I'm in last middle school year and want to learn High School maths in depth — I want to grasp the behind the scenes and learn proofs. What are good books to self study HS maths this way? In what order should I study?

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    $\begingroup$ This depend on what your school teaches at the high school level. Have you taken a course in algebra? Does this answer your question? Good Pre-Calculus book? $\endgroup$
    – Brian
    Jan 20, 2020 at 22:26
  • $\begingroup$ I remember we had some books by Dolciani which were pretty good. $\endgroup$
    – user403337
    Jan 20, 2020 at 22:31
  • $\begingroup$ @Brian I'm ending with Bhaskara formula part of this year. I learnt just at this point (I don't know whether this is international order or not). $\endgroup$
    – user743574
    Jan 20, 2020 at 22:36
  • $\begingroup$ This is not a perfect fit, but you might take a look at The Art of Problem Solving, volumes 1 and 2. But keep in mind that these books are aimed at training Olympiad level problem solvers, and the problems you find in those books might be way, way more challenging than typical high school math problems. So you must never be discouraged if you struggle with them a lot. There are other textbooks from artofproblemsolving.com written in a similar spirit. $\endgroup$
    – littleO
    Jan 20, 2020 at 22:38
  • $\begingroup$ Gelfand's book Algebra looks like it might be good, but I haven't read it myself. $\endgroup$
    – littleO
    Jan 20, 2020 at 22:40

3 Answers 3


Much of high-school mathematics consists of learning technical prerequisites to calculus. To most students, this creates a false impression of what mathematics is: they come to think it consists of learning algorithms to be applied mechanically. One can avoid that while remaining within the curriculum provided one is careful to understand the reasoning involved. There are also books for high-school students that give a more realistic picture of mathematics, many of them found in good high-school libraries, some published by the Mathematical Association of America and some by others. One that I've liked since I discovered it when I was 15 is C. Stanely Ogilvy's Excursions in Geometry.


I add to the answer of Chris a very nice book in English language. I have discovered this morning that some examples are taken from my textbook in italian language.

The name of the book it is the necklace of JAMES STEWART

Here there is a preview of Algebra: https://www.stewartcalculus.com/data/CALCULUS_8E_ET/upfiles/6et_reviewofalgebra.pdf


We went prealgebra, algebra, Geometry, algebra ll, math analysis, calculus.

As mentioned I remember Dolciani et al.

When you get to calc try to remember Best and Penner. You'll love it.


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