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Need help - Developing a self study plan as a high schooler

  1. Jan 5, 2016 #1
    Currently a junior in high school taking Pre-Calc. Next year I'll be taking Calc 1, Statistics, and MAYBE Calc 2 (if it's offered in the second semester).

    I'm wanting to learn more math than I currently am however. I love math, and I want to have a very strong background before I go into college (where I will be going into engineering, which requires plenty of math). I want to start now, but I'm not sure what to do.

    I want to start self-studying/ reading up on college-level math. Is it possible to do this while still in the process of taking pre-calc? I've actually thought about starting to self-study Calc 1 at the same time as I'm taking pre-calc, even though I would be officially taking Calc 1 at my school next year. Is this a bad thing to do? I want to be self-studying math from now until when I graduate (3 semesters, one summer). I'm hoping to develop some sort of schedule that I can follow. I'm okay with some rigor and difficult subjects, as I am very disciplined and eager to learn more.. but I'm not a genius or anything (32 math ACT, 130 IQ).

    It was a little difficult to articulate my situation, but hopefully you get the gist. Can anyone help me?
  2. jcsd
  3. Jan 5, 2016 #2
    It wouldn't hurt to read ahead on calculus I suppose to get an idea of what it's all about, but I would seriously focus on building a strong background in algebra/precalculus before moving on. I believe this is where most people fail in calculus classes.
  4. Jan 5, 2016 #3
    Yes, there are plenty of self-study options open for you. Here are some options that you might want to look at:
    1) Calculus
    If you know trigonometry, basic geometry like equations of lines and are comfortable with algebra, then you will have no problem with calculus. I recommend the online free book https://www.math.wisc.edu/~keisler/calc.html It's an excellent book, with excellent explanations. It has the additional benefit that it treats the very important notion of infinitesimals rigorously, as opposed to other calculus books.

    2) Geometry
    The most important math book ever written is Euclid's Elements. Why not take some time going through this excellent book. You will become comfortable at proofs, geometry, and you'll gain a whole lot of maturity. The Elements is the book that almost every mathematician in the history has read, and it continues to be a beautiful piece of writing. I don't think anybody is really able to grasp the history of math without this book.

    3) Abstract Algebra
    Yes, abstract algebra. It is usually seen as something very difficult that people take only after calculus, but it can in fact be learned very early on. Calculus is not a prerequisite at all. Only a willingness to work hard is important. Good books are Pinter's "A book on abstract algebra", together with the very beautiful (but lacking enough problems) "Groups and symmetry" from Armstrong.

    4) Linear algebra
    I personally think linear algebra is somewhat more difficult than abstract algebra. But that doesn't mean you're not able to do it. You can start by learning about matrices, their operations, determinants, solving systems of equations. Then you can start with the really important stuff: vector spaces. Again, calculus is not a prerequisite here.

    Feel free to PM me if you wish to know more!
  5. Jan 5, 2016 #4
    Thanks for the info!

    I've heard that that calc book recommended plenty of times, and I'm definitely okay with going through it. However, how would you compare reading through that book versus doing a Calc 1 course through coursera (it's free) - https://www.coursera.org/learn/calculus1 [Broken]
    Last edited by a moderator: May 7, 2017
  6. Jan 5, 2016 #5
    I don't know about these precise courses, but I've always been very unimpressed with coursera as a formal learning device. It's great if you want to get the gist of something, but not if you want to know something well. In my opinion, it lacks many problems, a good feedback system and depth. You can do better for self-study. I guess as a secondary resource, it's ok. But going through an actual book is a skill on its own that needs to be mastered.
  7. Jan 5, 2016 #6
    Okay. I may start out taking a look at both then deciding which method of self-studying suits me better.

    Thanks for the advice
  8. Jan 5, 2016 #7
    At the risk of sounding annoying, but it's not about the method which suits you better. Of course, the coursera course will suit everybody better. But that doesn't mean that basing yourself primarly on coursera will be beneficial in the long run. It's not about "which method suits me better now", but about "which will get me the best results in the long run".
  9. Jan 5, 2016 #8
    I see what you mean.

    I'll self-study using Keisler's then (probably going to buy a paperback of it instead of using the online pdfs). Another question, do you think this book could be completed by the start of my senior year (one semester and summer)? I'd be most likely going through it 20-30 mins/day.
  10. Jan 5, 2016 #9
    No, at a rate of 30 minutes a day, you can't hope to complete this book in that timeframe. That is, unless you skip important things like the problems. Don't forget that Keisler covers calculus I to III in his book. So you're looking at three semesters of college-level material.
  11. Jan 5, 2016 #10
    OH I thought it was just Calc 1. I'm definitely okay with not completing it in that time-frame then.

    Would you happen to know which chapters are which calculus levels?
  12. Jan 5, 2016 #11
    Chapter 1-6 seems to be roughly Calc I
    Chapter 6-9 seems to be Calc II
    Chapters 10-13 are standard in Calc III
    Chapter 14 is something you might see in one of those three courses, but I don't know which one (probably calc II).
  13. Jan 5, 2016 #12

    Thanks a lot for the help.
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