Good and free books for a 17 year old

In short; money is really tight at the moment and need to save up for university. I'm a 17 year old student who have just finished basic multivariable calculus and differential equations.

I was wondering if you could recommend some free or very very cheap books, which have a reasonable standard. I'm mostly aiming for books covering either of these, but feel free to add others as well: Linear Algebra, Real/Complex analysis, Logic, (number theory, topology).

I am aware that free/gratis content might not be the best, and can be full of errors, but it's better than nothing, right?

Solution 1:

Everything by Robert Ash, especially Real Variables with Basic Metric Space Topology. It covers a substantial part of Rudin's Principles with more intuitive explanations and even (gasp) illustrations. I haven't really read his books on other subjects (complex analysis, algebra, probability, etc), but they appear to be of reasonable quality, and definitely free.

Solution 2:

I have used many of the free math textbooks on this page and found that they are generally good.

If you are looking to buy some cheap books, dover publishes a lot of math textbooks for $<\$10$ but you will have to investigate yourself to find out which of these are worth buying (a few are dry and dated).

Solution 3:

I am a big fan of Kenneth Bogart's Combinatorics Through Guided Discovery, freely available here. Combinatorics is a beautiful subject and the problem oriented approach is particularly well-suited for this field.