Learning the "language" of math?

Oddbio

I just got a new book: "Mathematics for Physics and Physicists" by Walter Appel.
But, all the stuff in there is like another language to me almost. The thing is, that it actually seems quite basic and not too hard to understand (after I spend about an hour or so looking up notation and terms they use).

It starts off just going over the foundation of the integral, starting with Riemann sums and all that, but everything is done with set theory, and topological spaces, normed vector spaces, and a lot of symbols I'd never seen before.

To be honest, I'm not discouraged I think it would be awesome if I could learn this stuff, but it just begs the question.. why have I not been taught that stuff in school? I've already made it through Calculus 3 and differential equations but have never seen any of this. You'd think that it would be taught. What I'm covering now in the book is taught in Pre-Cal, but the way it's done here makes my Calculus 3 class look like 4th grade math.
Then on top of that, this book is supposed to be for physics students entering graduate school (which isn't too far off for me) and yet the book just starts using all of those math tools like if we should already know it.
The book was originally in French though, so perhaps it isn't catered to how dumbed down the schooling is over here in the US.

So I'm wondering, how did the rest of you learn those things? Right now I'm just looking each one up case by case on wikipedia.. I'm doing ok so far, but it would be nice if there was just a single source I could go to and read all about it and then tackle the book without having so many questions. Any ideas?

rochfor1

Take a nice introductory course to real analysis/read the textbook for one. You'll be swimming in norms and metrics and topologies.

rochfor1

Also,

Because you've only taken Calc 1-3 and Diff Eq. It's best to understand the most concrete examples before you generalize them.

Oddbio

Thank you for the reply.
I must admit that this post was probably 20-30% rant. I think I was just frustrated. But I'm doing better now :) I'll be taking applied analysis soon. Hopefully I'll see some more of this material.

rochfor1

Good. A decent real analysis course will go a long way towards answering a lot of your questions.

khemist

I am in a similar situation as yourself, taking calc 3 now and taking diff equations next semester. I was watching a video on quantum mechanics, and when I attempted to research the math a bit more, I found it was was over my head. I went to a local university library, UC berkeley in fact, and purchased a library membership. I left the campus with 3 books: elementary topology, hilbert spaces, and quantum field theory.

My guess is your school has a pretty extensive library. I would recommend going to the library within your math or physics department (if there is one). Just wander in areas that you find interesting, and pick out some books that you think you will like.

samuelarnold

My experience tells me that a very small portion of the population really understands what math is. Your work is one of few that brings the real process to an accessible level.

math4math

Go for the basics of, what you want to learn.

anonymity

All good advice. I personally agree with the notion that if you're interested in this new type of math, you should take an introductory proof course. Some schools throw you right into analysis or abstract/linear algebra, others will give you a more basic introduction to proofs in something like set theory and then let you decide if you wish to continue (ie, give you a topic that will allow you to focus on the methodology of proof writing, instead of smashing your head into the wall about the concepts, as well as learning "the language of mathematics" at the same time).

A great book, which I personally own and have seen recommended left and right on these forums, is "How to prove it"

http://www.amazon.com/s/ref=nb_sb_no...ove+it&x=0&y=0

Really good book and a great introduction to the methods of proofs and logical mathematics. I have not read it cover to cover, but don't regret the investment. It's a great reference, even if you don't read it word for word. But you certainly can if you want to see it NOW.

The book may be less rigorous than you would like (a motivated high school student or economics major is likely capable of reading and fully understanding it), but that may not be the worst thing, given your lack of background.

If this isnt your cup of tea, ask around for a good INTRODUCTORY book on proofs/set theory/linear algebra/analysis...