for a long time in the subjects of the university I learned to use complex numbers, to do derivatives, to sum series, and a lot more of things ...

To this day I use them, but as a tool, without really understanding the why of things, almost all the books I have used to learn, only teach you the method and tell you much above what is or is, but They do not explain why.

Some time ago I saw some pretty good books for statistics, but I would like to know if you know of a book that explains things well conceptually for other areas like calculation.

Any favorite book


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  • $\begingroup$ My advice would be to search on the forums, where many similar questions are answered. Also, evoking those questions too soon is not so easy (learning abstract algebra or functional analysis before real analysis is not really possible) $\endgroup$ – reuns Jan 22 '17 at 18:21
  • $\begingroup$ Hi eslop, by 'calculation' do you mean caculus? $\endgroup$ – shredalert Jan 22 '17 at 18:22

It sounds like you want a real analysis book, like Rudin's Principles of Mathematical Analysis.

You start off by assuming you know what the rationals are, then the real numbers. Then, proving a bunch of properties of real numbers, then rigorously defining things like continuity, differentiability, sums, integrability, etc.

  • $\begingroup$ Rudin's book actually assumes the rationals as given in constructing the reals... and also leaves some gaps for the reader to fill in. Moreover, Rudin's book would be challenging for a newcomer - to say nothing of it being exclusively dedicated to analysis. $\endgroup$ – Chris Jan 22 '17 at 18:21
  • $\begingroup$ @Chris - thanks, its been a while. The highlighted topics would be covered in a first analysis course though. $\endgroup$ – Batman Jan 22 '17 at 18:22

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