Algebraic number theory and Fermat's Last Theorem:
Updated to reflect current research, Algebraic Number Theory and Fermat’s Last Theorem, Fourth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematics—the quest for a proof of Fermat’s Last Theorem. The authors use this...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton ; London ; New York
CRC Press, Taylor & Francis Group
2020
|
| Ausgabe: | Fourth edition, first issued in paperback 2020 |
| Schlagworte: | |
| Zusammenfassung: | Updated to reflect current research, Algebraic Number Theory and Fermat’s Last Theorem, Fourth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematics—the quest for a proof of Fermat’s Last Theorem. The authors use this celebrated theorem to motivate a general study of the theory of algebraic numbers from a relatively concrete point of view. Students will see how Wiles’s proof of Fermat’s Last Theorem opened many new areas for future work.New to the Fourth EditionProvides up-to-date information on unique prime factorization for real quadratic number fields, especially Harper’s proof that Z(v14) is EuclideanPresents an important new result: Mihailescu’s proof of the Catalan conjecture of 1844Revises and expands one chapter into two, covering classical ideas about modular functions and highlighting the new ideas of Frey, Wiles, and others that led to the long-sought proof of Fermat’s Last TheoremImproves and updates the index, figures, bibliography, further reading list, and historical remarksWritten by preeminent mathematicians Ian Stewart and David Tall, this text continues to teach students how to extend properties of natural numbers to more general number structures, including algebraic number fields and their rings of algebraic integers. It also explains how basic notions from the theory of algebraic numbers can be used to solve problems in number theory |
| Beschreibung: | Algebraic Methods: Algebraic Background. Algebraic Numbers. Quadratic and Cylclotomic Fields. Factorization into Irreducibles. Ideals. Geometric Methods: Lattices. Minkowski's Theorem. Geometric Representation of Algebraic Numbers. Class-Group and Class-Number. Number-Theoretic Applications: Computational Methods. Kummer's Special Case of Fermat's Last Theorem. The Path to the Final Breakthrough. Elliptic Curves. Elliptic Functions. Wiles's Strategy and Recent Developments. Appendices: Quadratic Residues. Dirichlet's Units Theorems |
| Beschreibung: | xix, 322 Seiten Illustrationen 229 mm |
| ISBN: | 9780367658717 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV046916466 | ||
| 003 | DE-604 | ||
| 005 | 20201103 | ||
| 007 | t | ||
| 008 | 200928s2020 a||| |||| 00||| eng d | ||
| 020 | |a 9780367658717 |c pbk |9 978-0-367-65871-7 | ||
| 024 | 3 | |a 9780367658717 | |
| 035 | |a (OCoLC)1220878556 | ||
| 035 | |a (DE-599)BVBBV046916466 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-29T | ||
| 100 | 1 | |a Stewart, Ian |d 1945- |e Verfasser |0 (DE-588)124091598 |4 aut | |
| 245 | 1 | 0 | |a Algebraic number theory and Fermat's Last Theorem |c Ian Stewart (University of Warwick, United Kingdom), David Tall (University of Warwick, United Kingdom) |
| 250 | |a Fourth edition, first issued in paperback 2020 | ||
| 264 | 1 | |a Boca Raton ; London ; New York |b CRC Press, Taylor & Francis Group |c 2020 | |
| 300 | |a xix, 322 Seiten |b Illustrationen |c 229 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Algebraic Methods: Algebraic Background. Algebraic Numbers. Quadratic and Cylclotomic Fields. Factorization into Irreducibles. Ideals. Geometric Methods: Lattices. Minkowski's Theorem. Geometric Representation of Algebraic Numbers. Class-Group and Class-Number. Number-Theoretic Applications: Computational Methods. Kummer's Special Case of Fermat's Last Theorem. The Path to the Final Breakthrough. Elliptic Curves. Elliptic Functions. Wiles's Strategy and Recent Developments. Appendices: Quadratic Residues. Dirichlet's Units Theorems | ||
| 520 | |a Updated to reflect current research, Algebraic Number Theory and Fermat’s Last Theorem, Fourth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematics—the quest for a proof of Fermat’s Last Theorem. The authors use this celebrated theorem to motivate a general study of the theory of algebraic numbers from a relatively concrete point of view. Students will see how Wiles’s proof of Fermat’s Last Theorem opened many new areas for future work.New to the Fourth EditionProvides up-to-date information on unique prime factorization for real quadratic number fields, especially Harper’s proof that Z(v14) is EuclideanPresents an important new result: Mihailescu’s proof of the Catalan conjecture of 1844Revises and expands one chapter into two, covering classical ideas about modular functions and highlighting the new ideas of Frey, Wiles, and others that led to the long-sought proof of Fermat’s Last TheoremImproves and updates the index, figures, bibliography, further reading list, and historical remarksWritten by preeminent mathematicians Ian Stewart and David Tall, this text continues to teach students how to extend properties of natural numbers to more general number structures, including algebraic number fields and their rings of algebraic integers. It also explains how basic notions from the theory of algebraic numbers can be used to solve problems in number theory | ||
