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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.


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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 '14 at 17:36

I would suggest these two books -



May be after that you can explore books suggested in other posts.

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If you have not already done so, find a book with a chapter on the logical (axiomatic) foundations of the real number system. It is often poorly taught or not taught at all and many people graduate high school with only a vague idea of why 1=(0.3333333....)x3=0.999999....... Also a chapter on the logical basis for the complex numbers will be helpful, eventually.Doing exercises and problems will likely help more than summarizing .Differential equations arise even in some of the most elementary physics so there's no reason not to learn some of the theory as soon as you know some basic calculus. I have yet to see a calculus text intended only for high school that was worth reading. APOSTOL, as cited in an answer above,is a good choice.Most if not all of the introductory books I learned from are likely out of print by now.

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I have some online mathematics exercises / tutorials (autocorrected), ranging from kindergarten to college, at:

Also, the material is public-domain. You can copy the entire website if you like and alter it to fit your own purposes.

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