User pedro madrid - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T09:58:23Z http://mathoverflow.net/feeds/user/27601 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/110612/background-reading-for-proving-irrationality-of-real-numbers/110854#110854 Answer by Pedro Madrid for Background Reading for Proving Irrationality of Real Numbers Pedro Madrid 2012-10-27T20:30:49Z 2012-10-27T20:30:49Z <p>Thank you everybody for your valuable help. MathOverflow is a great place to learn! Definitely I'll open an account! I can see I'm getting good answers. </p> <p>Benjamin Dickman, thanks for suggesting me reading Sondow's article on the irrationality of $e$, a geometric approach. I downloaded the paper from arxiv. </p> <p>Robert Israel, I looked at Baker's book and it has the kind of things I'm looking for. I'll start with something more modest suggested by BSteinhurst. Then I'll switch to Baker. Thank You!</p> <p>Todd Timble and Quid, thanks for the reference on Michel Waldschmidt's webpage. Those are exactly the kinds of things I feel atracted to! I didn't knew about Schanuel's conjecture. Sure, I know many problems, specially those ones that are easy to understand, are extremely hard! Also usually those hard problems are not solved directly. Usually an equivalent statement is proved, where the equivalent statement requires high level mathematics like complex analysis, elliptic curves, ... (That's the good thing about abstractions, once they are constructed, there is more freedom to move, to think and to operate in the abstract setting and solve particular problems.). </p> <p>Alexandre Eremenko, I knew about Apery's theorem ($\zeta (3) \in \mathbb{Q}^c$). I have the paper too. The zeta function evaluated at positive odd integers is still a mystery. I didn't knew about Mahler, Shidlovski, Gelfond and Siegel (I saw those names in Michel Waldschmidt's webpage too). I'll keep this in mind to enforce my background. Thanks. </p> <p>BSteinhurst, thanks for the reference, looks a good start for me! I want to see historical context and ideas of the proofs. That book looks great! Soon I'll order it! Thanks. </p> <p>Andreas Holmstrom, thanks for Wikipedia's reference. The article I'll keep in mind in the future! </p> <p>I'm serious about this. I appeciate all your help. I have more than enough material to start working hard (of course, after defending my thesis). </p>