I am a high student and doing the general math course at my high school, it will cover:
Next year I want to enroll in a science degree and major in mathematics and statistics.
So I was wondering what I have to know to prepare adequately as the math I am doing won't suffice.
Also with the topics can you post learning material (links, books, articles, videos) and how good is Khan Academy?
Thank you very much !!!
For starting your mathematics journey you have to work on three areas which are considered as foundations for reading advanced math.
Linear Algebra, Calculus, Probability - These topics are essential for your future goals in your mathematical investigations.
For linear algebra, MIT courses are really good. There are bunch of books out there for linear algebra, like Here.
For calculus, you can read Thomas calculus. That's what I read calculus from as a starting point.Furthermore, you can go further and after finishing a introductory calculus book which teaches you the basic principles that whole subject floats on you can go and read a book written By Callahan which analyzes calculus from Linear Algebra point of view. This way you can improve your skills by learning the combination of both subjects. Indeed, linear algebra alone seems to be really abstract but if you apply it to other branches of mathematics then you find it really useful and you will get lots of insights about where and why(s) of the linear algebra itself.
For probability theory, again, there are tons of courses available online. Since you'll be a novice, I recommend you to get familiar with the basic definitions and principles of the subject before buying a thick book to start your journey through. A First Course in Probability by Sheldon Ross is among the classics. More info Here.
After having a decent knowledge of there areas, you can concentrate on whatever you want. Mathematics is vast. You can learn more about Combination of Differential mathematics with Calculus ideas called differential geometry.
Now it's time to prepare a pen and paper and do mathematics.
A strong base in Precalculus course (US curriculum) is highly recommended. It'd be nice to learn the basics of differential and integral calculus as well, but your university will certainly cover that.
Focus on learning precalc thoroughly, and if you have time, begin study of calculus. However, in college, as Joel commented, retake calculus from the beginning. It takes a bit of "mathematical maturity" to fully appreciate the subtleties of calculus. I've found a lot of students, very clever ones included, just want to bypass their course requirements, and as a result, they end up cramming too much calculus in too short of a time.
As for how to learn, you have some options. The ideal option is to hire a dedicated tutor to compose a curriculum and guide you through a textbook. If this isn't accessible, the internet has great resources. Khan Academy and PatrickJMT come to mind. You can always teach yourself, through a textbook, which would be doable for the Precalc material. However, at a high school level, I do recommend some direct guidance.
You mentioned Khan Academy, and I'll vouch for his videos. They're a great asset, and the bonus is that there's a message forum accompanying every video. KA has a pretty strong user-base, so you'll likely get good community response to your questions.
As a rough guide, you'll want to progress in this order:
As for textbooks, for precalc I recommend:
Read the textbooks. Outside of tutoring, outside of watching videos... read! It's challenging, yes, but it's so worth it. If you don't understand something, read it again. If that doesn't work, come here.
Expect to dedicate a minimum of six months for Precalculus study and six months for Calculus I. If time is of essence, don't try to cover everything, but rather work steadily through. Contact a university math adviser to inquire about their program. Remember, a college wants to help you succeed; the adviser will inform of what courses you'll need to take.
