<p>I'm interested in learning some math over summer and during senior year.</p>
<p>I'm a high school junior who took calc BC and did pretty well. However, I'll be taking stats next year because my school doesn't offer multivariable. I considered the option of taking MV at the local community college, but the transporation + etc isn't feasible.</p>
<p>Nevertheless, I'd like to learn some math over summer and during senior year. I believe the course after calc BC is usually multivariable. However, I'm mostly interested in developing a strong math foundation for college classes. I've heard that linear algebra differs from calc, which is a lot of repetition.</p>
<p>What should I learn over summer to give me a small idea of what college math will be like? I found that calc BC was mostly learning formulas and applying them. Should I learn MV calc, or try linear algebra? Thanks for any help.</p>
<p>There’s no point in learning Multivariable Calculus without knowing some Linear Algebra. That is to say, if you want to learn some REAL Multivariable, some Linear Algebra is essential. I highly recommend the book by Hubbard and Hubbard. Great mini introduction to Linear Algebra and Multivariable Calculus, with random analysis stuff.</p>
<p>looking at the table of contents for that text, it looks a lot harder than a regular calculus III text. it looks completely self-contained, though, so in principle, you could learn from it. i wouldn’t worry too much if you don’t get a lot from it–there are classes in college where you learn this stuff.</p>
<p>if you decide to go this route, here are some notes for a multivariable calculus class that is in a similar style. they may be worth reading as a supplement to the above text:</p>
<p>I will agree with L’Hopital that linear algebra (as well as a rigorous course in single-variable calculus and basic topology) are essential for a rigorous study of multivariable calculus in n-dimensional space. However, I much prefer a concrete computational first exposure to the subject. I “learned” multivariable calc the rigorous way and got nothing out of the class, except a background in topology and practice with epsilon-delta proofs. I had to go back and study multivariable calculus concretely in 2 and 3 dimensions (using MIT’s video lectures, actually) before the abstract version made sense.</p>
<p>I strongly recommend MIT’s Open courseware. I have been learning physics on my own time for a couple months now, the database is extremely useful.</p>