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Advice on Self Teaching Mathematics Please

  1. Jun 27, 2011 #1
    When I self-teach myself mathematics or physics for that case, I like to run through every single problem in the chapter. The outcome... teriible terrible pace...

    Is this necessarily a bad thing or a good thing?

    How do you guys study mathematics?

    In need of advice. Thank you.
     
  2. jcsd
  3. Jun 28, 2011 #2

    Stephen Tashi

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    You'd get better advice if you revealed the specific subjects you study.

    Most people progress slowly by self-study and faster by interacting with instructors and other students and keeping up with the hectic pace of a formal course. They may not learn the material as thoroughly in a formal course and are often forced to tackle topic B before they completely understand topic A. People who do self-study can avoid such discomfort, but, as you observed, they cover material more slowly.

    What is liable to happen when person does self-teaching in mathematics is that they find the formal definitions unsatisfactory and so they invent their own versions of what these definitions mean. This gives them a permanent disability in discussing mathematical ideas. People with such tendencies need a teacher!

    What are your objectives? For example, are you studying in order to pass a placement test or do well in a future course? There is a difference between understanding and drill. For example, one may understand how to solve maxima and minima problems, but a person who drills at this type of problem will do them quicker and do better on a placement test.

    My own interests are in specific practical problems. I tend to hunt down the mathematics needed to solve a practical problem, learn the applicable part as quickly as I can and only work problems in books if they look interesting or completely baffling. (I'm not trying to drill and I'm not studying for an exam.)

    While doing my daily physical exercise, I watch education DVDs about math, chemistry or foreign languages. I don't try to pay attention to every word. I listen to them over and over, Pehaps I learn a few things.
     
  4. Jun 28, 2011 #3
    I self taught myself for almost 2 years, it definitely goes much slower than being in a classroom. And this is with good reason because you don't have someone holding your hand through the material. Also you don't have the pressure of school driving you through problem sets.

    I recommend a tutor if you can't take classes right now because they will be able to guide you much better than yourself. Also, a good tutor will keep you motivated when things get kinda bland. For instance, when I used to meet with my tutor, he would show me things that were much more advanced. It was equivalent to learning a couple basics on an instrument and then seeing how it would fit into an entire song.

    When I was self studying I mostly worked on fun ideas. I would glance through my book and see a topic that looked interesting and play with it. If I needed more math I would learn the things I needed and then go back to that fun topic with more ammo. It made things feel more rewarding than just doing problem sets.
     
  5. Jun 28, 2011 #4
    Oops I thought I wrote down what subject. As of now I am self-teaching calculus. My objective is to breeze through my future calculus course and to master the art of solving problems. Throughout high school I've always slacked off in solving problems, and I want to catch up on my problem solving skills. I feel that if I keep doing calculus problems I will get smarter in how to tackle problems. And since I am a physics major I am well aware that math is the language of physics, so I would like to get as much mastery of math as possible.

    The problem though, I have a pretty slow pace going through all the calculus problem. For example, in the section I am in right now there are 104 problems. And since I've slacked off before it tends to take me a long while to figure things out as I try to build my base.

    By the way, do you pay for those educational DVD's or get them online?

    I can't afford a tutor, I am just self-studying so I can get a head start on my class and just for fun lol.

    I like the idea of the way you self-study but I don't know how it will work in calculus.
     
  6. Jun 28, 2011 #5
    Understandable. There's a lot of resources online for self studying. Youtube, Open courses at various universities, etc. Flip through any book or some lecture notes and you'll find something that interests you. Then find video lectures on that topic and go nuts. Some of the lectures I've found that made it seem like 10 self study hours to 1 hour of video. Ultimately, make it fun.
     
  7. Jun 28, 2011 #6
    I understand derivatives and I've watched MIT and khanacademy lectures, I just need to apply my knowledge. For that I need to practice and learn how to tackle these problems, which I use cramster to help (I have their membership).

    In case you don't know, cramster has the step-by-step solution to all the problems. Though sometimes I find it hard to follow the mathematical reasoning in how they got the step then the frustration begins. lol
     
  8. Jun 28, 2011 #7

    Stephen Tashi

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    The one's I watch while exercising are DVDs that I bought. They are rather light and superficial DVDs, mostly by "The Standard Deviants". (You can probably find them for sale used.) I watch other more serious DVDs when I want to give my full attention to material.

