Encyclopedia of Mathematics? (non-alphabetical)

Do you know any encyclopedia of mathematics which is in non-alphabetical order, like it starts from basic mathematics and then goes up to very advanced level?

And what’s the difference between say, if I am studying calculus from a mathematical encyclopedia and if I am studying calculus from a university based calculus textbook?

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I would call such an encyclopedia a series of textbooks. I think the closest thing should be all the Elements of Mathematics books by Bourbaki. They start with simple topics like set theory and algebra that do not have any prerequisites and try to cover all those topics completely. Anyone who read them will however tell you that it is nigh impossible to learn something from them as a beginner, they are books that you read to further your knowledge in a topic that you already know or to look up general versions of some theorems.

Another thing with mathematics is that there is no real definite order of topics. There are obviously some dependencies, but in general some topics are just so highly interleaved that you have to take on both in parallel, while other topics are so far apart that you can do them in any order. However it is best to continuously revisit older topics anyway, because one always misses the details on the first try. There is also the fact, that it is impossible to know all of mathematics, there is simply to much of it. Even people who did nothing else than mathematics for decades will tell you that the topics of which they only know the basics far outnumber those they are comfortable in.

In general I would say, get some good textbooks. Not only for the order of topics but also for all the exercises in them. You can learn all the theorems, but without actually trying to use them you will not really understand them anyway.

You might be interested in Mathematics 1001: Absolutely Everything That Matters About Mathematics in 1001 Bite-Sized Explanations by Richard Elwes (Firefly Books, 2010).

The author’s website is here. A review can be found here. I have a copy of it and it’s extremely good. A high school student will be able to understand the first few paragraphs of each topic, and a smart undergraduate student will be able to understand the most difficult parts.

You can try with Encyclopedia of Mathematical Sciences. It is a multi-volume work of surveys, and some volumes start at an elementary level, like the one by Shafarevich on algebra. The whole work is not as elementary as calculus, though.