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- About this Textbook
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The theory of algebraic function fields has its origins in number theory, complex analysis (compact Riemann surfaces), and algebraic geometry. Since about 1980, function fields have found surprising applications in other branches of mathematics such as coding theory, cryptography, sphere packings and others. The main objective of this book is to provide a purely algebraic, self-contained and in-depth exposition of the theory of function fields.
This new edition, published in the series Graduate Texts in Mathematics, has been considerably expanded. Moreover, the present edition contains numerous exercises. Some of them are fairly easy and help the reader to understand the basic material. Other exercises are more advanced and cover additional material which could not be included in the text.
This volume is mainly addressed to graduate students in mathematics and theoretical computer science, cryptography, coding theory and electrical engineering.
- Reviews
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From the reviews of the second edition:
"In this book we have an exposition of the theory of function fields in one variable from the algebraic point of view … . The book is carefully written, the concepts are well motivated and plenty of examples help to understand the ideas and proofs and so it can be used as a textbook for an introductory course on the (classical) arithmetic of function fields with an application to coding theory." (Felipe Zaldivar, MAA Online, January, 2009)
- Table of contents (9 chapters)
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Foundations of the Theory of Algebraic Function Fields
Pages 1-44
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Algebraic Geometry Codes
Pages 45-65
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Extensions of Algebraic Function Fields
Pages 67-154
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Differentials of Algebraic Function Fields
Pages 155-184
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Algebraic Function Fields over Finite Constant Fields
Pages 185-215
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Table of contents (9 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Algebraic Function Fields and Codes
- Authors
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- Henning Stichtenoth
- Series Title
- Graduate Texts in Mathematics
- Series Volume
- 254
- Copyright
- 2009
- Publisher
- Springer-Verlag Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- eBook ISBN
- 978-3-540-76878-4
- DOI
- 10.1007/978-3-540-76878-4
- Hardcover ISBN
- 978-3-540-76877-7
- Softcover ISBN
- 978-3-642-09556-6
- Series ISSN
- 0072-5285
- Edition Number
- 2
- Number of Pages
- XIV, 360
- Additional Information
- Originally published in the series: Universitext
- Topics
