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Learning How to Learn: How Do You Self-Study?

  1. May 2, 2009 #1
    I know that college is mainly about teaching yourself how to learn and study on your own. My question is; how do you teach yourself things like math or sciences? Obviously with a course, you read the textbook, do the problems, and take the tests. Self-study would probably be similar but without the deadlines and help of a professor or TA. I'm looking to self-study Calc II this summer, so any tips or experience would be greatly appreciated :)
     
  2. jcsd
  3. May 2, 2009 #2
    The first step is always do find a good text book that surveys the field you want to learn about. If you know the name of the field then this can be as simple as doing a search on Amazon and reading through user reviews. If you don't even know the name of the field, ask some professors. Once you have a book, you just have to read it.

    Sometimes when trying to learn a new subject you will encounter a part of the book that just doesn't make sense to you. It can be helpful to move on and come back to it because maybe later on something you read will clear it up. Take notes about the specific parts you had trouble understanding and make sure to come back to them. After isolating the specific problems you can maybe focus more on that part to figure it out. Also try googling the subject. If all else fails buy another book and read a different interpretation of the problem.
     
  4. May 2, 2009 #3

    Nabeshin

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    My advice would be try to discipline yourself. I honestly believe that a classroom style learning is a very good way to learn the material, so I try to simulate it as much as possible by trying to, say, read a chapter a week and do the associated problems (The problems are obviously necessary. You won't learn calculus if you just read the book, you've got to do it yourself). It works a lot better if you want to use the calc II for something too because you can diverge into your own interests and apply it to something that might be more interesting than cut and dry textbook problems (depending on the textbook though, there might be extended problems which are more like projects than exercises).

    That's my two cents, because I know for me if I don't have a fire under my *** I just sit around watching stargate all day :P
     
  5. May 2, 2009 #4
    Does this mean if I'm like 10% efficient at taking online courses, I will be miserable at a college setting? Man I hate online courses.

    Actually... it's not bad, it's just when I got to get through some random subject, I get slapped right across the face.
     
  6. May 2, 2009 #5

    fluidistic

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    If I wasn't studying in a University but rather self-studying maths/physics, I would check out the assignments students from big name universities get assigned and try to do them. (You can check this on the Internet). This goes along with reading books on the studied subjects. I would study the courses in a logic path, as Universities generally do.
    In both math and physics, the most important thing to my eyes is to do as exercises as one can.
    The only very big sad part of self-studying would be the lab part of physics. I don't know how it could be replaced. (By imagination? No... it cannot.)
     
  7. May 2, 2009 #6

    diazona

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    It is? ;-)

    When trying to teach yourself a math/physics-type subject, I think the most important thing is to do problems and work through the calculations and derivations yourself. Often you won't be able to understand something from just reading it; you really need to do it. Whenever I'm teaching myself something (or even taking a class) I usually try to rewrite the material from whatever textbook I'm using, filling in any steps I don't fully understand - it's kind of like writing a book of my own. It takes a lot of time but it's always tremendously helpful.
     
  8. May 3, 2009 #7

    chiro

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    I'm not sure if it relates to your course but Michael Spivaks Calculus on Manifolds is a great book if you have done some linear algebra know about sets and have done Calc I.

    The book is fairly thin but looks can be deceiving. Its essentially the material for an honours course in this material. Even if you don't get all of it straight away I'm sure that it will benefit you by being at least aware of the nature of how mathematicians "think" and that is important. Mathematicians have the tendency to generalize and abstract in very distinct ways and its these thought patterns that set a precedent for problem solving. Whenever you get a new way of analyzing or looking at something, that will become a valuable tool in your problem solving tool kit.

    In terms of self study I think the best thing to know that you're on the right track is to do one of the following:

    1) Do some exercises and see how you go with the solutions
    2) Have a stack of material all on the one topic and cross reference all material with other material so that you have a pretty consistent picture of what is being talked about

    Everyone has a different viewpoint on the subject. For example one person will teach trigonometry by just blurting out the sin cos tan ratios and then discussing a circle. Another will go into detail but outlining the ratios, the infinite formulas, the differential calculus, and summarize the whole thing but saying how all of these things are related to say the understanding of the world (take quantum mechanics and wave functions for example).

    In these two things there is a huge difference about what message is gotten across to the reader. One teaches you to memorize concepts and the other aims at giving you deep understanding. Although its hard to get deep understanding from most texts, the more you have the better chance you will obtain that.

    Thats also the benefit of being taught by a master. The master will have studied these particular topics and they will have gained insight into them in which their job is more or less to share that insight with their students so that they can carry on in a sense from where the master is leaving off. But I don't discourage you to learn by yourself because I applaud you for having the desire to do so. You're in a better position to gain more from both standpoints but with the wealth of material that has been written out there on every possible and probable subject, your bound to find at least one resource which can communicate our current understanding of a particular subject.

