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John Stillwell:

Numbers and Geometry - edition reliée, livre de poche

1997, ISBN: 0387982892

[EAN: 9780387982892], Neubuch, [SC: 0.0], [PU: Springer New York], GEOMETRIE; RAUMLEHRE; ZAHLENTHEORIE; AREA; PRIME; VOLUME; CALCULUS; SET, Druck auf Anfrage Neuware - Printed after order… Plus…

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Stillwell, John:

Numbers and Geometry (Undergraduate Texts in Mathematics) - edition reliée, livre de poche

1997, ISBN: 9780387982892

Springer, Gebundene Ausgabe, Auflage: 1998, 357 Seiten, Publiziert: 1997-10-30T00:00:01Z, Produktgruppe: Buch, 1.52 kg, Verkaufsrang: 2671331, Geometrie, Naturwissenschaft & Mathematik, F… Plus…

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Stillwell, John:
Numbers and Geometry (Undergraduate Texts in Mathematics) - edition reliée, livre de poche

1997

ISBN: 9780387982892

Springer, Gebundene Ausgabe, Auflage: 1998, 357 Seiten, Publiziert: 1997-10-30T00:00:01Z, Produktgruppe: Buch, 1.52 kg, Verkaufsrang: 2671331, Geometrie, Naturwissenschaft & Mathematik, F… Plus…

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Stillwell, John:
Numbers and Geometry. - edition reliée, livre de poche

1997, ISBN: 9780387982892

[PU: New York, Springer (Undergraduate Texts in Mathematics / UTM) 1997], XIV, 357 S. (24 cm) illustrierter Pappband / gebundene Ausgabe First Edition; (Mit 95 Abbildungen); Sehr guter Zu… Plus…

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ISBN: 0387982892

Médias > Livres > Mathématiques Undergraduate Texts in Mathematics, [PU: Springer]

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Numbers and Geometry (Undergraduate Texts in Mathematics)
Auteur:
Titre:
ISBN:

9780387982892


A beautiful and relatively elementary account of a part of mathematics where three main fields - algebra, analysis and geometry - meet. The book provides a broad view of these subjects at the level of calculus, without being a calculus book. Its roots are in arithmetic and geometry, the two opposite poles of mathematics, and the source of historic conceptual conflict. The resolution of this conflict, and its role in the development of mathematics, is one of the main stories in the book. Stillwell has chosen an array of exciting and worthwhile topics and elegantly combines mathematical history with mathematics. He covers the main ideas of Euclid, but with 2000 years of extra insights attached. Presupposing only high school algebra, it can be read by any well prepared student entering university. Moreover, this book will be popular with graduate students and researchers in mathematics due to its attractive and unusual treatment of fundamental topics. A set of well-written exercises at the end of each section allows new ideas to be instantly tested and reinforced.

Informations détaillées sur le livre - Numbers and Geometry (Undergraduate Texts in Mathematics)


EAN (ISBN-13): 9780387982892
ISBN (ISBN-10): 0387982892
Version reliée
Livre de poche
Date de parution: 2007
Editeur: Springer
364 Pages
Poids: 0,707 kg
Langue: eng/Englisch

Livre dans la base de données depuis 2007-06-03T21:59:18+02:00 (Zurich)
Page de détail modifiée en dernier sur 2024-03-03T15:58:31+01:00 (Zurich)
ISBN/EAN: 9780387982892

ISBN - Autres types d'écriture:
0-387-98289-2, 978-0-387-98289-2
Autres types d'écriture et termes associés:
Auteur du livre: gehring, stillwell john, john still, john main, geometry
Titre du livre: mathematics, numbers and geometry, john stillwell, undergraduate

Données de l'éditeur

Auteur: John Stillwell
Titre: Undergraduate Texts in Mathematics; Numbers and Geometry
Editeur: Springer; Springer US
343 Pages
Date de parution: 1997-10-30
New York; NY; US
Langue: Anglais
52,38 € (DE)
53,85 € (AT)
75,15 CHF (CH)
Available
XIV, 343 p.

