Nutzen Sie unsere Filialabholung und erhalten Sie diesen Artikel versandkostenfrei in Ihrer Filiale!

Elements of Number Theory

This book is intended to complement my Elements oi Algebra, and it is similarly motivated by the problem of solving polynomial equations. However, it is independent of the algebra book, and probably easier. In Elements oi Algebra we sought solution by radicals, and this led to the concepts of fields and groups and their fusion in the celebrated theory of Galois. In the present book we seek integer solutions, and this leads to the concepts of rings and ideals which merge in the equally celebrated theory of ideals due to Kummer and Dedekind. Solving equations in integers is the central problem of number theory, so this book is truly a number theory book, with most of the results found in standard number theory courses. However, numbers are best understood through their algebraic structure, and the necessary algebraic concepts­ rings and ideals-have no better motivation than number theory. The first nontrivial examples of rings appear in the number theory of Euler and Gauss. The concept of ideal-today as routine in ring the­ ory as the concept of normal subgroup is in group theory-also emerged from number theory, and in quite heroic fashion. Faced with failure of unique prime factorization in the arithmetic of certain generalized "inte­ gers" , Kummer created in the 1840s a new kind of number to overcome the difficulty. He called them "ideal numbers" because he did not know exactly what they were, though he knew how they behaved.
Rezension
From the reviews:
"Solving equations in integers is the central problem of number theory, so this book is truly a number theory book, with most of the results found in standard number theory courses. ... The book is clearly written, well organized and is a very pleasurable reading: it is an excellent and very useful undergraduate textbook. However, thanks to the many examples and exercises, it is well suitable for independent study, as well." (Lászlo Megyesi, Acta Scientiarum Mathematicarum, Vol. 71, 2005)
"In this carefully crafted undergraduate number theory text, Stillwell walks the reader through the main topics that belong in any introduction to number theory ... but he does so in a way that highlights the beguiling nature of number theory problems and keeps their rich history alive. ... This book has some additional features that will draw you to order it for your courses. ... Stillwell ... presents a compelling argument for studying the ancient and modern problems of number theory ... ." (Gwynneth G. H. Coogan, Mathematical Reviews, 2004 j)
"A solid systematic introduction to (algebraic) number theory which is truly elementary in the sense that a bright young undergraduate could make rapid unaided progress through this book. ... There are lots of goodies in the sidelines and the attention to clarity of writing and to pedagogic care give it a high rank amongst competing texts. ... Stillwell's book makes a very positive contribution to the coherence of the subject, which adds ... to the satisfaction of studying it." (John Baylis, The Mathematical Gazette, Vol. 88 (512), 2004)
"Stillwell has taken very careful aim at his target audience and hit them squarely between the eyes. ... the author has done a wonderful job of conveying his obvious love of the subject to the reader. ... The author ... covers basic classical number theory. ... Each chapter opens with a substantial preview stating the central concepts which are about to appear. ... In short, this book is a delight to read and is ideally suited to a beginning course in number theory." (Ralph H. Buchholz, The Australian Mathematical Society Gazette, Vol. 31 (1), 2004)
"The book is a concise introduction to number theory and some related algebra, with an emphasis on solving equations in integers. ... The historical development has been followed where it helps to motivate the introduction of new concepts, but modern proofs have been used where they are simpler, more natural, or more interesting. ... Also, this is the only elementary number theory book that includes significant applications of ideal theory." (Zentralblatt für Didaktik der Mathematik, February, 2003)
"The text would be suitable for the standard elementary number theory course. ... could serve as an introduction to algebraic number theory. ... has a number of unusual and attractive features. ... there is much in this book that would make it an appealing choice for a group of able mathematics majors. ... the book under review provides a valuable and original alternative to the many current texts on introductory number theory." (David W. Boyd, SIAM Review, Vol. 46 (2), 2004)
Portrait
John Stillwell is a professor of mathematics at the University of San Francisco. He is also an accomplished author, having published several books.
… weiterlesen
In den Warenkorb
Filialabholung

Versandkostenfrei

Beschreibung

Produktdetails


Einband gebundene Ausgabe
Seitenzahl 256
Erscheinungsdatum 13.12.2002
Sprache Englisch
ISBN 978-0-387-95587-2
Verlag Springer
Maße (L/B/H) 235/155/20 mm
Gewicht 1240
Abbildungen 2 schwarzweisse Abbildungen,
Auflage 2003
Buch (gebundene Ausgabe, Englisch)
44,99
inkl. gesetzl. MwSt.
Versandfertig in 3 - 5 Tagen
Versandkostenfrei
In den Warenkorb
Filialabholung

