Im a junior in high school, since I was young I've had a profound interest in Math, and I'd always looked forward to high school mathematics. Little did I know, Special education had taken away what thought I'd be entitled to- A quality education. I had once been surrounded by brilliant minds that were far more capable than I was, and the rivalry between us had motivated us to get ahead of the class. I came from a private school in which the average student was 2-3 years ahead of any public school curriculum. Long story short, I'm in a public school with Adolescents that abhor learning, on a daily basis, they have the audacity to disparage their education. Though there are individuals who share a similar passion to my own, they are few in number. my high school years are drawing to an end, and I feel that its in my own hands to educate myself in the beauty that is math. In every class I understand the subject before the teacher can finish stating it, I learn much faster and retain much more info than my peers. They take notes – I don't, because I feel that learning comes from paying attention to whats being taught/conveyed to us during class.
My question is how would I teach myself? Only recently have I found out that there are holes in my knowledge due to my time in special education. I want to teach myself algebra 2 from the ground up, but where would I start? Every book I can get a hold of offers problems rather than concise explanations. I want to find a book, and price isnt an issue, that can teach me EVERYTHING about algebra 2. Afterwords, I'd like to know If I'd be able to do the same for pre-calculus and Calc itself. I feel that with dedicated study (2-3 hours a day) I may be able to finish calc by July/August… Maybe even sooner. But the books I have don't explain WHY you do things, just how. There are multiple occasions in which I question something I dont understand, but there is no explanation. The books I have rely on being active in class. I want to teach myself these simple mathematics, so if possible, please point me in the direction of a book that can convey algebra 2 from the ground up (not that I don't HAVE knowledge of the subject, It's just filled with holes of which I can't locate. I dont know what Im supposed to know, but I dont know WHAT IT IS im supposed to know. Its like finding a needle in the wrong haystack)
Best Answer
Something that I would keep in mind is that there are different philosophies about how one does mathematics depending on whether or not you are looking for applications in science/engineering/economics, OR if you want to study mathematics from a proof-based approach (which is how mathematicians typically approach the subject). It sounds like you want to understand why certain things are true as opposed to how to carry out computations. In order to do this (at least for calculus) you're going to want to study a subject called real analysis, which is essentially a proof-based approach to understanding calculus except that you look at topics from a much broader perspective. To learn this from self-study may honestly be an up-hill climb, but certainly not impossible depending on your interest and dedication. An important part of it is learning how to write mathematically. For a good gentle introduction to proof-writing and analysis I would recommend this this book. There are other good books on calculus which focus on a computational approach (I definitely would recommend both approaches to the subject), a great free one is by the famous MIT mathematician Gilbert Strang.
In terms of learning algebra II, I would just jump ahead in the book you're in. It's really not a subject that is understood from a proof-based mathematical approach (there is a subject called abstract algebra, but I really doubt this is what you want to learn right now; it's quite different than anything one typically encounters in high school, though I do know a good introductory book for it).