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Can be able to learn a lot out of self-studing

  1. May 5, 2009 #1
    Lately I've been self-studying math in order to learn physics. Today, i just finished a 500 page book on algebra that I've been working on for a month and a half. There were problems and solution that i had to work through in order to understand. Now i feel like i learned a lot but one thing still bugs me. That is, since i'm going to move on to geometry then trigonometry then calculus and so on,,, will it be an effective way of learning. I know that you can learn a lot more in a class (well, at least i think you can) but i'm in grade seven so i have to wait a long time before i get there. I'm just really interested in these topics but i'm afraid if i learn only out of books, i might be wasting my time. So, can someone tell if keep studying the way i do, if i will be able to learn just as much as i would from a class. I'm a straight A student so understanding the content won't be that big of a problem, i hope. And can you tell me if i will be able to finish calculus and differential equations by the end of grade eight or even earlier. And yes i'm aware that there are different levels of algebra and calculus so can you also tell me what level should i have at the least before starting physics?

    Thanks for your patience and your help in advance!
  2. jcsd
  3. May 5, 2009 #2


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    No one here will be able to tell you that. I advice you not to worry about such things.
  4. May 5, 2009 #3


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    Self-study may not be quite as effective as a class but I certainly wouldn't say it's a waste of time. No reason not to keep going, as long as you're interested and are able to understand things reasonably well.

    It's certainly possible to study physics without knowing calculus - that's done in some high school classes and low-level introductory college classes (for non-physicists) - but the insight you can get without calculus is fairly limited. I wouldn't bother trying to learn physics once without calculus if you're just going to learn it again with calculus; better to become comfortable with the math first. (This comes from experience: in high school I took AP Physics B, a non-calculus based class, and except for being an easy A I think it was mostly a waste of my time.) Of course, you can start studying the physics and only look up the math as you need it, which is a decent way to go, but don't skip over mathematical concepts you don't understand.
  5. May 5, 2009 #4
    I agree with dx. Since you're only in 7th grade I would just fun with it and learn at your own pace. Why put so much pressure on yourself to learn what would be 2 years at the university level into 1 year at a young age?

    I find that I learn a lot self studying, but there have been times where I missed something very obvious because it wasn't spelled out to me as it would be in a classroom. When you're working on a topic try and find multiple resources to learn from. Different books, tutorials, youtube videos, etc. Good luck.
  6. May 5, 2009 #5
    I wouldn't focus too much on the physics that you'll be doing in a few years because you still have a lot of math to learn. You should learn to love the math because the math can as fun to learn as the physics and the ability to solve hard math problems will transfer to physics. Hopefully you're studying from a good, challenging textbook -- ie one that's not used in the average (American?) high school class -- because if you're not then the math can be entirely uninteresting. I also find that in order to master the material covered in high school without doing mindless repetition, the difficultly of the problems you solve needs to be higher because you'll be doing less of them.
    Last edited: May 5, 2009
  7. May 5, 2009 #6
    that's why i ask what math i need at the least for physics, because i want to narrow it down as much as i can (while not skip important information) so that i won't need to spend that much time learning math than i do physics. And yeah i do enjoy doing math it's like a hard problem to solve but i'd rather solve physics problems with them.
  8. May 5, 2009 #7


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    You could start with precalculus and then calculus (I and II). From what I've read here, it seems that trigonometry is a prerequisite for precalculus so be sure knowing it well.
    With that under your belt you can study introductory mechanics and even more. It's the very basic math needed to start physics seriously.
  9. May 5, 2009 #8
    well, really quantum mechanics and relativity are the subjects in my most interest. Although stating that, i would still love to learn classical mechanics because that's the only one i can actual use in my life right now. But how long might it take to learn the mathematics of these subjects, at the rate i'm going at?
  10. May 5, 2009 #9


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    I myself didn't reach QM! So I don't know what math exactly you need in order to study it.
    But I'm almost sure vector calculus is needed, a lot of DE and why not a bit of complex analysis. Ah, and certainly some probability along with linear algebra.
    I've no idea about Relativity. But a certain thing is that for both QM and Relativity you'll need to study mechanics formally, i.e.: the Lagrangian and Hamiltonian for example. This isn't covered in introductory courses, however it's still mechanics. A good understanding of classical mechanics is a must when it comes to QM and R.
    Hence beside a mathematical background, you also need some good physics background in order to study QM and R.
    It seems extremely hard to achieve before reaching university. Imagine if it's hard for many university students that study physics and math and nothing else, it can be only a very very very hard for a high schooler (but not impossible... well I think so) goal to achieve.
    Because if you're still in high school, I think it matters more to get good grades in all the disciplines you are taught than to study what you really love. You'll do that at university. My advice is take as much maths/physics as you can in high school and set your goal to enter a good university. Once you're there, don't worry, you will have to study what you love and you'll likely do well.
  11. May 5, 2009 #10
    Unless, of course you're a genius or a child prodigy. My biggest goal in life is to win a Nobel prize in physics and become bigger than Einstein. Imagine how impressive that would look on your résumé.:tongue2:
  12. May 5, 2009 #11
    Methinks Einstein would've spent more time studying and exploring and less time asking a million questions on internet forums.
  13. May 5, 2009 #12
    If your bigger than Einstein, you probably won't need a resume.:smile:

