자료유형  

 단행본

International Standard Book Number  

9781400841714 (electronic bk.)

International Standard Book Number  

1400841712 (electronic bk.)

International Standard Book Number  

0691151199

International Standard Book Number  

9780691151199

Library of Congress Call Number  

QA343 .As987 2012

Dewey Decimal Classification Number  

515.983

Main Entry-Personal Name  

Ash, Avner , 1949-

Publication, Distribution, etc. (Imprint  

Princeton : Princeton University Press, 2012

Physical Description  

1 online resource (276 p)

General Note  

Description based upon print version of record.

General Note  

Epilogue

Bibliography, Etc. Note  

Includes bibliographical references and index.

Formatted Contents Note  

완전내용Cover; Title; Copyright; Contents; Preface; Acknowledgments; Prologue; PART I: DEGREE; Chapter 1 Degree of a Curve; 1. Greek Mathematics; 2. Degree; 3. Parametric Equations; 4. Our Two Definitions of Degree Clash; Chapter 2 Algebraic Closures; 1. Square Roots of Minus One; 2. Complex Arithmetic; 3. Rings and Fields; 4. Complex Numbers and Solving Equations; 5. Congruences; 6. Arithmetic Modulo a Prime; 7. Algebraic Closure; Chapter 3 The Projective Plane; 1. Points at Infinity; 2. Projective Coordinates on a Line; 3. Projective Coordinates on a Plane

Formatted Contents Note  

완전내용4. Algebraic Curves and Points at Infinity5. Homogenization of Projective Curves; 6. Coordinate Patches; Chapter 4 Multiplicities and Degree; 1. Curves as Varieties; 2. Multiplicities; 3. Intersection Multiplicities; 4. Calculus for Dummies; Chapter 5 Bézout's Theorem; 1. A Sketch of the Proof; 2. An Illuminating Example; PART II: ELLIPTIC CURVES AND ALGEBRA; Chapter 6 Transition to Elliptic Curves; Chapter 7 Abelian Groups; 1. How Big Is Infinity?; 2. What Is an Abelian Group?; 3. Generations; 4. Torsion; 5. Pulling Rank; Appendix: An Interesting Example of Rank and Torsion

Formatted Contents Note  

완전내용Chapter 8 Nonsingular Cubic Equations1. The Group Law; 2. Transformations; 3. The Discriminant; 4. Algebraic Details of the Group Law; 5. Numerical Examples; 6. Topology; 7. Other Important Facts about Elliptic Curves; 8. Two Numerical Examples; Chapter 9 Singular Cubics; 1. The Singular Point and the Group Law; 2. The Coordinates of the Singular Point; 3. Additive Reduction; 4. Split Multiplicative Reduction; 5. Nonsplit Multiplicative Reduction; 6. Counting Points; 7. Conclusion; Appendix A: Changing the Coordinates of the Singular Point; Appendix B: Additive Reduction in Detail

Formatted Contents Note  

완전내용Appendix C: Split Multiplicative Reduction in DetailAppendix D: Nonsplit Multiplicative Reduction in Detail; Chapter 10 Elliptic Curves over Q; 1. The Basic Structure of the Group; 2. Torsion Points; 3. Points of Infinite Order; 4. Examples; PART III: ELLIPTIC CURVES AND ANALYSIS; Chapter 11 Building Functions; 1. Generating Functions; 2. Dirichlet Series; 3. The Riemann Zeta-Function; 4. Functional Equations; 5. Euler Products; 6. Build Your Own Zeta-Function; Chapter 12 Analytic Continuation; 1. A Difference that Makes a Difference; 2. Taylor Made; 3. Analytic Functions

Formatted Contents Note  

완전내용4. Analytic Continuation5. Zeroes, Poles, and the Leading Coefficient; Chapter 13 L-functions; 1. A Fertile Idea; 2. The Hasse-Weil Zeta-Function; 3. The L-Function of a Curve; 4. The L-Function of an Elliptic Curve; 5. Other L-Functions; Chapter 14 Surprising Properties of L-functions; 1. Compare and Contrast; 2. Analytic Continuation; 3. Functional Equation; Chapter 15 The Conjecture of Birch and Swinnerton-Dyer; 1. How Big Is Big?; 2. Influences of the Rank on the Np's; 3. How Small Is Zero?; 4. The BSD Conjecture; 5. Computational Evidence for BSD; 6. The Congruent Number Problem

Summary, Etc.  

요약Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. The Clay Mathematics Institute is offering a prize of 1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem.The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from so.

Subject Added Entry-Topical Term  

Counting

Subject Added Entry-Topical Term  

Elliptic functions

Subject Added Entry-Topical Term  

Curves, Elliptic

Subject Added Entry-Topical Term  

Number theory

Subject Added Entry-Topical Term  

MATHEMATICS / Complex Analysis.

Subject Added Entry-Topical Term  

Elliptic functions.

Subject Added Entry-Topical Term  

Curves, Elliptic.

Subject Added Entry-Topical Term  

Number theory.

Subject Added Entry-Topical Term  

MATHEMATICS / Algebra / Abstract.

Added Entry-Personal Name  

Gross, Robert.

Additional Physical Form Entry  

Print version / Ash, AvnerElliptic Tales : Curves, Counting, and Number Theory. Princeton : Princeton University Press,c2012. 9780691151199

Electronic Location and Access  

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Control Number  

joongbu:423291