國立高雄大學圖資館 |

Language: English

Back

Algebraic curves and Riemann surfaces for undergraduatesthe theory of the donut /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Algebraic curves and Riemann surfaces for undergraduatesby Anil Nerode, Noam Greenberg.
Reminder of title:	the theory of the donut /
Author:	Nerode, Anil.
other author:	Greenberg, Noam.
Published:	Cham :Springer International Publishing :2022.
Description:	xvi, 450 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Curves, Algebraic.
Online resource:	https://doi.org/10.1007/978-3-031-11616-2
ISBN:	9783031116162$q(electronic bk.)

Algebraic curves and Riemann surfaces for undergraduatesthe theory of the donut /
Nerode, Anil.

Algebraic curves and Riemann surfaces for undergraduatesthe theory of the donut /[electronic resource] :by Anil Nerode, Noam Greenberg. - Cham :Springer International Publishing :2022. - xvi, 450 p. :ill., digital ;24 cm.

1 Introduction -- Part I Algebraic curves -- 2 Algebra -- 3 Affine space -- 4 Projective space -- 5 Tangents -- 6 Bézout's theorem -- 7 The elliptic group -- Part II Riemann Surfaces -- 8 Quasi-Euclidean spaces -- 9 Connectedness, smooth and simple -- 10 Path integrals -- 11 Complex differentiation -- 12 Riemann surfaces -- Part III Curves and surfaces -- 13 Curves are surfaces -- 14 Elliptic functions and the isomorphism theorem -- 15 Puiseux theory -- 16 A brief history of elliptic functions.

The theory relating algebraic curves and Riemann surfaces exhibits the unity of mathematics: topology, complex analysis, algebra and geometry all interact in a deep way. This textbook offers an elementary introduction to this beautiful theory for an undergraduate audience. At the heart of the subject is the theory of elliptic functions and elliptic curves. A complex torus (or "donut") is both an abelian group and a Riemann surface. It is obtained by identifying points on the complex plane. At the same time, it can be viewed as a complex algebraic curve, with addition of points given by a geometric "chord-and-tangent" method. This book carefully develops all of the tools necessary to make sense of this isomorphism. The exposition is kept as elementary as possible and frequently draws on familiar notions in calculus and algebra to motivate new concepts. Based on a capstone course given to senior undergraduates, this book is intended as a textbook for courses at this level and includes a large number of class-tested exercises. The prerequisites for using the book are familiarity with abstract algebra, calculus and analysis, as covered in standard undergraduate courses.

ISBN: 9783031116162$q(electronic bk.)

Standard No.: 10.1007/978-3-031-11616-2doiSubjects--Topical Terms:

190871
Curves, Algebraic.

LC Class. No.: QA565 / .N47 2022

Dewey Class. No.: 516.352

Algebraic curves and Riemann surfaces for undergraduatesthe theory of the donut /
LDR:02709nmm a2200325 a 4500 001 634541
003 DE-He213
005 20230116113209.0
006 m d
007 cr nn 008maaau
008 230529s2022 sz s 0 eng d
020 $a 9783031116162$q(electronic bk.)
020 $a 9783031116155$q(paper)
024 7 $a 10.1007/978-3-031-11616-2 $2 doi
035 $a 978-3-031-11616-2
040 $a GP $c GP
041 0 $a eng
050 4 $a QA565 $b .N47 2022
072 7 $a PBMW $2 bicssc
072 7 $a MAT012010 $2 bisacsh
072 7 $a PBMW $2 thema
082 0 4 $a 516.352 $2 23
090 $a QA565 $b .N451 2022
100 1 $a Nerode, Anil. $3 339405
245 1 0 $a Algebraic curves and Riemann surfaces for undergraduates $h [electronic resource] : $b the theory of the donut / $c by Anil Nerode, Noam Greenberg.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a xvi, 450 p. : $b ill., digital ; $c 24 cm.
505 0 $a 1 Introduction -- Part I Algebraic curves -- 2 Algebra -- 3 Affine space -- 4 Projective space -- 5 Tangents -- 6 Bézout's theorem -- 7 The elliptic group -- Part II Riemann Surfaces -- 8 Quasi-Euclidean spaces -- 9 Connectedness, smooth and simple -- 10 Path integrals -- 11 Complex differentiation -- 12 Riemann surfaces -- Part III Curves and surfaces -- 13 Curves are surfaces -- 14 Elliptic functions and the isomorphism theorem -- 15 Puiseux theory -- 16 A brief history of elliptic functions.
520 $a The theory relating algebraic curves and Riemann surfaces exhibits the unity of mathematics: topology, complex analysis, algebra and geometry all interact in a deep way. This textbook offers an elementary introduction to this beautiful theory for an undergraduate audience. At the heart of the subject is the theory of elliptic functions and elliptic curves. A complex torus (or "donut") is both an abelian group and a Riemann surface. It is obtained by identifying points on the complex plane. At the same time, it can be viewed as a complex algebraic curve, with addition of points given by a geometric "chord-and-tangent" method. This book carefully develops all of the tools necessary to make sense of this isomorphism. The exposition is kept as elementary as possible and frequently draws on familiar notions in calculus and algebra to motivate new concepts. Based on a capstone course given to senior undergraduates, this book is intended as a textbook for courses at this level and includes a large number of class-tested exercises. The prerequisites for using the book are familiarity with abstract algebra, calculus and analysis, as covered in standard undergraduate courses.
650 0 $a Curves, Algebraic. $3 190871
650 0 $a Geometry, Algebraic. $3 190843
650 0 $a Riemann surfaces. $3 247448
650 1 4 $a Algebraic Geometry. $3 274807
650 2 4 $a Functions of a Complex Variable. $3 275780
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 273786
700 1 $a Greenberg, Noam. $3 940993
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-031-11616-2
950 $a Mathematics and Statistics (SpringerNature-11649)