Making Transcendence Transparent
An Intuitive Approach to Classical Transcendental Number Theory
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ISBN-13:
9780387214443
Veröffentl:
2004
Erscheinungsdatum:
28.07.2004
Seiten:
263
Autor:
Edward B Burger
Gewicht:
553 g
Format:
244x177x25 mm
Sprache:
Englisch
Beschreibung:
This is the first book that makes the difficult and important subject of transcendental number theory accessible to undergraduate mathematics students.
While the theory of transcendental numbers is a fundamental and important branch of number theory, most mathematicians know only its most elementary results. The aim of "Making Transcendence Transparent" is to provide the reader with an understanding of the basic principles and tools of transcendence theory and an intuitive framework within which the major results can be appreciated and their proofs can be understood. The book includes big picture overviews of the over-arching ideas, and general points of attack in particular arguments, so the reader will enjoy and appreciate the panoramic view of transcendence. It is designed to appeal to interested mathematicians, graduate students, and advanced undergraduates.
* A prequel to transcendence * Incredible numbers incredibly close to modest rational numbers * The powerful power series for e * Conjugation and symmetry as a means towards transcendence * The analytic adventures of exp(z) * Debunking conspiracy theories for independent functions * Class distinctions among complex numbers * Extending our reach through periodic functions * Transcending numbers and discovering a more formal e * Selected highlights from complex analysis
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