A Course in Complex Analysis and Riemann Surfaces

Lingua: inglese

Editore: American Mathematical Society, US, 2014

0821898477 / 9780821898475

Serie: Libro 128 di 190 - Graduate Studies in Mathematics

Da: Rarewaves.com USA, London, London, Regno UnitoRarewaves.com USA

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Complex analysis is a cornerstone of mathematics, making it an essential element of any area of study in graduate mathematics. Schlag's treatment of the subject emphasizes the intuitive geometric underpinnings of elementary complex analysis that naturally lead to the theory of Riemann surfaces. The book begins with an exposition of the basic theory of holomorphic functions of one complex variable. The first two chapters constitute a fairly rapid, but comprehensive course in complex analysis. The third chapter is devoted to the study of harmonic functions on the disk and the half-plane, with an emphasis on the Dirichlet problem. Starting with the fourth chapter, the theory of Riemann surfaces is developed in some detail and with complete rigor. From the beginning, the geometric aspects are emphasized and classical topics such as elliptic functions and elliptic integrals are presented as illustrations of the abstract theory. The special role of compact Riemann surfaces is explained, and their connection with algebraic equations is established. The book concludes with three chapters devoted to three major results: the Hodge decomposition theorem, the Riemann-Roch theorem, and the uniformization theorem. These chapters present the core technical apparatus of Riemann surface theory at this level. This text is intended as a fairly detailed, yet fast-paced intermediate introduction to those parts of the theory of one complex variable that seem most useful in other areas of mathematics, including geometric group theory, dynamics, algebraic geometry, number theory, and functional analysis. More than seventy figures serve to illustrate concepts and ideas, and the many problems at the end of each chapter give the reader ample opportunity for practice and independent study.…

Codice articolo LU-9780821898475

Titolo
A Course in Complex Analysis and Riemann Surfaces
Autore
Wilhelm Schlag
Editore
American Mathematical Society, US
Anno di pubblicazione
2014
Condizione
New
Rilegatura
Hardback
Lingua
inglese
ISBN 10
0821898477
ISBN 13
9780821898475
Peso dell'articolo
846 grammi
Serie
Libro 128 di 190: Graduate Studies in Mathematics

Rarewaves.com USA

London, London, Regno Unito

Venditore con 5 stelle

Venditore AbeBooks dal 11 giugno 2025

Tariffe di spedizione da Regno Unito a U.S.A.

ArticoloDa 12 a 17 giorni lavorativiDa 12 a 17 giorni lavorativi
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