I'm an undergraduate student in Mathematics who has to do a short essay about very basic Trascendental Number theory. In particular, I have to study the proof of trascendence of $e$ and $\pi$, and I was looking for some more advanced theorem to study: unfortunately all the material I find is too advanced/requires too much knowledge about analytic number theory. Do you know some introductive book about this subject/some -not too difficult- result I can study?

Thanks in advance =)

  1. The book https://books.google.co.in/books/about/Transcendental_Numbers.html?id=-4jkAwAAQBAJ&redir_esc=y, where some of the proofs are readable directly and appear to be elementary.

  2. Notes at http://www.math.nus.edu.sg/~urops/Projects/transcendental.pdf for transcendence of $\pi$.

  3. Notes at http://www.math.utk.edu/~freire/m400su06/transcendence%20of%20e.pdf for transcendence of $e$.

  4. Notes of Kannan Soundararajan for both at http://math.stanford.edu/~ksound/TransNotes.pdf covers the two proofs on pages 3 and 4.


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