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How do I get better at math?

  1. Aug 19, 2014 #1
    Hi, I'm new to the forum.

    All throughout my childhood and elementary school I was very bad at math - probably the worst in the class - it just didn't interest me, so I never did my homework, and when I did, I didn't understand it. Now I'm in high school. The last 6 months I've had the obligatory math course on the lowest level (1), where I was lucky to finish with a D in oral and written maths. This was in part because I found it uninteresting, but mostly because I had a lousy teacher, and my class mates were a bit stupid.

    Wondering what to do with my life, I decided it would be a good idea to have just an average understanding of maths, so some months ago (to my own and my family's immense suprise) I decided to take it on level 2 (out of 3). Yesterday was my first lesson, and I liked it very much. We solved equations (which I never really learned) but it was not too hard.

    With that said, I want to become really strong in mathematics. I was wondering if there are any good learning resources (preferably free, but if not it's ok) on the internet for someone on my level. I'm basically bad at everything in maths. Any good books, videos, lectures, apps, I want them all. I would love to solve equations on a daily basis, so some websites that will give you equations and answers would be very good.

    Last thing, I've always wondered, and never really understood... how come maths fit with reality so well? How can we make predictions of the universe with a pen and paper, and have it fit with reality?

    Thanks so much and sorry for the long post.
  2. jcsd
  3. Aug 19, 2014 #2


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    Hello, and welcome.

    Try Khan Academy. Click on "subjects" at the top, and then "math". There's also a book called "Basic Mathematics" by Serge Lang that I've seen other people recommend, but I haven't even looked inside it, so I can't tell if it's at the right level for you.

    No one really knows. A partial answer is that there's so much mathematics that no matter what reality is like, there's going to be a piece of mathematics that approximates it. But that doesn't really answer why so much in reality can be approximated by pretty simple mathematics.
    Last edited: Aug 19, 2014
  4. Aug 19, 2014 #3


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    There is The World (out there) and all organisms living in it survive in part by actively modelling it and its changes in some sense. Animals model it neurophysiologically. The model has to really correspond in some way to the World Reality to work and to survive. In our case this is thinking about it. The math is not in the Universe IMHO, it is in our thinking. Or it is our thinking.

    But there is plenty of time to sort that out. More useful to you now I think will be:

    1. You already have one advantage: you are doing it not because you have to, and from sounder than usual motives, e.g. sound curiosity. The less you have to and the more don't worry about how your are doing, the more relaxed you can be, the better it will go, at least that's my experience.

    2 For a specific source about how to do it (and 'do it' not just 'learn it' is an important part) I strongly recommend Polya's "How to solve it" which I often mention in this forum. Short cheap book, but also come back to it after a year or two and then again.
  5. Aug 21, 2014 #4


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    you can only be good in math by practise, practise and practise just like in chess, no one can claim an understanding of mathematics as it is very wide, one may be good in abstract math but not in applied , though if given time he/she can understand the latter, in short a math proffesor in applied math may have difficulty in pure math and conversely, this may only be mitigated by putting time and practise in the area
  6. Aug 21, 2014 #5
    Timothy Gowers: Mathematics: A Very Short Introduction is v. good on this, and on Mathematics in general (including on what to read...) He's a Cambridge Professor & Fields medallist.
  7. Aug 21, 2014 #6

    jim hardy

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    Work tons of exercise problems. A good textbook author makes them demonstrate points one at a time and grows your knowledge. You have the luxury of time so you can work them all.

    Fifty years ago my textbook was "Calculus and Analytical Geometry" by Thurman S Peterson. It was an interesting book - the chapters alternated - one of math technique , the next one of practical real world problems using the technique just taught. I too suffered with math and thought his book hard at the time, but it was a useful reference the rest of my career.

    Probably somebody here knows of a more recent good book.
  8. Aug 23, 2014 #7
    It seems to me that you haven't identify your real problem yet. It is not common to be bad in "every" aspect of math. Some people are bad in algebra, but good in calculus, or the other way around, or they feel more confortable with numbers and values, or more confortable with abstract principles. Anyway, if you feel that you just can't solve any kind of problems, your issue is more likely to be with abstract principles. I do not think that there is any good and direct way to "understand equations" as you said. You just need to get the intuition and be able to compare it with actual theorems and ideas that you can use to solve problems. The best way to get the intuition is by listening very carefully to good lectures, try ocw of mit. Personally, I do not think anyone can learn real math from Khan Academy, but he is good in building the intuition.

    I use the software Mathematica like a second brain as a daily basis, you can start trying Wolfram Alpha. Anyway, you wouldn't know what to do if you haven't face problems that need to understand math principles. Try following an entire course from ocw mit from start to end, and use the textbook they recommend (I would start with single variable calculus), try to do every problem in the textbook, if after an hour your sheet is blank, look for the way to solve it in the internet, or check with wolfram alpha. The next problem woulb be easier to you, and you will build your intuition from time to time.
  9. Aug 23, 2014 #8


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    Math knowledge is cumulative. If you stumble on understanding the basic concepts of algebra, it is highly unlikely that you will be successful understanding more advanced math. I have yet to come across this mythical person who was 'good' at calculus yet had a poor understanding of algebra or trigonometry. If you are uncomfortable dealing with manipulating numbers (addition, subtraction, multiplication, and division), which is about as concrete as math gets, it is unlikely that you will be comfortable with, let alone grasp, the more abstract aspects of this field.

    The PF homework forums are chock full of examples of students who become stuck doing their homework because they lack fundamental math knowledge and skills, sometimes knowledge and skills which should have been mastered in elementary school, yet the student has not managed to grasp by the time he has entered high school or even college.

    In short, if you want to get better at math, start with the basics, work at them until you master them, and then move on to something more advanced. As always, work as many problems as you can, as this will broaden you experience in identifying and applying the math concepts which are useful at solving problems.
  10. Aug 23, 2014 #9
    Actually I was talking about comparing linear algebra with calculus, usually, in some places, when someobe begin his education , this two subjects are presented at the same time, and one can feel more comfortable with one rather than the other, but if you just can't get any of them, the problem can be dealing with abstract principles.
  11. Aug 23, 2014 #10
    Hello I thank of math as a discovery and you are right math is everywhere and that is why people should love it. Look in to physics more and you will see.
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