Learning Advanced Math During a Break

[Miike012]

The courses I've taken are algebra, trig, calculus 1 and 2 with analy. geometry and elementary linear algebra. Now that I have a three month break I plan on reviewing calc 1 and 2, and linear algebra. I would also like to learn a new topic but I don't know what subjects would be in my range of experience. I was thinking discrete math or set theory. Would those topics be difficult to learn on my own? Suggestions on other topics are welcomed.

 

[micromass]

No, it wouldn't be that difficult to learn on your own. Would you like book recommendations for the topics you listed??

Calculus: Now that you already know the basic calculus, I think Spivak is well within the range of your abilities.
https://www.amazon.com/dp/0914098918/?tag=pfamazon01-20

Linear algebra: Try Friedberg or Lang.
https://www.amazon.com/dp/0130084514/?tag=pfamazon01-20
https://www.amazon.com/dp/1441930817/?tag=pfamazon01-20

Discrete math: I learned the topic from Grimaldi's book and it was quite good. The book by Knuth is also quite popular.
https://www.amazon.com/dp/0201726343/?tag=pfamazon01-20
https://www.amazon.com/dp/0201558025/?tag=pfamazon01-20

Set theory: You probably mean a basic proof book. I think Velleman covers quite a lot of set theory so that would be a good first book.
https://www.amazon.com/dp/0521675995/?tag=pfamazon01-20

As for other topics. You might want to look at abstract algebra. A decent first book is Pinter: https://www.amazon.com/dp/0486474178/?tag=pfamazon01-20