<p>So I have completed an AP Calc but I want to learn more math/ further calculus, proofs, analysis (great intersts of mine) how would i be able to further study this high school?</p>
<p>Well you could always self teach but are you interested in the actual course in high school or what?</p>
<p>Get Michael Spivak’s book “Calculus”. It’s a great transition to higher math and very well written. I also advise studying some linear algebra.</p>
<p>How do you know that book is good? I’m kind of interested in good math books too.</p>
<p>^Well, for one I worked through (most of) it myself, and it was a great way of getting familiar with proofs, especially since I had already seen the concepts in the non-rigorous “calculus for scientists/engineers” sequence. And it’s not just me - the book seems to be almost universally praised. </p>
<p>The reasons it’s so good is because it combines a conversational, easy going, and clear exposition with excellent problems. Lots of other books are good at one or the other. The exposition may be great, but the problems are “drill problems” that require little insight to solve. Or the exposition may be terrible or non-existent, even if the problems are great. </p>
<p>Spivak’s book, on the other hand, is very strong in both aspects. He writes in an extremely understandable style that’s enjoyable to read and easy to understand. Everything is well motivated, and the subject is developed in a way that always keeps the “big picture” in sight. You really get the sense of what calculus is all about after working through it, instead of just a bunch of formulas and theorems. </p>
<p>Of course, the most important part of any math text is the problems, and they are really excellent. Almost none of them require routine busy work to solve. They range in difficulty from fairly easy to extremely hard, but they are almost always interesting and REALLY deepen your understanding of the subject (as a good problem always should). Working through the majority of problems in this book is a great way to develop your math skills, both for calculus specifically and in general.</p>
<p>One thing I should probably mention is that Spivak’s book does assume you know how to write a proof, even your not necessarily that familiar with them. If you’ve never seen a proof before, you may want to look up some tutorials on the Internet or possibly skim through a book like Daniel Velleman’s “How to Prove It”.</p>