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Self studying math topics over the summer

by glen37
Tags: math, studying, summer, topics
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May12-10, 05:28 PM
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this year I finished calculus BC, which is the equivalent of calc 1 and 2. I feel as though I've completely mastered the material and I'm ready to start moving on before I enter university next year. The next math classes I'd be taking would be differential equations, calc 3 (multivariable calculus) and linear algebra and I'm looking to get a head start on them over the summer since math is what I really want to do. I don't want to buy any textbooks for them so does anyone know good online resources for these subjects?

also I feel focusing on all this calculus business may be boring at times over the summer so I'm open to any other mathematical subjects that are interesting and I can delve into at any pace I want.

anyone have ideas? these are some interesting lectures i'm looking at right now but I really want to have a strong foundation in these topics.
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May12-10, 05:33 PM
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I don't know about the other two, but I've watched some of Gilbert Strang's linear algebra lectures and they're quite good. My first exposure to linear algebra was a summer class (can it already be 20 years ago?) that used Strang's "Linear Algebra and Its Applications" as the text, which I enjoyed at the time:

I see that the online course includes three quizzes and the final exam, but I don't see any homework problems. (But check out the final exam: "closed book, ten wonderful problems.") You will probably want to find a good source of problems if you want to gain any mastery over the material. I don't know any good online sources offhand, but if you have access to a decent library you can always borrow Strang's book.
May12-10, 07:23 PM
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I feel as though I've completely mastered the material
You haven't completely mastered Calculus until you can do most, if not all, of Spivak's problems.

May12-10, 10:00 PM
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Self studying math topics over the summer

Quote Quote by thrill3rnit3 View Post
You haven't completely mastered Calculus until you can do most, if not all, of Spivak's problems.
This sounds like a good idea and I think I'll actually work through this book. Are there solutions?

Are there books similar to spivak for the other topics I listed that build up a strong foundation and focus on proofs? I'm really looking to prepare myself for undergraduate studies in math.

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