    Anyway I wish you well.
     
  9. May 3, 2009 #8
    If you can program, I'm a firm believer that there's no better way to thoroughly understand something, in-grain it in your memory, and at the same time highlight any possible misunderstandings you might have, than to write a generic program encapsulating the concepts and unit-test it.
     
  10. May 3, 2009 #9

    diazona

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    I'd agree with that ;-) I sometimes use that as a metric of whether I understand something - if I can program a computer to do it, it means I know how to do it. (And then I forget how to do it, because it's so easy to just delegate to the computer... that's the downside)
     
  11. May 3, 2009 #10

    Landau

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    I have always thought about doing this, but have never actually done it because it's so time-demanding. I am sure it will be very helpful!
     
  12. May 3, 2009 #11
    I have to second this technique. Trying to explain something in your own words can be difficult, but it's very rewarding, and (in my experience) you almost always notice some subtlety you didn't realize existed before.
     
  13. May 3, 2009 #12
    Definitely do what others have said and get a good textbook so that you can do the problem sets, etc. But, whenever I'm self-studying, I use as many resources as possible. For example, when I taught myself Calc I, I didn't even have a textbook, but I would read several, several websites about each topic. There's an abundant amount of material on the internet such as MIT's OpenCourseWare and even a bit of videos on YouTube.
     
  14. May 3, 2009 #13
    I hate to pull the "Feynman did that" cliche, but he did. He had many Math/Physics notebooks. I remember from the Surely You're Joking book, he said how he needed to write down everything he learned to really understand it. He came up with his own Trig Function names. Haha, love that guy.

    http://content.cdlib.org/view?docId=kt5n39p6k0&chunk.id=scopecontent-1.7.4&brand=oac

    -Check out "Working Notes and Calculations" section.
     
  15. May 3, 2009 #14

    Ben Niehoff

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    For learning mathematics, it's very important to practice by "playing" with the mathematics! When you learn a new technique, just try playing around with the formulas, applying it to different situations, ask yourself "What happens if I do X?", and then discover the answer.

    Try to come up with problems that are a bit of a challenge, just to see if you can figure them out. For example, if you had just learned integration by substitution, try playing around with different substitutions and see how complicated a function you can come up with and still integrate.

    Whenever your textbook says "We state the following without proof ...", have a shot at trying to prove those things. They might seem formidable (that's why they are left out of the book), but try them anyway. Ask yourself, how would I approach this problem? What do I know already, and what do I need to find out? How can I break it up into smaller problems? What happens if I try X? Experiment.

    When your textbook does give proofs, try to prove them yourself first! Refer to the textbook's proof when you get stuck. And see if you can think of any alternative methods to prove the same thing.
     
  16. May 3, 2009 #15
    The one thing I do find, is that you are only pretending you know something until you can solve the problems.
    You HAVE to go through the problem sets, even when just self learning, unless you are only learning as a preview for later course work in which case just looking through ideas suffices but is not optimal.

    Problems force you to cement your understanding. Do more, more, more, more problems.
     
  17. May 3, 2009 #16
    Often what's missing from self-studying is direction. It doesn't suffice to simply pick up a book and read it. It is completely inefficient. There needs to be specific, challenging yet achievable short term goals set. The class model is the ideal. The best to do is to look at a educational institution's schedule for a class covering most of what one wishes to learn and try to follow it as close as possible - also it is essential to do the exercises that are given in that particular class; the reason being that the instructor knows best about what kind of exercises best test and complement the course material, as well as which ones present a right level of difficulty.
     
  18. May 4, 2009 #17
    I have a Physics exam this month and I am doing self study for it. I have read Halliday and done its problems. But the level of the exam is really tough and only 7 people get selected out of 500. I have been doing problems from Irodov also. But some days I get really tired and start surfing the net thinking I know it all. I have got to stay focused but sometimes I am just not able to. And when I get back to study then problems that I had done easily earlier seem impossible and I have to pull myself together and read all over again and I get angry over myself for ignoring studies. Can anyone suggest something that might remedy my situation?
     
  19. May 4, 2009 #18

    Landau

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    For one thing, just lock yourself up for a few hours, maybe go to the library, any place where there is no distraction possible; forcing yourself to study.
     
  20. May 4, 2009 #19
    Haha, that's exactly what I do. My class textbook has excellent problems, but terrible chapters. Last semester I ended up using the Halliday/Resnick book as well as the Berkeley Physics Course vol. II in order to understand the concepts and get better derivations for things.

    Resnick/Halliday is very good for understanding the concepts, but applying them, its best to use your own class' text since your teacher picked it because he likes it and will probably use similar questions on the exam.

    Study in GROUPS, I find that helps immensely. So long as you don't get off task, it ensures that you're doing it right...
     
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