Struggling in Algebraic Structures Class? Tips for Success and Self-Esteem Boost

[zoner7]

So yea, In my algebraic structures class I've got a C that is quickly charging towards a D or F...
as the material gradually becomes tougher, I my understanding of the concepts diminish with every class, and all the while my homework grades read lower and lower numbers.

I've been seeing my teacher(his office hours and my free barley sync, however), I've been working my *** off, I attempted to find a student tutor by emailing every single mathematics major and I've looked at online sources, all to no avail. I'm getting my *** kicked in this class, which isn't even particularly difficult. I just can't seem to grasp the ideas.

Does anyone have some ideas or suggestions to direct me towards success in this class? I'm a good student, but I feel like a complete idiot in this class. Its messing with my self-esteem.

proofs = hard

 

[qspeechc]

What book are you using? Perhaps the course/books you are using are too advanced, try Fraleigh or Gallian, perhaps they're simpler than what you're using. Also try Velleman's "How to Prove It" or Solow "How to Read and Do Proofs".

Is this your first course where you're required to do proofs? If it is, trying dropping the course if possible, and taking an easier course that gently introduces you to proofs, most universities use a linear algebra course for this, or they have have some "Introduction to proofs" course or something.

I also found myself in your position. In my first course where I had to do proofs I did badly, I got 60%. I thought I was just too stupid to do proofs. During the holiday I went through my notes in detail, took all my lecturers advice seriously, and just worked my butt off. Now I am averaging 95% in abstract algebra and real analysis. The point is you have to memorise the definitions and theorems (and understand them) and know them very well, see how they are used in the proofs and examples given in the book, think of why things are in the theorems/definition, make up you're own examples etc. Of course you need to know the necessary logic and set theory. Mathematics is not a passive act, you have to go through your book with pencil in hand, working things out along the way. It takes effort.

 

[zoner7]

Yea, this is my first course that requires proofs. I'm currently enrolled in the prerequisite for linear algebra. At my school, before you reach the advanced math class, we have a very inflexible curriculum. So I'm basically taking the lowest level course that is proof-based, which is also the only course available to me that uses proofs.

We are using Gilbert's Element of Modern Algebra. I understand the proofs when I read them; I just can't apply them.

I'll try to work even harder than I am now. Picking up a couple of new textbooks when I go home for break sounds like a good idea. I've got one more opportunity to prove that I am capable of pursuing a mathematics major, that is, on my test the day after thanksgiving break. If I perform poorly I will have to drop the class, as well as sacrifice any possibility of ever majoring in math, and have to live with a gigantic W (withdrawal) on my transcript. If i continued the course if I do badly on that test, I will be risking a D or F, which would completely destroy my transcript.

So yea... I guess more hard work is the only solution. And I'm working so hard already. This feels like such a daunting task...

Are there any good online resources that somebody can recommend to me?

 

[kodiakghost]

A couple W's aint that bad. Just don't have a dozen of them. But I guess my first question for you would be do you enjoy proofs?

I ended up pressing through a mathematics major, but in retrospect, I think I would have been happier doing engineering. I liked math when it was more computationally oriented and more grounded in applications.

I'd say figure out what kind of math you like the most. It may be that a math major wouldn't make you happiest. The bottom line is if you're busting your *** on something and it's not working out, then you either need to change your approach or change your goals. Because there is definitely a limit to the amount of effort you can effectively put into something.

 

[zoner7]

I'm a bit of a perfectionist, unfortunately... My grades are nearly perfect at a school that loves grade deflation. A W is like a slap across the face, plus it means that I need to take summer school to graduate. I suppose, at the very least, I'm determined to succeed.

I enjoy the proofs, at least when I finally arrive upon the correct answer. That's quite a good feeling. But I do agree that I think i enjoy the more applied math over the pure math. That is why I'm considering a physics major, which, unfortunately, I hear is one of the toughest - if the the toughest - major at my school. Something like 7 kids choose to major in physics each year... Barley any of them.

Maybe I will reevaluate my passion for mathematics. But in the meanwhile, i still need to focus on passing this course. I'm doing extensive googling to find online books ect.

 

[rocomath]

I understand the proofs when I read them; I just can't apply them.

Say no more.

 

[zoner7]

ehh? is that supposed to me you have an answer and are about to type it up now? :) I hope

 

[Vanadium 50]

Usually, "I understand them, I just can't do them on my own" really means "I don't understand them but think I do." Recognizing that the problem is with understanding of the material is the first step.