Studying tips for higher math (analysis, linear algebra, etc.)???

[BamBam215]

I can wing computational math easily by studying at the last minute. But my next few courses to finish my degree includes many many theoretical math classes (i.e. Real Analysis I & II, Linear Algebra, Abstract Algebra, etc.)

I am finding it very difficult to study for these courses, especially at the last minute. But even when I try to study ahead, it's very difficult to grasp a flow of what's going on. The proofs in these courses are the simple basic stuff that we use secondhand without much thought as to why they work, thus it becomes very difficult to prove. I know I'm supposed to basically "forget" and start from scratch. I'm supposed to gradually prove things and then use it later to prove other things. But it's difficult to keep track of what has been proven and what I can use. This is VERY difficult coupled with the fact that I now have to write and read in math symbols, makes studying very frustrating.

Can anyone who has suffered through these kind of courses give some tips on how you went about handling it?

 

[DrPizza]

Linear Algebra was a breeze..... abstract algebra required a bit of studying.... It was incredibly easy, once I figured out what it was that it was..... so simple, yet the profs made it seem much more complicated than it really was. Nonetheless, I had to figure a lot of that one out myself.... which meant a lot of time. I'd study with a group for any of those 3 classes... Do you have a "math clique" to hang out with? We had 10 students at the most in any of those classes.... studying together was a great help... someone always seems to understand a topic completely and can explain it to everyone else.... but no one ever seemed to be the expert a majority of the time.... we took turns quite a bit.

 

[BamBam215]

nah. throughout my years of college, i never really studied with groups. actually never ever did. whenever i try to study with friends, it was difficult to concentrate. i guess if it was with strangers, it'd be different. but i have grown accustom to studying alone.

 

[rob3rt]

i majored in math and i also found that study groups really helped out a lot. i'm not sure about your friends, but the people in my group were really smart and we also got distracted, but in the end we finished the weekly assignments. as far as doing it last minute, we did the same. i believe once a week we had an all-nighter to finish it up. if i had trouble understanding concepts they would help me out, and i would do the same if they were confused.

linear algebra is not that difficult at all and you wont need a study group. we had mentor sessions that were held once a week and those really helped me out, i'm not sure if you guys have that. abstract algebra was .... well pretty darn abstract and i HIGHLY recommend you work with someone else. i didnt take real analysis so i can't offer any advice, but if its anything like mathematical analysis, then GOOD LUCK!

i totally understand your feelings towards proving things are just too easy but hard to say on paper. if your linear algebra class is theoretical like mines was it will definitely help you in your proofs, which you will need for abstract algebra.

 

[BamBam215]

i should have paid attention in linear algebra I when it was still computational and i was introduced to some concepts. now in linear algebra II, it's all concepts wtf is a basis? ehe.

 

[eLiu]

Originally posted by: BamBam215 i should have paid attention in linear algebra I when it was still computational and i was introduced to some concepts. now in linear algebra II, it's all concepts wtf is a basis? ehe.

(layman's def) basis is the mininum number of vectors needed to express a vector space...then blah blah blah they have to be linearly independent...and blah blah blah all the vectors in the space are a linear combo of teh basis...i think that covers it...

anyway, linalg = EASY..like omg wow that was some dumb sh!t. Abstract Algebra isn't too hard until you get deep (graduate level)...and i have 0 experience w/analysis, so i can't help you there. Supposedly, the same skills that help you in abstract will help you in analysis--proofs, logical thinking, etc.

edit: abstract takes getting used to...like it's weird....hence the name. But once you figure out the basics...everything flows off of it. It's just like in calculus, once you understand the basics behind double, then triple integration...learning n-th dimensional integrals isn't that much of a stretch anymore, but learning double/triple was probably more difficult.

 

[BamBam215]

i mean i know what a basis is now but i went through the first year of linear algebra and passed the course without even knowing what it was. ahaha. abstract algebra is the final course in my major so im guessing it's the ultimate tough man course. i'll be happy with a D in that class (as long as i get a B in another class to average it out of course ).

 

[eLiu]

it's the last? Weird...it comes pretty early at NCSU...like before analysis, but after linalg. Just b/c it comes later doesn't mean it's hard. A lot of math courses are like, dependent on the person (for difficulty). Like my professor for calc3 said he tore apart stuff like abstract & topology..but analysis always had a way of kicking his ass. My teacher for calc BC (high school) couldn't stand/do abstract...but he was god at calculus/analysis. Soo...you just get to wait and see Best of luck...remember, math kicks ass

 

[ryzmah]

If you're not really gifted at theoretical math (proof-writing) I'd suggest taking it slowly. Make sure you understand the proofs you go through in class/text and then use that structure as a basis for your own proofs. Keep track of what you've proved thus far - that's what you can use in your later proofs. You'll pick up reading math symbols pretty quickly - if you're having trouble keeping up in class ask the prof. If you're not sure on writing, just keep everything in plaintext and try to convert it after you're done. Another thing to consider is asking grad students for help - it depends on you're school but it's likely that 1/4 of the math grad students are focusing on modern algebra.

 

[BamBam215]

i don't know why so many people say linear algebra is fun. the computational portion is relatively okay but the theoretical portion is dry as a mofo. it makes real analysis seems so much more fun.