| 650 | 4 | |a bisacsh / MATHEMATICS / Number Theory | |
| 650 | 4 | |a bisacsh / MATHEMATICS / Combinatorics | |
| 700 | 1 | |a Tall, David |d 1941- |e Verfasser |0 (DE-588)1050906004 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe, Hardcover |z 978-1-4987-3839-2 |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-032325776 | ||
Datensatz im Suchindex
| _version_ | 1804181800710307840 |
|---|---|
| adam_txt | |
| any_adam_object | |
| any_adam_object_boolean | |
| author | Stewart, Ian 1945- Tall, David 1941- |
| author_GND | (DE-588)124091598 (DE-588)1050906004 |
| author_facet | Stewart, Ian 1945- Tall, David 1941- |
| author_role | aut aut |
| author_sort | Stewart, Ian 1945- |
| author_variant | i s is d t dt |
| building | Verbundindex |
| bvnumber | BV046916466 |
| ctrlnum | (OCoLC)1220878556 (DE-599)BVBBV046916466 |
| edition | Fourth edition, first issued in paperback 2020 |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03296nam a2200349 c 4500</leader><controlfield tag="001">BV046916466</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20201103 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">200928s2020 a||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780367658717</subfield><subfield code="c">pbk</subfield><subfield code="9">978-0-367-65871-7</subfield></datafield><datafield tag="024" ind1="3" ind2=" "><subfield code="a">9780367658717</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1220878556</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV046916466</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-29T</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Stewart, Ian</subfield><subfield code="d">1945-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)124091598</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Algebraic number theory and Fermat's Last Theorem</subfield><subfield code="c">Ian Stewart (University of Warwick, United Kingdom), David Tall (University of Warwick, United Kingdom)</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Fourth edition, first issued in paperback 2020</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boca Raton ; London ; New York</subfield><subfield code="b">CRC Press, Taylor & Francis Group</subfield><subfield code="c">2020</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xix, 322 Seiten</subfield><subfield code="b">Illustrationen</subfield><subfield code="c">229 mm</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Algebraic Methods: Algebraic Background. Algebraic Numbers. Quadratic and Cylclotomic Fields. Factorization into Irreducibles. Ideals. Geometric Methods: Lattices. Minkowski's Theorem. Geometric Representation of Algebraic Numbers. Class-Group and Class-Number. Number-Theoretic Applications: Computational Methods. Kummer's Special Case of Fermat's Last Theorem. The Path to the Final Breakthrough. Elliptic Curves. Elliptic Functions. Wiles's Strategy and Recent Developments. Appendices: Quadratic Residues. Dirichlet's Units Theorems</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Updated to reflect current research, Algebraic Number Theory and Fermat’s Last Theorem, Fourth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematics—the quest for a proof of Fermat’s Last Theorem. The authors use this celebrated theorem to motivate a general study of the theory of algebraic numbers from a relatively concrete point of view. Students will see how Wiles’s proof of Fermat’s Last Theorem opened many new areas for future work.New to the Fourth EditionProvides up-to-date information on unique prime factorization for real quadratic number fields, especially Harper’s proof that Z(v14) is EuclideanPresents an important new result: Mihailescu’s proof of the Catalan conjecture of 1844Revises and expands one chapter into two, covering classical ideas about modular functions and highlighting the new ideas of Frey, Wiles, and others that led to the long-sought proof of Fermat’s Last TheoremImproves and updates the index, figures, bibliography, further reading list, and historical remarksWritten by preeminent mathematicians Ian Stewart and David Tall, this text continues to teach students how to extend properties of natural numbers to more general number structures, including algebraic number fields and their rings of algebraic integers. It also explains how basic notions from the theory of algebraic numbers can be used to solve problems in number theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">bisacsh / MATHEMATICS / Number Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">bisacsh / MATHEMATICS / Combinatorics</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Tall, David</subfield><subfield code="d">1941-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1050906004</subfield><subfield code="4">aut</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe, Hardcover</subfield><subfield code="z">978-1-4987-3839-2</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-032325776</subfield></datafield></record></collection> |
