I appreciate your advice though. I just don't see it being very practical in my case.

Get a book where half the exercises are answered in the back of the book or get one with a study guide/student solutions manual.

I used Contemporary Abstract Algebra by Gallian but I think Farleigh's book is better, probably because it is easier and I don't like abstract algebra but anyway...

 

[micromass]

The only issue with self-studying is how am I going to know that my work is correct without some feedback from a grader? I appreciate your advice though. I just don't see it being very practical in my case.

Post solutions on the homework section of this site. Our feedback can be as good (if not better) than the graders'...

 

[Nano-Passion]

Post solutions on the homework section of this site. Our feedback can be as good (if not better) than the graders'...

You could also see if they have the book with solutions on cramster.com

 

[hitmeoff]

The only option on the feedback thing would be to post it here.

Unfortunately, for proof based courses there a re two issues:
1. There is usually more than one way to prove something (although usually, the problems are structured in such a way that there is usually a preferred way to prove something). So just because your proof doesn't math the proof in the solutions manual/cramster, I doesn't meant its wrong.
2. Unless you have the Instructor's Solutions Manual, most proofs probably won't be covered in the back of the book. Even if you have the instructor's solutions manual, it is meant for...the instructor. Which means the proofs are super duper clean, tidy and dense...written so a grad student or professor can read it easily, not necessarily the undergraduate student, so those proofs may be very hard to understand.

Im going to go against the grain...sorta, and just give you something to think about: If you have a hard time writing proofs (don't worry we all do, it never gets easy), then that means you just have not had much experience with upper level math. Proofs and proof writing should be the focus of the course. Algebra is NOT the easiest first taste of abstract math, in fact most people think its the HARDEST class of your upper level math career.

I can understand why you THINK you hate Algebra. My first try at it, I was not ready for all the proofs, all the abstraction, I sat there always thinking "who cares". I dropped the class, TWICE! Eventually I got my proof writing sea legs going and have go on to get A's in Group Theory, and Ring and Field Theory, I am not taking Galois theory and while still very though (I may get a B), I am damn glad I saw it through. Now Algebra is my favorite branch of math and its probably going to be what I specialize in when I go to grad school.

Not saying you will love it, just saying that Algebra is often a brick wall for a lot of people and if you don't feel you learned anything and you were just on "Cruise control" just wandering aimlessly with this stuff, it might be worth it to give it another go, perhaps with another instructor. I have found that the right instructor can make a world of difference. Consider also that you already have been exposed to SOME concepts, now you will be able to really have time to think about how to start attacking problems, because the concepts at least will be slightly familiar.

 

[elfboy]

Once you venture into the world of abstract algrbra (Gauss and beyond) it's a whole new ballgame..you will need to study it over and over to get the hang of it because these are very difficult concepts that don't have repetitive, obvious rules.