A course in complex analysis and riemann surfaces (Record no. 55788)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03201nam a22002777a 4500 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20191022120725.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 191022b ||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470454722 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515.93 SCH |
| 100 ## - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Schlag, Wilhelm |
| 245 ## - TITLE STATEMENT | |
| Title | A course in complex analysis and riemann surfaces |
| Statement of responsibility, etc | / Wilhelm Schlag |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication, distribution, etc | Providence, Rhode Island |
| Name of publisher, distributor, etc | : American Mathematical Society, |
| Date of publication, distribution, etc | 2014 |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | xv, 384 pages |
| Dimensions | ; 27 cm. |
| 490 ## - SERIES STATEMENT | |
| Series statement | Graduate studies in mathematics, v. 154. |
| 505 ## - FORMATTED CONTENTS NOTE | |
| Contents note | From i to z: the basics of complex analysis --<br/>From z to the Riemann mapping theorem: some finer points of basic complex analysis --<br/>Harmonic functions --<br/>Riemann surfaces: definitions, examples, basic properties --<br/>Analytic continuation, covering surfaces, and algebraic functions --<br/>Differential forms on Riemann surfaces --<br/>The theorems of Riemann-Roch, Abel, and Jacobi --<br/>Uniformization.<br/> |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | Complex analysis is a cornerstone of mathematics, making it an essential element of any area of study in graduate mathematics. Schlag's treatment of the subject emphasizes the intuitive geometric underpinnings of elementary complex analysis that naturally lead to the theory of Riemann surfaces. The book begins with an exposition of the basic theory of holomorphic functions of one complex variable. The first two chapters constitute a fairly rapid, but comprehensive course in complex analysis. The third chapter is devoted to the study of harmonic functions on the disk and the half-plane, with an emphasis on the Dirichlet problem. Starting with the fourth chapter, the theory of Riemann surfaces is developed in some detail and with complete rigor. From the beginning, the geometric aspects are emphasized and classical topics such as elliptic functions and elliptic integrals are presented as illustrations of the abstract theory. The special role of compact Riemann surfaces is explained, and their connection with algebraic equations is established. The book concludes with three chapters devoted to three major results: the Hodge decomposition theorem, the Riemann-Roch theorem, and the uniformization theorem. These chapters present the core technical apparatus of Riemann surface theory at this level. This text is intended as a fairly detailed, yet fast-paced intermediate introduction to those parts of the theory of one complex variable that seem most useful in other areas of mathematics, including geometric group theory, dynamics, algebraic geometry, number theory, and functional analysis. More than seventy figures serve to illustrate concepts and ideas, and the many problems at the end of each chapter give the reader ample opportunity for practice and independent study. --Provided by publisher |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematics |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Analysis |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Riemann surfaces -- Textbooks. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Functions of complex variables. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Riemann surfaces. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Functions of a complex variable -- Instructional exposition (textbooks, tutorial papers, etc.) |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Functions of a complex variable -- Instructional exposition (textbooks, tutorial papers, etc.) |
| 700 ## - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Schlag, Wilhelm |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | Mathematics Departmental Library |
| Withdrawn status | Lost status | Source of classification or shelving scheme | Damaged status | Not for loan | Home library | Current library | Date acquired | Total Checkouts | Full call number | Barcode | Date last seen | Price effective from | Koha item type |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Dewey Decimal Classification | Mathematics Departmental Library | SNU LIBRARY | 22/10/2019 | 515.93 SCH | M029 | 22/10/2019 | 22/10/2019 | Mathematics Departmental Library |
