What is undergraduate math like beyond the calculus sequence?

[Pascal's Pal]

I currently attend a community college.

For several semesters I did poorly--failed one class and dropped out of a fair amount, but then I turned things around and consistently received decent grades. The track I am currently on is "Business Administration"--in short, I plan to study accounting, but I kind of don't want to go to college to merely learn a trade, so I want to supplement my job training with the acquisition of knowledge of eternal value. Math seems to fit this description.

When I was dropping classes, one class I dropped several times was Pre Calc with Trig. As much as I tried it seemed that I simply couldn't get the material. I guess the placement test was wrong or I wasn't trying hard enough. Anyway, for one semester I avoided it and simply got an intermdiate algebra textbook from my library and worked it cover to cover. I tried the course again and got an A, and afterwards I took Calc 1 and 2 and got As in them too. Currently I'm enrolled in linear algebra, and all the other math courses my community college offers (Calc 3, Diff Q) seem doable. In short, I'm sort of on a roll, but what is math like beyond the calculus sequence and is it doable for someone with mere average math smarts?

[PowerIso]

Well, I'm going to state this. Doing well in math has little do with natural ability but more to do with work. My example is a friend of mine who is absolutely brilliant in mathematics. He ended up failing Calc II with a 44. He did little work and it showed in his grade and in his understanding. He later retook the course and ended up with an A but only after he did all his work and went to class!

So Calc III and Diff Q are more than doable for someone like yourself (hey, I managed!).

As for the question presented in the title, the math because more complicated per se. It is less computational and more theoretical. As my professor told me in my first proof writing class, "Congratulations, you have moved passed engineering type math and into real math!"

Upper level math will require you to think harder than you had to before, remember a lot more, and understand basic logic. It takes a lot of hard work, but if you are willing to spend the time, you can do it.

[ice109]

proof based math is very little like the math you've been doing. in each section of problem in your calc book look for the ones that start with "prove that..." do a couple, if you enjoy it then you might enjoy pure math. personally i like reading proofs but hate doing em

[proton]

the appendix of your calculus book may cover a few of the proof techniques, such as induction, contradiction, contrapositive, etc. There should be example problems that use these techniques. Then, you can try to do problmes that involve proofs. Only problem is that the book doesnt give the answer for proof problems

[mathis314]

proof based math is very little like the math you've been doing. in each section of problem in your calc book look for the ones that start with "prove that..." do a couple, if you enjoy it then you might enjoy pure math. personally i like reading proofs but hate doing em

I'm actually just the opposite, i like doing proofs but it takes a lot out of me to read some one else's.

[PowerIso]

I'm actually just the opposite, i like doing proofs but it takes a lot out of me to read some one else's.

I agree. While doing a proof you can at least understand where you are coming from, while reading a proof by someone else, it takes a lot more effort to understand all the steps. At least for me. I used to hate reading proofs presented in my Calc book, because, at the time, I couldn't figure out how the writer was clever enough to prove the statements. Now, I understand more, but with my current level of math, I still feel, "how did this guy do it!?" Oh well, :D

[mathwonk]

undrgrad:

calc - diff eq - linear alg - sev vbls calc - series and sequences - proofs and logic - analysis (metric spaces) - groups, rings, fields - topology -

grad:
infinite diml linear alg (banach space) - measure theory - algebraic topology - homological algebra - dif geom/manifolds - alg geom, curves surfaces, abeian varieties, moduli - group reps - quantum groups - numerical analysis -------