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Has anybody read Khinchin's book on continued fractions by dover publications? It's like a fantasy book in my eyes. I can read it twice a year and still get excited every time in the grand finale! And it's all pure mathematics - he develops the theory of continued fractions with integral elements from null to diofanat equations, best rational approximations and he even proves great results in measure theory (the final result at least was proven by him) and I just love it.

However, I can't find any books like this one - which talks about the throry of a specific, rather small field and shows the developments in the field as a true storyline, and yet all rigorous and consistent, from null to advanced topocs. Besicovitch's book "almost periodic functions" is another fine example of the kind of books I look for. Does anyone have any suggestions for such books?

My mathematical maturity is of beginner masters degree, and I would like my reading to be challenging.

Thanks in advance, Or

Or Kedar
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  • Ian Stewart Galois Theory (but avoid the third edition, apparently: https://mathoverflow.net/questions/29710/older-editions-of-which-books-were-better-than-the-new-ones?rq=1 ) – Elle Najt Jul 05 '17 at 08:49
  • Thanks! Actually, I'm gonna study galois theory next year in university. But this direction sounds good, any other recommendations on your mind? – Or Kedar Jul 05 '17 at 12:09
  • Maybe Guillemin and Pollack differential topology? – Elle Najt Jul 05 '17 at 13:00
  • You may get better answers if you narrow things down, your back ground, for example. The meaning of beginner masters degree is extremely wide and diverse... – Elle Najt Jul 05 '17 at 13:01
  • Okay thanks! Differential topology sounds good. And you're right, I didn't think of it. I finish now my first year in bachelor degree, but my mathematical maturity is much higher. I took introduction to topology, set theory, I've worked with complex analysis (wiener hopf technique - factorization into upper and lower half planes analytic functions), I am familiar with algebraic structures... even a topic in standard analysis such as almost periodic functions or continued fractions will be sufficient. – Or Kedar Jul 05 '17 at 13:53
  • Bromwich: Infinite Sequences And Series.... Carslaw: Fourier Series.... Coxeter: Introduction To Geometry.... Hobson: Trigonometry....Ahlfors: Complex Calculus.... – DanielWainfleet Jul 05 '17 at 19:55

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