Versandkostenfrei

Andere Kunden interessierten sich auch für

  • 39524867
    English G Access - Allgemeine Ausgabe / Band 3: 7. Schuljahr - Workbook mit Audios online
    von Jennifer Seidl
    Schulbuch (Taschenbuch)
    9,25
  • 32632713
    English G Lighthouse - Allgemeine Ausgabe / Band 2: 6. Schuljahr - Workbook mit Audios online
    von Gwen Berwick
    (2)
    Schulbuch (Taschenbuch)
    9,50
  • 32281116
    English G Access - Allgemeine Ausgabe / Band 1: 5. Schuljahr - Workbook mit Audios online und MyBook
    von Jennifer Seidl
    Schulbuch (Taschenbuch)
    9,25
  • 29358095
    English G Lighthouse - Allgemeine Ausgabe / Band 1: 5. Schuljahr - Workbook mit Audios online
    von Gwen Berwick
    Schulbuch (Taschenbuch)
    9,50
  • 41443715
    English G Lighthouse - Allgemeine Ausgabe / Band 4: 8. Schuljahr - Workbook mit Audios online
    von Gwen Berwick
    (2)
    Schulbuch (Taschenbuch)
    9,50
  • 14270454
    English G 21 - Ausgabe D / Band 2: 6. Schuljahr - Workbook mit Audios online
    von Jennifer Seidl
    (4)
    Schulbuch (Taschenbuch)
    10,50
  • 37916446
    English G Access - Allgemeine Ausgabe / Band 2: 6. Schuljahr - Workbook mit Audios online
    von Jennifer Seidl
    Schulbuch (Taschenbuch)
    9,25
  • 44439521
    English G Lighthouse - Allgemeine Ausgabe / Band 5: 9. Schuljahr - Workbook mit Audios online
    von Gwen Berwick
    Schulbuch (Taschenbuch)
    9,50
  • 11596566
    English G 21 - Ausgabe D / Band 1: 5. Schuljahr - Workbook mit Audios online
    von Jennifer Seidl
    (1)
    Schulbuch (Taschenbuch)
    10,50
  • 27328269
    English G 21 - Erweiterte Ausgabe D / Band 6: 10. Schuljahr - Workbook mit Audios online
    von Jennifer Seidl
    Schulbuch (Taschenbuch)
    10,50
  • 27328230
    English G 21 - Ausgabe B / Band 6: 10. Schuljahr - Workbook mit Audios online
    von Jennifer Seidl
    Schulbuch (Taschenbuch)
    10,50
  • 15244899
    Green Line 3. Workbook mit Audio-CD.
    von Elizabeth Daymond
    (7)
    Schulbuch (Geheftet)
    10,50
  • 41492607
    Context - Berlin/ Brandenburg/ Mecklenburg-Vorpommern / Schülerbuch (kartoniert)
    von Gerit Fredrich
    Schulbuch (Taschenbuch)
    23,50
  • 31405171
    Game of Thrones 5-Copy Boxed Set
    von George R. R. Martin
    (7)
    Buch (Taschenbuch)
    25,90 bisher 37,49
  • 27328209
    English G 21 - Ausgabe A / Abschlussband 6: 10. Schuljahr - 6-jährige Sekundarstufe I - Workbook mit Audios online
    von Jennifer Seidl
    Schulbuch (Taschenbuch)
    10,50
  • 37943581
    English G Access 02: 6. Schuljahr. Klassenarbeitstrainer mit Audio-Material online, Lösungen online und Lerntipps
    von Bärbel Schweitzer
    Schulbuch (Taschenbuch)
    11,50
  • 34809997
    Playway. Für den Beginn ab Klasse 3 / Activity Book mit Audio-CD 4. Schuljahr
    Schulbuch (Kunststoff-Einband)
    10,25
  • 33724912
    Playway 3. Jahrgangsstufe 3. Activity Book mit Audio-CD
    (1)
    Schulbuch (Kunststoff-Einband)
    10,25
  • 27328231
    English G 21 - Grundausgabe D / Band 6: 10. Schuljahr - Workbook mit Audios online
    von Jennifer Seidl
    Schulbuch (Taschenbuch)
    10,50
  • 38451425
    Context Starter / Schülerbuch (kartoniert)
    von Carl Bamber
    Schulbuch (Taschenbuch)
    19,99

Kundenbewertungen


Es wurden noch keine Bewertungen geschrieben.

Wird oft zusammen gekauft

Elements of Number Theory - John Stillwell

Elements of Number Theory

von John Stillwell

Buch (gebundene Ausgabe, Englisch)
44,99
+
=
English G Lighthouse - Allgemeine Ausgabe / Band 3: 7. Schuljahr - Workbook mit Audios online - Gwen Berwick

English G Lighthouse - Allgemeine Ausgabe / Band 3: 7. Schuljahr - Workbook mit Audios online

von Gwen Berwick

Schulbuch (Taschenbuch)
9,50
+
=

für

54,49

inkl. gesetzl. MwSt.

Alle kaufen