BB; Hardcover, Softcover / Mathematik/Arithmetik, Algebra; Zahlentheorie; Verstehen; Area; Prime; Volume; calculus; set; Number Theory; Geometry; Geometrie; BC

1 Arithmetic.- 1.1 The Natural Numbers.- 1.2 Division, Divisors, and Primes.- 1.3 The Mysterious Sequence of Primes.- 1.4 Integers and Rationals.- 1.5 Linear Equations.- 1.6 Unique Prime Factorization.- 1.7 Prime Factorization and Divisors.- 1.8 Induction.- 1.9* Foundations.- 1.10 Discussion.- 2 Geometry.- 2.1 Geometric Intuition.- 2.2 Constructions.- 2.3 Parallels and Angles.- 2.4 Angles and Circles.- 2.5 Length and Area.- 2.6 The Pythagorean Theorem.- 2.7 Volume.- 2.8* The Whole and the Part.- 2.9 Discussion.- 3 Coordinates.- 3.1 Lines and Circles.- 3.2 Intersections.- 3.3 The Real Numbers.- 3.4 The Line.- 3.5 The Euclidean Plane.- 3.6 Isometries of the Euclidean Plane.- 3.7 The Triangle Inequality.- 3.8* Klein’s Definition of Geometry.- 3.9* The Non-Euclidean Plane.- 3.10 Discussion.- 4 Rational Points.- 4.1 Pythagorean Triples.- 4.2 Pythagorean Triples in Euclid.- 4.3 Pythagorean Triples in Diophantus.- 4.4 Rational Triangles.- 4.5 Rational Points on Quadratic Curves.- 4.6* Rational Points on the Sphere.- 4.7* The Area of Rational Right Triangles.- 4.8 Discussion.- 5 Trigonometry.- 5.1 Angle Measure.- 5.2 Circular Functions.- 5.3 Addition Formulas.- 5.4 A Rational Addition Formula.- 5.5* Hubert’s Third Problem.- 5.6* The Dehn Invariant.- 5.7* Additive Functions.- 5.8* The Tetrahedron and the Cube.- 5.9 Discussion.- 6 Finite Arithmetic.- 6.1 Three Examples.- 6.2 Arithmetic mod n.- 6.3 The Ring ?/n?.- 6.4 Inverses mod n.- 6.5 The Theorems of Fermat and Wilson.- 6.6 The Chinese Remainder Theorem.- 6.7 Squares mod p.- 6.8* The Quadratic Character of-1 and.- 6.9* Quadratic Reciprocity.- 6.10 Discussion.- 7 Complex Numbers.- 7.1 Addition, Multiplication, and Absolute Value.- 7.2 Argument and the Square Root of -1.- 7.3 Isometries of the Plane.- 7.4 The GaussianIntegers.- 7.5 Unique Gaussian Prime Factorization.- 7.6 Fermat’s TWo Squares Theorem.- 7.7* Factorizing a Sum of Two Squares.- 7.8 Discussion.- 8 Conic Sections.- 8.1 Too Much, Too Little, and Just Right.- 8.2 Properties of Conic Sections.- 8.3 Quadratic Curves.- 8.4* Intersections.- 8.5 Integer Points on Conics.- 8.6* Square Roots and the Euclidean Algorithm.- 8.7* Pell’s Equation.- 8.8 Discussion.- 9 Elementary Functions.- 9.1 Algebraic and Transcendental Functions.- 9.2 The Area Bounded by a Curve.- 9.3 The Natural Logarithm and the Exponential.- 9.4 The Exponential Function.- 9.5 The Hyperbolic Functions.- 9.6 The Pell Equation Revisited.- 9.7 Discussion.
Highly accessible, the book presupposes only high school algebra and therefore can be read by any well prepared student entering university Written by a clear and skillful author who has published several successful books at Springer Contains a highly unique treatment of fundamental topics in algebra, analysis, and geometry, at an elementary level with an historical perspective

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