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I am a high student and doing the general math course at my high school, it will cover:

  • Geometry
  • Graphs and Relations
  • Matrices
  • Statistics

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 !!!

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    $\begingroup$ I would recommend you take Trigonometry, Precalculus, and Caclulus courses before you start university. Then take Calculus again at the university. For any science, calculus is the backbone of everything. The better you know it, the easier everything will be. This also applies for statistics. For online resources, Coursera is a good place to go. It wont make you an expert, but it will get you started. Also MIT OpenCourseware would be a good place to look for some basic classes. $\endgroup$ – Joel Apr 8 '15 at 15:11
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    $\begingroup$ You're best off looking at the universities/colleges curriculum for the maths and stats subjects. Then discuss it with someone in the maths and stats school at the university/college. $\endgroup$ – Mattos Apr 8 '15 at 15:11
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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:

Algebra2

Trigonometry

Precalculus

Differential-calculus

Integral-calculus

As for textbooks, for precalc I recommend:

  • Precalculus by Cynthia Young This is a fantastic, thorough textbook. I use this with my tutoring students.
  • For calculus, I like either Stewart's or Thomas'. Both are popular, so you may want to check with potential universities and just buy whatever text they plan on using to save some money.

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.

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  • $\begingroup$ Can I just use Khan Academy to learn everything under 'High School and Beyond'? What I mean is will KA teach me Calc I & II, Linear Algebra just as good as reading from a text book? Also after finishing KA can I go onto repeating what I learnt but this time through a text book? $\endgroup$ – George Apr 9 '15 at 5:42
  • $\begingroup$ In theory, sure. Sal Khan does a great job teaching the relevant concepts. But watching videos solely is not the best way to learn. You have to sweat. Read the books and work through exercises. It's often neglected by younger, sharp students who don't need the knowledge in their formative courses, but realize the concepts you'll be addressing will quickly grow in difficulty. The stronger your foundations, the more successful you'll be. If you can struggle through the proofs in your textbooks and understand them, you'll be serving yourself a huge favor. It's all about hard work :) $\endgroup$ – zahbaz Apr 9 '15 at 5:48
  • $\begingroup$ That's what I mean. I want to learn Pre-Calc, Calc I and II, Algebra II, Linear Algebra and Trigonometry through KA. But then go back and re-learn it through text-books? How many text books should I read on any given particular topic? You might say 'Until you get it', but I have noticed that even large, comprehensive books leave out different things compared to others. $\endgroup$ – George Apr 9 '15 at 6:18
  • $\begingroup$ It sounds like a good plan. Just find one comprehensive textbook per topic (Precalc, Calc, and maybe Lin Alg) and stick to it. If some explanation doesn't suffice, then search elsewhere. For a rough study plan, check out Young's Precalculus table of contents. Tackle the topics of Ch1-6, then approach 7,8,9,10 in whatever order best suits your needs. $\endgroup$ – zahbaz Apr 9 '15 at 6:40
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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.

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