Transcendental numbers

From Liouville's explicit constructions and algebraic heights to Hermite and Lindemann, auxiliary functions, elliptic transcendence, Roth's theorem, E-functions and algebraic independence.

1. Algebraic and transcendental numbers; Liouville's theorem
2. Heights of algebraic numbers
3. Hermite and the transcendence of e
4. Lindemann, pi and the Lindemann–Weierstrass theorem
5. Siegel's lemma, analytic estimates and the six exponentials theorem
6. Gelfond–Schneider and Hilbert's seventh problem
7. The Schneider–Lang criterion
8. Weierstrass functions, elliptic values and periods (in preparation)
9. Quasi-periods, complex multiplication and the modular invariant (in preparation)
10. The index method for rational approximation
11. Wronskians and Roth's rational-point lemma
12. Roth's theorem and its consequences
13. Mahler's classification of transcendental numbers
14. E-functions and the Siegel–Shidlovsky theorem
15. Algebraic independence and Schanuel's conjecture

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