<p>Ok, so.. I've just been thinking.
After I finish Calculus BC this year.. I want to go even further into math.</p>
<p>However.. I don't just want a plug and chug course. I want a course that TEACHES me mathematics. Something that requires me to think, and has me use prior knowledge to do more complex things.</p>
<p>So what options are there?</p>
<p>Don’t you have an F in BC right now?</p>
<p>Raised it up.</p>
<p>Take linear algebra or differential equations and try seeing whether those are plug and chug courses.</p>
<p>After a certain point, they are. I want something different. Complex, mind-blowing.
I might as well do an AoPS course.</p>
<p>Get some good textbooks and read through them. The problem with taking “College-Level” classes in HS is that you can only do so at CCs and Junior Colleges which are highly unlikely to be proof-based never mind interesting… At the same time DO NOT SKIP MVC or Linear Algebra!</p>
<p>You’ll need MVC down pat before you should even think of analysis (I recommend Apostol’s books)</p>
<p>As for LinAlg, I recommend “Linear Algebra Done Right” by Axler. This book, more than teaching you Linear Algebra shows what a beautiful proof is.</p>
<p>to be honest, you’re not ready for “real” math. you have to get through all the plug and chug before you can move on to what “real math” is – proofs. so just take linear algebra, differential equations, and mutlivariable calculus and then you can move on to the “intro to real math” classes</p>
<p>It’s awesome that your school even offers anything after BC, mine doesn’t. I would suggest telling your guidance counselor how you feel and diving into your coursebook to see what you’re interested in. I’m sure you’ll find something great :D</p>
<p>I also recommend that you look at Maths Olympiad stuff, USAMO problems do not require anything that you do not know (the IMO does not require calc even) and are a way to get you to learn the art of proof (speaking of which "The Art and Craft of Proof by Paul Zeitz is a good book)</p>
<p>I do have AoPS books for the AMC and what not, but I’m looking for something more.</p>
<p>My local CC doesn’t even have MVC. I need to go find a college that offers it.</p>
<p>^ To whom is that comment addressed?</p>
<p>Really just in general, but the AoPS part was to you.</p>
<p>Also, my parents are sketchy on spending money for math books.</p>
<p>OK by Olympiad I was not thinking AMC… The AMC is mostly lateral thinking puzzles and some processof elimination. I was thinking USAMO stuff so that you actually do some proofs. As for the money for math books, you an always do what I did and get them off ebay. They version you get will probably be a Chinese knock-off but inside the cover it will be all the same stuff and it is far far cheaper than buying the textbooks retail (also even so, the textbooks will be way cheaper than signing up for the full class at a local school)</p>
<p>Ah, that makes sense.</p>
<p>I probably will end up self-studying those 3 courses, and doing the USAMO stuff.
I’ll look them up.</p>
<p>I don’t really see the point of working on USAMO type problems if you can’t qualify for it. Work on learning what you need for the AMC 12 and AIME first.</p>
<p>Take Diff Eq’s and Multivariable at a CC. Axler is a good book for Linear Algebra. Combinatorics is another subject that you could learn on your own before/while taking MV.</p>
<p>I have an electronic copy of Axler that I acquired for free. Not sure where I got it…</p>
<p>^ You and your pdf books… Did you at least print it of hole punch it and stick it in a binder?</p>
<p>There is no “after calc.” You just keep taking more obscure and less applicable math until your mind breaks and you spiral into an existential black hole from which you can never escape. Quantum physicists, people involved in the philosophy of AI, and angsty pseudo-intellectuals will all meet this same fate.</p>
<p>The thing is, math that is taught to most people is still in fact that “prior knowledge” advanced mathematics would require you to draw on. If you’re not going for advanced degrees in math or engineering, you most likely won’t be learning much more past diff Eqs (if you’re not in STEM, you probably don’t need to go past lin alg and multivar). Even for engineering mechanics courses that are heavy in applied math, it’s still usually plug-and-chug. You either need to look into AoPS stuff (if you’re looking for new ways to apply old ideas) or wait until you start going for your masters or Ph.D in math. </p>
<p>^ Did you know you can just buy hole-punched paper?! Cause I didn’t until this semester. Now I print out random crap and stick them in binders just because I can.</p>
<p>^ I actually did… I learned that last year when I wrote a supplement to go along side Rudin that was basically the same stuff rephrased to be far less terse.</p>
<p>Still, computers won’t print on it. At least they won’t adapt to the fact that there is a hole in the paper without making weird looking artificial margins.</p>
<p>I have 20 e-books, so the cost of printing them out is somewhat prohibitive.</p>