Functions of a Complex Variable
by Thomas S. Fiske
Publisher: John Wiley & sons 1907
Number of pages: 122
In the following pages is contained a brief introductory account of some of the more fundamental portions of the theory of functions of a complex variable. It is hoped that the present work will give the uninitiated some idea of the nature of one of the most important branches of modem mathematics.
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by Curtis McMullen - Harvard University
Contents: Maps between Riemann surfaces; Sheaves and analytic continuation; Algebraic functions; Holomorphic and harmonic forms; Cohomology of sheaves; Cohomology on a Riemann surface; Riemann-Roch; Serre duality; Maps to projective space; etc.
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The text for advanced undergraduates and graduates, it offers a concise treatment, explanations, problems and solutions. Topics include elementary theory, general Cauchy theorem and applications, analytic functions, and prime number theorem.
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