    Be sure to look in the "Math & Science Learning Materials" section of the forum.
     
  9. Jun 29, 2011 #8
    If you're trying to teach yourself calculus, try Spivak.....Very reader friendly, it's perfect for beginners.....the problems are nice. Supplement it with Courant and Hardy if you want more rigour. That's what I did.
     
  10. Jun 29, 2011 #9
    The big question though is if it is wise to go through pretty much every single problem or do enough to have a good understanding of the material. Maybe I should at least do every other problem (odds)?

    Eh maybe its a stupid question..
     
  11. Jun 29, 2011 #10
    This is a tough question to answer. Some authors leave significant results (results that other authors may write explicitly as theorems) as exercises. When reading the problems it can be tough to guage which problems are the most important. This is where a teacher helps.

    However, "self-teaching" is a very valuable skill. You won't always have somebody else to rely on.

    EDIT: Actually, your original question ISN'T tough to answer. You usually do not have to go through every single problem in a section in order to learn the material adequately. The question that IS tough to answer is "Which problems do I do?"
     
    Last edited: Jun 29, 2011
  12. Jun 29, 2011 #11
    I've been studying through a differential equations textbook because I'll be taking a course in it this fall. I do about ten problems per section, sometimes less, sometimes more. I'm not trying to master the material. I'm trying to understand it. You should too. You'll have to go through the course no matter what, so just do a cursory run through the material and you'll be just as golden as if you'd done every single problem.
     
  13. Jun 29, 2011 #12
    To stringy and angry citizen, I feel that if I do all of the problems then I will get better at math and physics as a result. I also feel that I will have a much easier time understanding further material and will have an easier time solving future problems as I build a good base.

    Thoughts?
     
  14. Jun 29, 2011 #13
    You'll be able to do even more problems when you're studying the material formally. By all means do more than necessary, but you're just self-studying right now. Go for breadth, not depth, at least for right now. That way you're very familiar with all the topics rather than intimately familiar with few topics, and clueless on others.
     
  15. Jun 29, 2011 #14
    Oh wow... pretty good point. Thanks!!

    So I was kinda wasting my time going through all the problems because its better to get yourself acquainted with the topics so you can get a better grasp of it later on and because the professor will help you problem solve later on as they lecture.

    So I'll skim on the topics now to be familiar and do all the problems for practice when the semester comes -- by then I'll probably go through the problems at a much faster pace.
     
  16. Jul 4, 2011 #15
    I'm in the same boat as Nano-Passion. I'd like to teach myself calculus. I'm a few years out of college, so I'm now brushing up on the prerequisites.

    It's been slow-going for me as well, but personally I've found that the hardest part is not self-motivation or knowing if you know the material, but finding the right resources.

    The best series of books I've found is the Master Math series (https://www.amazon.com/Debra-Anne-Ross/e/B002E428XW/ref=ntt_athr_dp_pel_pop_1). A mathematician from the 1990's named Morris Kline has also done some interesting work, and I may return to him.

    I've dabbled with the courseware at a website called Rapid Learning Center - the site has a good idea, but poor execution. I can't recommend it, but it's not worthless.

    I've also found that it's important to know how you learn. I read, create notes in PowerPoint slides that summarize the principles, constantly digest and synthesize the material, visually map it out, relate it to other areas I know, and then review it in some other form, book, or media. That tends to work for me. When I learn something that way, I know that I learn it, and it's personally rewarding.

    The internet is great as well for supplementary material, and in a sense it's made teaching professors less relevant. b/c when you have a problem, you can simply google it - even if you're studying graduate work, if you don't understand something, chances are it's a difficult concept, other people have had the same problem, and someone else has created an answer or video that makes sense. But the internet probably isn't sufficent alone to teach yourself math, b/c the info - even if it's in depth - is unorganized.

    I've sunk a lot of time in finding great reference books or even well-written textbooks. For me, it's clear that when I finally find the right ones, taking a formal course is not all that important. It's just that so many main-stream books are geared towards helping out with courses or tests, so good books are hard to find, but certainly exist.

    I find a lot of coursework boring and inefficient. I roll my eyes when I see an alphabetical list of key words at the back of a chapter. Key terms are necessary, but it's more to important to know principles, and how terms relate to principles - not how they relate to each other through their spelling.

    Anyway, that's just me. Would be interested in other resources, ideas, tips.
     
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