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I am currently in High School, possibly interested in pursuing a career in Mathematics or the Philosophy/Logic behind Mathematics. I don't have a lot of money for books or videos about Higher Mathematics, but I have been using Wikipedia to learn Maths.

I don't understand why nothing can be as concise and beautiful as Wikipedia. When we learned about functions in school, my teacher took an entire class just to explain them to us. He kept trying to use visuals and all these different tools to explain what a function is, and then, mildly confused, I looked up "function" on Wikipedia, and here is the definition I get:

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

I would much rather use Wikipedia to learn Mathematics, because of how concise it is. Sometimes I don't want to know every single thing about a function, I just want a sufficient definition.

Is there any encyclopedia or book that will have definitions and teach you Mathematics in this way? I'm not trying to sound egotistic. I am just a very fast learner and I would much rather blaze through a paragraph that explains things very concisely than spend hours learning the same material in different ways. Is Wikipedia good for learning Mathematics, or is there an alternative way to concisely learn what I want to know?

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closed as primarily opinion-based by Adam Hughes, jameselmore, Wojowu, JonMark Perry, Watson May 19 '16 at 18:13

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ No, wikipedia is not good for learn mathematics. Wikipedia is a compendium of facts and theorems and sometimes some proofs. The information is minimized and compressed, it is not good for learn something but it is good for searching information. $\endgroup$ – Masacroso May 19 '16 at 17:55
  • $\begingroup$ Wikipedia is fine for some things. I think the critical thing is to think hard about what you are learning. The key to that is doing plenty of problems, the harder the better. $\endgroup$ – almagest May 19 '16 at 17:57
  • $\begingroup$ Most math textbooks past calculus and "discrete mathematics" take this approach to definitions. A lot of people who are not so mathematically inclined find such definitions baffling, so teachers often need to give motivation. (I remember my frustration was in the supposedly "advanced" intro physics class in college, where we spent a class and a half talking about how to add vectors.) $\endgroup$ – Thomas Andrews May 19 '16 at 17:58
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    $\begingroup$ Possible duplicate of Are mathematical articles on Wikipedia reliable? $\endgroup$ – Wojowu May 19 '16 at 17:58
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    $\begingroup$ The accuracy of a wikipedia article on math is inversely proportional to its level. I'd be leery of the introductory articles on basic calculus and so on; but several of the K-theory pages,for example, were written by Andrew Ranicki himself. $\endgroup$ – anomaly May 19 '16 at 18:07
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Wikipedia is a good source for reminding yourself of definitions, and is generally accurate. However, learning math from Wikipedia is probably not a very effective strategy because it does not have a "path" for you to take and it is an extremely terse regurgitation of facts.

I would recommend the book "A Transition to Advanced Mathematics". Its pdf is freely available online and it provides a great introduction to proofs and basic set theory as well as some of the other foundational concepts in more advanced math.

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  • $\begingroup$ I'm only familiar with everything up to about an Intermediate Algebra class. I do have a book around the house called "What is Mathematics? Ideas and Methods". Do you think I am ready to transition to Advanced Mathematics right now? $\endgroup$ – user340812 May 19 '16 at 18:02
  • $\begingroup$ I think you should be ok. The book is relatively self-contained (it defines pretty much every piece of terminology it uses), and any algebra you would need is extremely basic stuff like how to FOIL, etc... $\endgroup$ – Ken Duna May 19 '16 at 19:53
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The others explained quite well how to use wikipedia. Good for you if you can get a good understanding of concepts only from definitions, it means you have good visualisation abilities. High school lessons are indeed full of drawings and examples (in some countries more than others), but the more advanced your classes are, the less explanations you will have. There will always be a point, though, where definitions will not be enough.

PS : I think you would be very interested in metamathematics (look up a little first order logic on wikipedia).

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    $\begingroup$ To the contrary, as classes get more advanced, you'll get more explanation and less detail (definitions and such). $\endgroup$ – Mariano Suárez-Álvarez May 19 '16 at 18:19

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