| id | DE-604.BV046916466 |
| illustrated | Illustrated |
| index_date | 2024-07-03T15:29:45Z |
| indexdate | 2024-07-10T08:57:25Z |
| institution | BVB |
| isbn | 9780367658717 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032325776 |
| oclc_num | 1220878556 |
| open_access_boolean | |
| owner | DE-29T |
| owner_facet | DE-29T |
| physical | xix, 322 Seiten Illustrationen 229 mm |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | CRC Press, Taylor & Francis Group |
| record_format | marc |
| spelling | Stewart, Ian 1945- Verfasser (DE-588)124091598 aut Algebraic number theory and Fermat's Last Theorem Ian Stewart (University of Warwick, United Kingdom), David Tall (University of Warwick, United Kingdom) Fourth edition, first issued in paperback 2020 Boca Raton ; London ; New York CRC Press, Taylor & Francis Group 2020 xix, 322 Seiten Illustrationen 229 mm txt rdacontent n rdamedia nc rdacarrier Algebraic Methods: Algebraic Background. Algebraic Numbers. Quadratic and Cylclotomic Fields. Factorization into Irreducibles. Ideals. Geometric Methods: Lattices. Minkowski's Theorem. Geometric Representation of Algebraic Numbers. Class-Group and Class-Number. Number-Theoretic Applications: Computational Methods. Kummer's Special Case of Fermat's Last Theorem. The Path to the Final Breakthrough. Elliptic Curves. Elliptic Functions. Wiles's Strategy and Recent Developments. Appendices: Quadratic Residues. Dirichlet's Units Theorems Updated to reflect current research, Algebraic Number Theory and Fermat’s Last Theorem, Fourth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematics—the quest for a proof of Fermat’s Last Theorem. The authors use this celebrated theorem to motivate a general study of the theory of algebraic numbers from a relatively concrete point of view. Students will see how Wiles’s proof of Fermat’s Last Theorem opened many new areas for future work.New to the Fourth EditionProvides up-to-date information on unique prime factorization for real quadratic number fields, especially Harper’s proof that Z(v14) is EuclideanPresents an important new result: Mihailescu’s proof of the Catalan conjecture of 1844Revises and expands one chapter into two, covering classical ideas about modular functions and highlighting the new ideas of Frey, Wiles, and others that led to the long-sought proof of Fermat’s Last TheoremImproves and updates the index, figures, bibliography, further reading list, and historical remarksWritten by preeminent mathematicians Ian Stewart and David Tall, this text continues to teach students how to extend properties of natural numbers to more general number structures, including algebraic number fields and their rings of algebraic integers. It also explains how basic notions from the theory of algebraic numbers can be used to solve problems in number theory bisacsh / MATHEMATICS / Number Theory bisacsh / MATHEMATICS / Combinatorics Tall, David 1941- Verfasser (DE-588)1050906004 aut Erscheint auch als Druck-Ausgabe, Hardcover 978-1-4987-3839-2 |
| spellingShingle | Stewart, Ian 1945- Tall, David 1941- Algebraic number theory and Fermat's Last Theorem bisacsh / MATHEMATICS / Number Theory bisacsh / MATHEMATICS / Combinatorics |
| title | Algebraic number theory and Fermat's Last Theorem |
| title_auth | Algebraic number theory and Fermat's Last Theorem |
| title_exact_search | Algebraic number theory and Fermat's Last Theorem |
| title_exact_search_txtP | Algebraic number theory and Fermat's Last Theorem |
| title_full | Algebraic number theory and Fermat's Last Theorem Ian Stewart (University of Warwick, United Kingdom), David Tall (University of Warwick, United Kingdom) |
| title_fullStr | Algebraic number theory and Fermat's Last Theorem Ian Stewart (University of Warwick, United Kingdom), David Tall (University of Warwick, United Kingdom) |
| title_full_unstemmed | Algebraic number theory and Fermat's Last Theorem Ian Stewart (University of Warwick, United Kingdom), David Tall (University of Warwick, United Kingdom) |
| title_short | Algebraic number theory and Fermat's Last Theorem |
| title_sort | algebraic number theory and fermat s last theorem |
| topic | bisacsh / MATHEMATICS / Number Theory bisacsh / MATHEMATICS / Combinatorics |
| topic_facet | bisacsh / MATHEMATICS / Number Theory bisacsh / MATHEMATICS / Combinatorics |
| work_keys_str_mv | AT stewartian algebraicnumbertheoryandfermatslasttheorem AT talldavid algebraicnumbertheoryandfermatslasttheorem |