Reddit reviews Calculus (Available 2010 Titles Enhanced Web Assign)

tl;dr: you need to learn proofs to read most math books, but if nothing else there's a book at the bottom of this post that you can probably dive into with nothing beyond basic calculus skills.

Are you proficient in reading and writing proofs?

If you aren't, this is the single biggest skill that you need to learn (and, strangely, a skill that gets almost no attention in school unless you seek it out as an undergraduate). There are books devoted to developing this skill—How to Prove It is one.

After you've learned about proof (or while you're still learning about it), you can cut your teeth on some basic real analysis. Basic Elements of Real Analysis by Protter is a book that I'm familiar with, but there are tons of others. Ask around.

You don't have to start with analysis; you could start with algebra (Algebra and Geometry by Beardon is a nice little book I stumbled upon) or discrete (sorry, don't know any books to recommend), or something else. Topology probably requires at least a little familiarity with analysis, though.

The other thing to realize is that math books at upper-level undergraduate and beyond are usually terse and leave a lot to the reader (Rudin is famous for this). You should expect to have to sit down with pencil and paper and fill in gaps in explanations and proofs in order to keep up. This is in contrast to high-school/freshman/sophomore-style books like Stewart's Calculus where everything is spelled out on glossy pages with color pictures (and where proofs are mostly absent).

And just because: Visual Complex Analysis is a really great book. Complex numbers, functions and calculus with complex numbers, connections to geometry, non-Euclidean geometry, and more. Lots of explanation, and you don't really need to know how to do proofs.

Two things:

1. Khan Academy!
   http://www.youtube.com/user/khanacademy#p/c/19E79A0638C8D449
   (I dunno why more people here don't seem to know about it).
   
   
2. Books, as mentioned.
   Personally I'd recommend these two:
   -http://www.amazon.com/gp/product/0470073330/ref=pd_lpo_k2_dp_sr_2?pf_rd_p=486539851&pf_rd_s=lpo-top-stripe-1&pf_rd_t=201&pf_rd_i=0471316598&pf_rd_m=ATVPDKIKX0DER&pf_rd_r=1S7Z2QKSMQM70SWRZQFT
   -http://www.amazon.com/Calculus-Stewarts-James-Stewart/dp/0495011606/ref=sr_1_1?ie=UTF8&s=books&qid=1279124596&sr=1-1
   
   You're probably gonna wanna go with earlier editions cuz they're way cheaper and say the same thing.

If you're trying to learn calculus on your own you're better off buying a used version of either of these books for cheap (or going to a library)


http://www.amazon.com/Thomas-Calculus-11th-George-B/dp/0321185587

or Stewart: http://www.amazon.com/Calculus-Stewarts-James-Stewart/dp/0495011606/ref=sr_1_1?ie=UTF8&s=books&qid=1268447623&sr=1-1

Schaums provides basic insight, and several practice problems. If you want to understand the theory, go for Stewart or Thomas.

You don't need to prepare, the placement test should put you in the class you need to be. Maybe brush up a bit on high school math (algebra/trig).

If you really want to get ahead, then Stewarts Calculus Book is a standard book that professors use.

I recommend Stewart's book for calculus. There are many computational problems and examples.
http://www.amazon.com/Calculus-6th-Edition-Stewarts-Series/dp/0495011606/ref=sr_1_2?ie=UTF8&qid=1371868204&sr=8-2&keywords=calculus+stewart
It's not too expensive if you buy it from an Amazon user. And the 6th edition will be fine. I actually like it more than the 7th edition.

One thing I found useful for doing this is Stewart's Calculus (many people will disagree with me here, but it was my old Calc book, so I didn't have to buy a new one, and I thought it was pretty decent). Don't worry about buying the latest version. you can probably find an old one in a used book store, or ebay or something, which will save you some bucks. The thing that kills Calc students is their poor algebra, so make sure you are rock-solid on that. You should be able to solve linear equations, quadratic equations, rational equations, and equations involving square-roots without a problem. You should also be able to graph all of these, and you should have a good understanding of exponents and logs. Don't spend much time reading the book, spend your time practicing, doing problem after problem until you really nail each one. If you can find a study-buddy, this will help a lot, as they will be able to point out where you are going wrong, and you will be able to teach them things (which is one of the best ways to learn).

Anyway, that's just some random advice, but I hope it helps. Good luck!

http://www.khanacademy.org/ is a pretty solid resource up through Linear Algebra. I'd recommend picking up a textbook in each subject so that you have a good list of examples and problems to work through to supplement Khan Academy. A used older edition of Stewart's Calculus would do good, it has everything as the newer ones and it is the standard calc textbook. Remember to keep doing problems, and don't stop, especially on the ones that are giving you the biggest headache! If you have any questions or problems ask /r/cheatatmathhomework or /r/learnmath.

Once you have an understanding of the basics, the MIT Open Courseware is a good source.

I would say that the best way to start is to pick a single book in Calculus, such as this or this or even this, and work all the way through it.

Then it is up to you; you could go straight towards Real Analysis; I recommend starting with a book that bears Intro in the name.

Or you could pursue a more collegiate curriculum and move onto Differential Equations and Linear Algebra, then Real Analysis.

I assume you are doing this all independently, so you should look at college sequences for math majors and the likes. You can mimic those, and look for online syllabi of the courses to make sure you are covering the appropriate material. This helps because it gives a nice structure to your learning.

Whatever the case, work through a calculus book, then decide what further direction you wish to take.

Sweet. I think the best curriculum to approach this with, assuming you're in this for the long haul, would be to start with building a good understanding of calculus, cover basic classical mechanics, then cover electricity and magnetism, and finally quantum mechanics. I'm going to leave math and mechanics mostly for someone else, because no textbooks come to mind at the moment. I'll leave you with three books though:

For Math, unless someone else comes up with something better, the bible is Stewart's Calculus

The other two are by the same author:

Griffith's Introduction to Electrodynamics

Griffith's Introduction to Quantum Mechanics

I think these are entirely reasonable to read cover to cover, work through problems in, and come out with somewhere near an undergraduate level understanding. Be careful not to rush things. One of the biggest barriers I've run into trying to learn physics independently is to try and approach subjects I don't have the background for yet: it can be a massive waste of time. If you really want to learn physics in its true mathematical form, read the books chapter by chapter, make sure you understand things before moving on, and do problems from the books. I'd recommend buying a copy of the solutions manuals for these books as well. It can also be helpful to look up the website for various courses from any university and reference their problem sets/solutions.

Good luck!