Complex Functions: An Algebraic and Geometric Viewpoint

Gareth A. Jones; David Singerman

doi:10.1017/CBO9781139171915

'...a very nice treatment which emphasizes the unity of mathematics...Several years ago the reviewer wanted to teach an undergraduate course that gave an introduction to hyperbolic geometry, Möbius transformations and discrete groups. There was no suitable undergraduate text. This book fills that void,'

Source: Mathematical Reviews

'Well motivated with good selection of problems at the end of each chapter.'

Source: American Mathematical Monthly

'...clear and well written...Its message, admirably conveyed, is that mathematics is not a collection of neat parcels, the contents of one being blind to the contents of another.'

Source: Times Higher Education Supplement

'…clearly presented … a delightful book …'

Source: American Scientist

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Complex Functions

An Algebraic and Geometric Viewpoint

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Contents

Frontmatter
pp i-iv

Contents
pp v-viii

Introduction
pp ix-xiv

1 - The Riemann sphere
pp 1-16

2 - Möbius transformations
pp 17-55

3 - Elliptic functions
pp 56-122

4 - Meromorphic continuation and Riemann surfaces
pp 123-216

5 - PSL(2, ℝ) and its discrete subgroups
pp 217-270

6 - The modular group
pp 271-317

Appendix 1 - A review of complex variable theory
pp 318-324

Appendix 2 - Presentations of groups
pp 325-326

Appendix 3 - Resultants
pp 327-330

Appendix 4 - Modern developments
pp 331-333

References
pp 334-336

Index of symbols
pp 337-338

Index of names and definitions
pp 339-342

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