Read Riemann Surfaces (Oxford Graduate Texts in Mathematics Book 22)

Riemann Surfaces (Oxford Graduate Texts in Mathematics Book 22)

Simon K. Donaldson

4.9/5 (28700 ratings)

Description: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, anddiverse 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 isnovel, 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.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Riemann Surfaces (Oxford Graduate Texts in Mathematics Book 22). To get started finding Riemann Surfaces (Oxford Graduate Texts in Mathematics Book 22), you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

Pages: —

Format: PDF, EPUB & Kindle Edition

Publisher: —

Release: —

ISBN: 0191545848

Description: 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, anddiverse 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 isnovel, 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.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Riemann Surfaces (Oxford Graduate Texts in Mathematics Book 22). To get started finding Riemann Surfaces (Oxford Graduate Texts in Mathematics Book 22), you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

Special Offer | $0.00

Special Offer! | $0.00

Riemann Surfaces (Oxford Graduate Texts in Mathematics Book 22)

Riemann Surfaces (Oxford Graduate Texts in Mathematics Book 22)

More Books

Riemann Surfaces (Oxford Graduate Texts in Mathematics)

Riemann Surfaces (Oxford Graduate Texts in Mathematics)

The Geometry of Four-Manifolds (Oxford Mathematical Monographs)

The Geometry of Four-Manifolds (Oxford Mathematical Monographs)

Geometry of Low-Dimensional Manifolds, Vol. 2: Symplectic Manifolds and Jones-Witten Theory (London Mathematical Society Lecture Note Series)

Geometry of Low-Dimensional Manifolds, Vol. 2: Symplectic Manifolds and Jones-Witten Theory (London Mathematical Society Lecture Note Series)

Geometry of Low-Dimensional Manifolds, Vol. 1: Gauge Theory and Algebraic Surfaces (London Mathematical Society Lecture Note Series)

Geometry of Low-Dimensional Manifolds, Vol. 1: Gauge Theory and Algebraic Surfaces (London Mathematical Society Lecture Note Series)

Floer Homology Groups in Yang-Mills Theory (Cambridge Tracts in Mathematics, Series Number 147)

Floer Homology Groups in Yang-Mills Theory (Cambridge Tracts in Mathematics, Series Number 147)

Different Faces of Geometry (International Mathematical Series, 3)

Different Faces of Geometry (International Mathematical Series, 3)

Geometric Analysis

Geometric Analysis

Tolkiens Erbe

Tolkiens Erbe

Selected Works (Springer Collected Works in Mathematics)

Selected Works (Springer Collected Works in Mathematics)