Self Studying Higher Level Math?

<p>Pretty much, next year I will have exhausted our school's math courses, with IB math HL, and senior year will be taking Calculus 2/3 up at the local community college. My question is, there isn't much...passion? drive? something like that..., in these classes, and I'd like to supplement whatever I'm learning in class with more diverse topics beyond the typical HS calculus track. </p>

<p>So basically, what I'm asking is, do you guys know any books I can use to study outside the typical calculus "box?" I'm currently using some MIT OCW videos to learn, but I learn better with a textbook... so any "classic" multi/linear algebra/diff equations books you guys can recommend? Thanks for your time!</p>

<p>[Amazon.com:</a> Elementary Analysis: The Theory of Calculus (9780387904597): Kenneth…](<a href=“http://www.amazon.com/Elementary-Analysis-Calculus-Kenneth-Ross/dp/038790459X/ref=sr_1_4?ie=UTF8&s=books&qid=1275283062&sr=8-4]Amazon.com:”>http://www.amazon.com/Elementary-Analysis-Calculus-Kenneth-Ross/dp/038790459X/ref=sr_1_4?ie=UTF8&s=books&qid=1275283062&sr=8-4) - Calc I & II. It’s an Analysis book, good place to go from Calc BC or IB HL if you want to study Math in college. I actually bought this book, I like it.</p>

<p>[Amazon.com:</a> Advanced Calculus of Several Variables (Dover Books on Advanced…](<a href=“http://www.amazon.com/Advanced-Calculus-Several-Variables-Mathematics/dp/0486683362/ref=sr_1_3?ie=UTF8&s=books&qid=1275283628&sr=8-3]Amazon.com:”>http://www.amazon.com/Advanced-Calculus-Several-Variables-Mathematics/dp/0486683362/ref=sr_1_3?ie=UTF8&s=books&qid=1275283628&sr=8-3) - Multivariable, you might find a better one out there, but this should be decent for self-learning above the level of a typical college course.</p>

<p>[Amazon.com:</a> Linear Algebra (9780486635187): Georgi E. Shilov: Books](<a href=“http://www.amazon.com/Linear-Algebra-Georgi-E-Shilov/dp/048663518X/ref=sr_1_2?ie=UTF8&s=books&qid=1275283245&sr=1-2]Amazon.com:”>http://www.amazon.com/Linear-Algebra-Georgi-E-Shilov/dp/048663518X/ref=sr_1_2?ie=UTF8&s=books&qid=1275283245&sr=1-2) & [Amazon.com:</a> Matrices and Linear Transformations: Second Edition (9780486663289):…](<a href=“http://www.amazon.com/Matrices-Linear-Transformations-Charles-Cullen/dp/0486663280/ref=sr_1_3?ie=UTF8&s=books&qid=1275283245&sr=1-3]Amazon.com:”>http://www.amazon.com/Matrices-Linear-Transformations-Charles-Cullen/dp/0486663280/ref=sr_1_3?ie=UTF8&s=books&qid=1275283245&sr=1-3) - Linear Algebra</p>

<p>[Amazon.com:</a> Linear Algebra: An Introductory Approach…](<a href=“http://www.amazon.com/Linear-Algebra-Introductory-Undergraduate-Mathematics/dp/0387909923/ref=sr_1_1?ie=UTF8&s=books&qid=1275283773&sr=1-1]Amazon.com:”>http://www.amazon.com/Linear-Algebra-Introductory-Undergraduate-Mathematics/dp/0387909923/ref=sr_1_1?ie=UTF8&s=books&qid=1275283773&sr=1-1) - Alternative Linear Algebra (I’ve seen this book, it’s very hard, but if you’re a very strong math student you might want to check it out.)</p>

<p>[Amazon.com:</a> Ordinary Differential Equations (9780486649405): Morris Tenenbaum, Harry Pollard: Books](<a href=“http://www.amazon.com/Ordinary-Differential-Equations-Morris-Tenenbaum/dp/0486649407/ref=sr_1_2?ie=UTF8&s=books&qid=1275283377&sr=1-2]Amazon.com:”>http://www.amazon.com/Ordinary-Differential-Equations-Morris-Tenenbaum/dp/0486649407/ref=sr_1_2?ie=UTF8&s=books&qid=1275283377&sr=1-2) - DiffEQ</p>

<p>All of those books should do a great job of putting you at a level ready for University level math as a math major.</p>

<p>Diversity can also include exploring earlier material at a much greater depth. Many students accelerate in math, but aren’t really strong at it.</p>

<p>Check out the Art of Problem solving books and website.</p>

<p>Thanks for the posts so far!</p>

<p>Your post Luminouzz, reminded me of another question I had.
I remember reading about the importance of learning proof based calculus, instead of the typical high school “plug in the numbers” method… any good texts for that?</p>

<p>Used to spend a lot of time on AoPS, but haven’t been as much recently… too much elitism a lot of times on the forums… xP just my opinion.</p>

<p>“I remember reading about the importance of learning proof based calculus, instead of the typical high school “plug in the numbers” method… any good texts for that?”</p>

<p>Absolutely that first book on my list. That’s what Analysis is.</p>

<p>Okay, I’m looking for where I can get it…textbooks are pricey.</p>

<p>Thanks for taking the time to help me out! Just an ignorant sophomore who would like to take a bigger leap into math!</p>

<p>Browse Dover’s website for something that looks interesting, since their books are cheap, and cross check for reviews on Amazon (and prices too).</p>

<p>I was actually going to buy a few til I realized that the UCLA library has just about all of them.</p>