    Now, for your main post. You can learn a lot from self-studying. If you enjoy devoting your time to the subjects then continue doing it. If you want to learn introductory physics at the college level, you should at least have studied the following: algebra, geometry, trigonometry, and some calculus (general ideas concerning limits, derivatives, and integrals should be sufficient at first). One of the disadvantages with self-studying could be your choice of textbooks. The textbook may not be rigorous enough for subsequent subjects. Also, by using only one textbook per subject, you have a narrow perspective on the subject, so it may be beneficial to learn from a couple different ones (maybe one that includes a college text) for each topic.
  14. May 5, 2009 #13


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    You're getting ahead of yourself. Quantum mechanics and relativity isn't going to mean much to you without a real understanding of classical mechanics.
  15. May 6, 2009 #14
    But you haven't had the chance to see any significant part of either of these subjects! Don't be too set on specific subjects because you might glance over something that you like even more.
  16. May 7, 2009 #15


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    Even if you're a straight A student I can take a stab by saying that you won't really understand everything even if you aced a test on the subject. The amount of interplay between different fields in mathematics is increasing and knowing a concept may mean understanding it from a wide variety of analytical viewpoints.

    Also different authors have garnered different experiences while learning so remember that a multitude of books can be useful in really learning something as the author has the ability to apply their perspective to the student when they are learning. It's like the difference between one book that says sin(x) = opp/hyp and another book going into everything from rotations in the plane, to physics, to fourier analysis and PDE's to the series and every known relationship of sin(x). Thats a huge difference and depending on the author you can get big gains out of some materials.

    I remember reading Weinbergs book on QFT and in it he talked about the history of the topic which gave me a really good understanding of the material moreso than I saw in the other books to help prep me. Thats the kind of difference you can get in some books. It's like instead of going straight to the Schroedinger Equation in QM to first starting off with the postulates like E=hf and then slowly working through to the PDE. It might be subtle but to me its a huge difference.

    So I say yes, you have the ability to learn a tonne if you self study and that tonne can be beneficial if you do it right.
  17. May 7, 2009 #16


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    I personally have always thought going to class was a waste of time and rationalized it like so: how can a professor at an average school explain something, in an surprisingly short amount of time, better than a top mathematician/physicist book author who has meditated on the most efficient and clearest way to present the material?!

    You do not even need calculus to start learning physics. I think that you should start by reading the 3 books by H. Benson that will initiate you to mechanics, electromagnetics and modern physics (in particular relativity and QM). And for these you need only basic algebra and basic trigonometry.

    For a good grasp of QM, you need calculus, basic ordinary differential equations, linear algebra and classical mechanics (university level.. ex: Simons or Taylor or Goldstein, and preferably up to the hamiltonian formalism). Calculus is hard to master, but once this is done, differential equations is extremely easy. Linear algebra is a different kind of mathematics and it takes some time getting used to it but it's not very hard either.

    For relativity, you need mostly algebra and trigonometry, but also a bit of calculus. Also classical mechanics at the level of Benson but higher is better and optional but preferable is electromagnetics at the university level (Griffiths) and up to the study of moving electric charges.

    Good luck to you and don't hesitate to post questions in the forums if you have any.
  18. May 7, 2009 #17
    Thanks, i'm much more motivated than before. I would like to learn physics as descriptive as i can so i'm probably going to use more difficult math to do so. Can anyone tell me a good classical mechanics, electromagnetic, and modern physics books that use math more advanced than algebra and trigonometry maybe calculus, differential equations, etc. Also, is there any good calculus textbooks that you know. I'm not going to use most of these for a while, i'm just curios.

    And, i know this is really random but are physics professors considered physicist?
  19. May 7, 2009 #18
    The pitfall of self-studying is that you may learn things the wrong way, and it is often a lot more difficult to unlearn those things than to learn them correctly the first time. Especially since you're so young, you will likely not be able to see how others teach and learn those things, the isolation could mean you will be learning many things incorrectly.
  20. May 7, 2009 #19


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