Donaldson, Simon Riemann Surfaces

ISBN 13: 9780199606740

Riemann Surfaces

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9780199606740: Riemann Surfaces

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.

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Recensione:

This clear and insightful text, from one of the foremost researchers in the field, is suitable for graduate or advanced undergraduate course on Riemann surfaces, and will provide fascinating reading for professional mathematicians. ( L'Enseignement Mathematique)

L'autore:

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.

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Simon Donaldson
Editore: Oxford University Press, United Kingdom (2011)
ISBN 10: 0199606749 ISBN 13: 9780199606740
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Descrizione libro Oxford University Press, United Kingdom, 2011. Paperback. Condizione libro: New. 230 x 152 mm. Language: English . Brand New Book. 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. Codice libro della libreria AOP9780199606740

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Simon Donaldson
Editore: Oxford University Press, United Kingdom (2011)
ISBN 10: 0199606749 ISBN 13: 9780199606740
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Descrizione libro Oxford University Press, United Kingdom, 2011. Paperback. Condizione libro: New. 230 x 152 mm. Language: English . Brand New Book. 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. Codice libro della libreria AOP9780199606740

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Descrizione libro OUP Oxford 2011-03-24, 2011. Condizione libro: New. Brand new book, sourced directly from publisher. Dispatch time is 24-48 hours from our warehouse. Book will be sent in robust, secure packaging to ensure it reaches you securely. Codice libro della libreria NU-LBR-00902536

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Descrizione libro Oxford University Press 2011-03-24, Oxford, 2011. paperback. Condizione libro: New. Codice libro della libreria 9780199606740

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Descrizione libro OUP Oxford, 2011. PAP. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria FU-9780199606740

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Descrizione libro 2011. Paperback. Condizione libro: New. 153mm x 232mm x. Paperback. 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.Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 304 pages. 0.452. Codice libro della libreria 9780199606740

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Descrizione libro Oxford Univ Pr, 2011. Paperback. Condizione libro: Brand New. 1st edition. 256 pages. 9.06x5.98x0.71 inches. In Stock. Codice libro della libreria __0199606749

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