Struggling with Advanced Calc: Should I Stick It Out?

[Howers]

Doing well in 2nd year but math is killing me. I've never been exposed to a course that is so theoretical. Its a multivariable course which emphasizes theorems and proofs. The proofs are a pain to work through, but I do understand the majority of them after several re-reads. I think there is a total of 3 I don't grasp.

Now the problem lies in the questions. Aside from the very few direct computational ones, I cannot answer any of the "Show that" or "prove that" ones. This usually ends up in me reading the solutions, then re-attempting the problem from scratch. The topological notations are also very technical and are its hard to develop an intuitive feel. The notatation is strange and there are virtually no diagrams to learn from.

I invest hours into this course but its not getting easier. My first assignment was a disaster, although its worth a tiny portion.

So my question is. Do I stay in the course? I really want to understand math but I don't know if all this theory is how I imagined it. Sometimes I sit at the book for like 5 hours per sitting. And I still can't answer most of the questions. Does one develop a "feel" for these questions after a while? Or do you need to develop them as a child? Its a year course so I don't mind staying for a while even if it means I end up with a B. But if it only builds from what I have a weak understanding of to begin with, I really can't risk a low mark. Then again, I really don't want to drop.

If you suggest I stay, can you please give me some advice as to how to solve Show that problems? I've been reading proofs and theorems for a month now and it hasnt helped.

 

[ice109]

what book are you using? understanding analysis by stephen abbott is supposed to be really good. there's also a lot of "how to write proofs" books

 

[mathwonk]

what book are you using? maybe we can recommend some better ones.

good ones include apostol, williamson crowell and trotter, courant of course, wendell fleming,

the main thing at fiorst is to grasp the idea of a gradient, or the derivative of a single valued function of several variables. it is a vector (or covector to be technical) whose entries are "partial derivatives.

it is the normal vector to the "level surface" of the function passing through the given point.

for proofs practice makes perfect. try reading some books on logic and proof, like allendoerfer and oakley, or even the first edition of jacobs' high school geometry book, not the third edition. consult my thread on who wants to be a... for references.

several people have written intro to analysis book designed to help with proofs, like arthur mattuck.

 

[leon1127]

If this is your first proof class, it might seem to be difficult because pre-college education doesn't really focus on proofs in america. I had the same situation too. The intuition you learn in proofs is very important for logical thinking.

 

[futurebird]

You are not the only one who has a hard time with this. At 27, I think.. Maybe I'm too old. But I'm an optimist, and when I looked back at a problem set from the first part of the course I was surprised to see that many of the hard problems seemed simple.

Maybe try that, it could boost your confidence.

Also I think for advanced calc, at LEAST 1hr per a page is normal, 5 for the really "bad" pages.

With me it's always the simple and "obvious" stuff that trips me up.

 

[Howers]

Folland's Advanced calculus is the text.

 

[PowerIso]

Ugh I used that text for multi variable, it's terrible. At least, it isn't a good book for an introduction to multi variable. I suggest you use the books mathwonk have listed.

 

[mathwonk]

and remember no one book is best for every topic.

 

[Asphodel]

Folland seems to have a knack for writing problems that you can figure out why the answer is what it is within a minute or two, but that then take a good 30-60 minutes to prove. ^_^

It's not that bad to read, but it's good to have other books around to look a topic up in if I'm not getting it. Not entirely helpful with doing proofs/homework given the time factor, but that seems to be something you just have to stick with and practice.

 

[SiddharthM]

i remember my first analysis class i was in the same situation. I ended up with a 45% on the first midterm (w/ the curve that was a C!) and after working much harder (like MUCH harder) i ended up acing the class.

You need to put in time and be patient because developing a knack for theoretical mathematics is generally very difficult. It will take some time for it to come. Don't get frustrated, and if you do, just think harder.

In other words, don't quit the class.