Making transcendence transparent : An intuitive approach to classical transcendental number theory

Includes Index

Preface : the journey ahead Number 0. A prequel to transcendence Number 1. Incredible numbers incredibly close to modest rationals Number 2. The powerful power series for e Number 3. Conjugation and symmetry as a means towards transcendence Number 4. The analytic adventures of e[superscript z] Number 5. Debunking conspiracy theories for independent functions Number 6. Class distinctions among complex numbers Number 7. Extending our reach through periodic functions Number 8. Transcending numbers and discovering a more formal e

The aim of Making Transcendence Transparent is to introduce readers to the major "classical" results and themes of transcendental number theory and to provide an intuitive framework in which the basic principles and tools of transcendence can be understood. The text includes not just the myriad of technical details requisite for transcendence proofs, but also intuitive overviews of the central ideas of those arguments so that readers can appreciate and enjoy a panoramic view of transcendence. In addition, the text offers a number of excursions into the basic algebraic notions necessary for the journey. Thus the book is designed to appeal not only to interested mathematicians, but also to both graduate students and advanced undergraduates.