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I'm an high school student who likes mathematics. So my question is the following. At this level of math is Wikipedia a good resource for expanding what I learn (e.g., I learn about something but I need to dig deeper)? At school for example I find these articles very interesting.

Trigonometric identities.

Complex number

Binomial theorem

and so on...

But I also like looking at some pieces of mathematics that aren't taught at school, like

Fibonacci number

and other articles... I also, of course, explore this site as well some youtube videos related to math (ex Numberphile on youtube)

So, let me reformulate the initial question. Is this "method" for learning math ok? I know that Wikipedia is not like a book for learning but quite often it has taught me something in a solid way. Also do you know other online resources, as well as books?

ps I'm not English (I'm Italian) so I made some errors

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  • $\begingroup$ Wikipedia is, in my experience, quite a good resource for looking up mathematics. $\endgroup$ – ÍgjøgnumMeg Apr 10 '17 at 19:38
  • $\begingroup$ Adams book on calculus I think is good for a high school student. $\endgroup$ – user392395 Apr 10 '17 at 19:39
  • $\begingroup$ There are online lecture notes on every subject in mathematics you would like to read, e.g., linear algebra, analysis, topology, geometry, abstract algebra, elementary number theory, etc. Start with any of these subjects. $\endgroup$ – Dietrich Burde Apr 10 '17 at 19:40
  • $\begingroup$ If you want something rigorous try out: Analysis with an Introduction to Proof: International Edition, 5/E. It was my first course at university. $\endgroup$ – user392395 Apr 10 '17 at 19:43
  • $\begingroup$ Wikipedia is great, but often I find better explanations on math.stackexchange and in good textbooks. $\endgroup$ – littleO Apr 10 '17 at 19:53
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The best method for learning at your level is to spend time thinking. While this sounds quite broad, it is the best advice that can be given. Let me elaborate. Say you are reading your textbook on quadratics. The author(s) defines a quadratic equation to be an equation of the form $$y = ax^2 + bx +c.$$ So instead of simply doing questions that test your computation ability, why don't you investigate what properties the quadratic has? For example, ask yourself, how many roots can an equation of this form have? You will find that it will have at most two (This is the fundamental theorem of algebra). Then you may proceed to ask, under what conditions do you have only one root, only complex roots, etc.

Then you may ask, how do I determine the gradient of such a function? This will lead to concepts of differentiation and calculus. Wikipedia is a good resource, but it should be used as more of a thought provoking resource.

EDIT: Also, a great thing I like to show kids that are in high school is something called modular arithmetic. You may enjoy this, https://en.wikipedia.org/wiki/Multiplicative_group_of_integers_modulo_n

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    $\begingroup$ @user49640 You have misunderstood what I have said. My advice wasn't to discover mathematics entirely. It is to work with the textbook and to try to at least discover some things for himself. I have been doing this for quite some time, although some areas are more difficult than others to do this, for example PDE, in most cases I can develop some basic ideas myself. $\endgroup$ – AmorFati Apr 11 '17 at 23:06
  • $\begingroup$ You're right, I missed the part of your answer where you mentioned working with a textbook. That being said, I still disagree with the idea that one can reasonably be expected to think of these things on one's own. If you're reading an algebra textbook, it's not particularly likely that you'll have the thought "How can I find the slope of a parabola at a point?" much less solve the problem. And it would be exceptional that out of the thousands of interesting little questions you can ask yourself, the one you pick would happen to be the basis for an entire branch of mathematics. $\endgroup$ – user49640 Apr 12 '17 at 0:33
  • $\begingroup$ @user49640 At a high school level this is quite difficult. At this stage, the biggest suggestion I would make would be to find a mentor who would help facilitate the discussion I initially mentioned. In saying this however, at a university level, this method of study should be the norm for growing mathematicians. $\endgroup$ – AmorFati Apr 12 '17 at 6:37

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