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Going to be starting grade 12 (pre-calculus) shortly and looking to get ahead. I would like to try some more rigorous stuff on my own and have a couple questions. Ideally I would like to be prepared for the math I will face in post secondary.

  • How can I get the most out of a math book, without a teacher?
  • Does summarizing chapters help?
  • Is it realistic to try and self teach myself up to differential equations?
  • What else should I be aware of when trying to self teach?

If anyone has good book recommendations from pre-calc -> differential equations I would enjoy suggestions.

-Thanks

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4 Answers 4

I think you could try Apostol's Calculus I and II. Both these books have a reputation for being amazingly clear, and they will give you an extremely good grasp of calculus. Vol I will introduce you to linear algebra, which you will need if you ever go beyond pre-calc. Vol II will cover multivariable calculus and some differential equations. Both books are long, but they're very well written!

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Concrete Mathematics: A Foundation for Computer Science would be my suggestion for a rather intense book but one that covers a number of areas within Mathematics at a rather advanced level at times though the book does have some humorous points at times.

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I basically taught myself calculus1-3 and differential equations back in college. I used James Stewart's book for Calculus and Zill's book for differential equations. However, when I reached Real Analysis and Abstract Algebra (courses mostly for math majors), I found it prudent to actually attend classes and take notes, as opposed to simply showing up for the exams when I took Calculus and Differential Equations.

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I've begun my own self-study/self-teaching of mathematics (here, in middle age). It's astounding how much can be forgotten in 20+ years, proving that math is one of those use-it-or-lose-it skills. Seriously, I've had to back all the way up to fractions. However, today, there are numerous resources that make learning on your own easier. I read reviews of textbooks (way too many) and study aids (and don't forget a workbook or two for practice-practice-practice), made wise decisions in which of those tools to arm myself with and am currently off and running. I have all I need to get through differential equations. My arsenal also includes the boon of DVD instruction. Of these, I might suggest the A+ Tutor DVDs (such as The Calculus I Tutor - search Amazon for any of them) and/or The Great Courses series (they have some awesome instructors on their DVDs - these are college profs, usually good ones). Being slightly dyslexic with a touch of ADD, I find it far easier to learn on my own than ever I did in a classroom - no time table, no pressure beyond my own discipline. And I love the DVDs - no college profs ever came with rewind buttons, and I can wear those puppies out, over and over, until it either clicks or finally sinks into my 46 y.o. brain. I say go for it - be resourceful in gathering your resources and don't forget to discipline yourself to actually sit down and do it. Give yourself goals and stick to your plan. You'll get there. Meanwhile, I plan on staving off the old-timer's disease (Alzheimer's) as loooooong as possible. Other people fancy retiring to make pottery and such. I plan on retiring and becoming a geologist - yeah, just for fun. Good luck, Kevin.

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Oh, yeah! And don't forget your TI calculator and a book (and/or DVD) on how to use it as well. You will need one. –  Middle-Aged in Memphis Feb 20 at 17:36

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