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I'm currently studying an engineering degree and I got fascinated about math. The issue here is that I want a single source to learn mathematics; I mean, I want to learn every single math topic pretty well. I found the Encyclopaedia of Mathematics, Hazewinkel. This is a collection of 10 volumes and 3 supplements. I just want to know if you consider this worth it for 2300 usd. If not, what source could you recommend to me? I know I can read a lot of sources and learn math; however, I dream of buying a single source and learning all of it. Thank you :)

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    $\begingroup$ Although the index volume is not available, many contents (not the same) therein are available at https://www.encyclopediaofmath.org/. $\endgroup$ – Orat Dec 28 '16 at 6:49
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    $\begingroup$ There is no such tome that encompasses all of mathematics. I do not believe learning from such an encyclopedia would be fruitful. You'll basically be starting from A and reading towards Z with no cohesive learning strategy. $\endgroup$ – zahbaz Dec 28 '16 at 6:50
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    $\begingroup$ Honestly, I don't understand the downvotes. The question is well articulated, and tagged right. Just because it doesn't necessarily have a single/simple answer that's not a good enough reason to downvote. $\endgroup$ – dxiv Dec 28 '16 at 7:44
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    $\begingroup$ That reference work is very much aimed at university libraries. I would expect that the only individuals who own it are Professor Hazewinkel and his mother. $\endgroup$ – TonyK Dec 28 '16 at 12:16
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    $\begingroup$ Like MathWorld? BTW with $2300 you would pay around 2 years of tuition fees in several European universities (if you are an EU citizen, otherwise it might be more expensive). $\endgroup$ – Andrea Lazzarotto Dec 29 '16 at 1:09
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For $\$2,300$? No, that's ridiculous. I'd honestly just recommend wikipedia, this site, etc.; but if you want a single text, I'd recommend the Princeton Companion to Mathematics. It's written (and written well) by accomplished and knowledgeable mathematicians, and it's very readable.

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I suspect you have vastly underestimated the breadth and depth of mathematics if you think you can "learn every single math topic pretty well" from an encyclopedia or any other source(s), but I commend you for your enthusiasm and ambition. What you can do is use an encyclopedia (online or otherwise) or tome such as The Princeton Companion to Mathematics (or as an engineering student, perhaps also The Princeton Companion to Applied Mathematics) to get acquainted with what mathematics is out there. When you find a topic that particularly interests you, attend a course on it or get hold of a good textbook to work through - one appropriate for your level and background. Naturally, you will run into difficulties and have questions. That is when a site such as this can be very valuable.

Learning mathematics from an encyclopedia will give you only superficial knowledge of a wide range of topics. If you choose this approach, be aware of this limitation, and use it primarily for orientation purposes.

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You have everything online, and it's for free.

Buying a collection of 10 volumes and 3 supplements is most likely not going to get you to your designated goal in a more fast / simple / thorough manner.

If you could scan the entire data source and instantly convert that into conceivable knowledge within your mind, then maybe it would be preferable, because you've got a single source for everything.

But it doesn't usually work this way.

You have to read chapter by chapter, statement by statement, and then do some practical exercise for every new topic.

So I suggest that you just go one topic at a time, and just look it up on the web.

From my experience, Wikipedia, WolframMathWorld, WolframAlpha and this website are the best online resources available.

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    $\begingroup$ WolframMathWorld is certainly very rich but suffers from uneven quality, which is striking for some articles when you compare them with theequivalent Wikipedia article. Personaly, I would add "cut the knot" site (cut-the-knot.org) which stresses proofs which is a very good thing for learning mathematics. $\endgroup$ – Jean Marie Dec 28 '16 at 8:59
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I guess you are rather new to math. Consider this: the Dutch logician Evert Beth made a bold estimate of the extent of math knowledge. He guessed in 1947(!) that an academic math student would be offered just about 1% of the available knowledge. Davis and Hersh (The Mathematical Experience) estimated (in 1984) the number of theorems published every year at 200,000. So that is what you are up to if you want to learn it "all".

As mentioned by others you don't have to spend a penny to learn math. It is all available on the net. Forget encyclopaedia and single source, you need multiple sources: books, lectures, exercises and foremost practice, practice and practice. Check out MOOC: Edx.org, coursera.org, Khan academy, MIT OpenCourseWare. Lots of educators publish their lecture notes, look for .edu sites. Excellent for beginners: PDF lecture notes of Paul Dawkins.

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