How to get "into" the math world

I only know about the high school bullshit. What books or sites would you recommend if I want to start to go deeper. I guess just as a general introduction or overview and also maybe some history. I don't know if it will help but I'm mainly interested in geometry, Trig, Calc and Astrophysics.

Then go to school.

>>1
Calc, trig, and geometry as you think of them (which is in the high school sense) are elementary and have little to do with what actual math is. The fields you will start to get into as an undergraduate math major are linear algebra, differential equations, real analysis, and abstract algebra. If you want to see what those are like, here are the books my college uses:

- analysis: Principle of Real Analysis by Rudin
- abstract algebra: Introduction to Abstract Algebra by Hungerford
- differential equations: Elementary Differential Equations by Boyce and DiPrime
- linear algebra: Applied Linear Algebra, by Shakiban

In real analysis, you will start with the definition of a set and work your way up to proving all the theorems you learned as "just true" in calculus. If you're interested in geometry, look into differential geometry. The book my school uses sucks, so you're on your own for that one.

>>3
couple typos, Principles* of real analysis and the second author of the diff. eqs book is DiPrima not DiPrime

>>3

Hey, I have Hungerford and Boyce/Diprima (I guess Boyce/Diprima is to Diff Eqs as Stewart is to Calculus 1).  As a lazy fool, I had to retake algebra, and on that go-round we used Gallian, an inferior text.

herstein's "Topics in Algebra" ftw, it's old as shit but still one of the better books out there, great exercies.

if you're gonna use boyce and diprima, get one of the earlier editions (2nd-7th), the later ones started dumbing a lot of shit down (they're up to about 37th edition now) and replacing insightful discussions with colorful pictures.