Riemann Surfaces
Mar 2011 · Oxford Graduate Texts in Mathematics Kitap 22 · OUP Oxford
3,7star
3 yorumreport
E-kitap
304
Sayfa
family_home
Uygun
info
reportPuanlar ve yorumlar doğrulanmaz Daha Fazla Bilgi
Bu e-kitap hakkında
The theory of Riemann surfaces occupies a very special place in mathematics. It is a culmination of much of traditional calculus, making surprising connections with geometry and arithmetic. It is an extremely useful part of mathematics, knowledge of which is needed by specialists in many other fields. It provides a model for a large number of more recent developments in areas including manifold topology, global analysis, algebraic geometry, Riemannian geometry, and diverse topics in mathematical physics. This graduate text on Riemann surface theory proves the fundamental analytical results on the existence of meromorphic functions and the Uniformisation Theorem. The approach taken emphasises PDE methods, applicable more generally in global analysis. The connection with geometric topology, and in particular the role of the mapping class group, is also explained. To this end, some more sophisticated topics have been included, compared with traditional texts at this level. While the treatment is novel, the roots of the subject in traditional calculus and complex analysis are kept well in mind. Part I sets up the interplay between complex analysis and topology, with the latter treated informally. Part II works as a rapid first course in Riemann surface theory, including elliptic curves. The core of the book is contained in Part III, where the fundamental analytical results are proved. Following this section, the remainder of the text illustrates various facets of the more advanced theory.
Kullanıcı puanları ve yorumlar
3,7
3 yorum
Yazar hakkında
Simon Donaldson gained a BA from Cambridge in 1979. In 1980 he began graduate work in Oxford, supervised by Nigel Hitchin and Sir Michael Atiyah. His PhD thesis studied mathematical aspects of Yang-Mills theory. In 1986, aged 29, he was awarded a Fields Medal and was elected to the Royal Society. He was Wallis Professor of Mathematics in Oxford between 1985 and 1998 when he moved to Imperial College London. Most of his work since has been on the interface between differential geometry and complex algebraic geometry. The recipient of numerous awards, including the Shaw Prize in 2009 with Clifford Taubes, he is also a Foreign Member of the US, French & Swedish academies. Donaldson has supervised more than 40 doctoral students, many of whom have gone on to become leading figures in research.
Bu e-kitaba puan verin
Düşüncelerinizi bizimle paylaşın.
Okuma bilgileri
Akıllı telefonlar ve tabletler
Android ve iPad/iPhone için Google Play Kitaplar uygulamasını yükleyin. Bu uygulama, hesabınızla otomatik olarak senkronize olur ve nerede olursanız olun çevrimiçi veya çevrimdışı olarak okumanıza olanak sağlar.
Dizüstü bilgisayarlar ve masaüstü bilgisayarlar
Bilgisayarınızın web tarayıcısını kullanarak Google Play'de satın alınan sesli kitapları dinleyebilirsiniz.
e-Okuyucular ve diğer cihazlar
Kobo eReader gibi e-mürekkep cihazlarında okumak için dosyayı indirip cihazınıza aktarmanız gerekir. Dosyaları desteklenen e-kitap okuyuculara aktarmak için lütfen ayrıntılı Yardım Merkezi talimatlarını uygulayın.
