Polynomial Diophantine Equations (Record no. 62966)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03602nam a22004695i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-031-62949-5 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20251030112928.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240901s2024 sz | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9783031629495 |
| -- | 978-3-031-62949-5 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1007/978-3-031-62949-5 |
| Source of number or code | doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA241-247.5 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBH |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT022000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBH |
| Source | thema |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Grechuk, Bogdan. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) | 83419 |
| 245 10 - TITLE STATEMENT | |
| Title | Polynomial Diophantine Equations |
| Medium | [electronic resource] : |
| Remainder of title | A Systematic Approach / |
| Statement of responsibility, etc. | by Bogdan Grechuk. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. 2024. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Cham : |
| Name of producer, publisher, distributor, manufacturer | Springer International Publishing : |
| -- | Imprint: Springer, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2024. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | XXII, 807 p. |
| Other physical details | online resource. |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS | |
| File type | text file |
| Encoding format | |
| Source | rda |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 1 Explicit Solutions to Small Equations -- 2 Existence of Polynomial Parametrizations -- 3 Equations in Two Variables -- 4 Explicit Descriptions of the Solution Sets -- 5 The Finiteness Problem -- 6 Existence of Non-Trivial Solutions to Homogeneous Equations -- 7 Existence of Integer Solutions -- 8 Alternative Orderings of Diophantine Equations -- 9 Solutions to Selected Exercises (by Ashleigh Wilcox). |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | This book proposes a novel approach to the study of Diophantine equations: define an appropriate version of the equation’s size, order all polynomial Diophantine equations by size, and then solve the equations in order. Natural questions about the solution set of Diophantine equations are studied in this book using this approach. Is the set empty? Is it finite or infinite? Can all integer solutions be parametrized? By ordering equations by size, the book attempts to answer these questions in a systematic manner. When the size grows, the difficulty of finding solutions increases and the methods required to determine solutions become more advanced. Along the way, the reader will learn dozens of methods for solving Diophantine equations, each of which is illustrated by worked examples and exercises. The book ends with solutions to exercises and a large collection of open problems, often simple to write down yet still unsolved. The original approach pursued in this book makes it widely accessible. Many equations require only high school mathematics and creativity to be solved, so a large part of the book is accessible to high school students, especially those interested in mathematical competitions such as olympiads. The main intended audience is undergraduate students, for whom the book will serve as an unusually rich introduction to the topic of Diophantine equations. Many methods from the book will be useful for graduate students, while Ph.D. students and researchers may use it as a source of fascinating open questions of varying levels of difficulty. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY | |
| Title | Springer Nature eBook |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031629488 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031629501 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031629518 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1007/978-3-031-62949-5">https://doi.org/10.1007/978-3-031-62949-5</a> |
| 912 ## - | |
| -- | ZDB-2-SMA |
| 912 ## - | |
| -- | ZDB-2-SXMS |
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