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Numbers and Geometry Stillwell, John Buch - Stillwell, John
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Numbers and Geometry Stillwell, John Buch - hardcover

ISBN: 9781461268673

Knicke und Markierungen sowie persönliche Notizen sind nicht vorhanden. Du bist Student in und suchst verzweifelt nach guter Fachliteratur?. Mathematik & Technik. Sprache: Englisch. Als G… More...

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Numbers and Geometry | John Stillwell | Taschenbuch | Undergraduate Texts in Mathematics | Paperback | xiv | Englisch | 2012 | Springer US | EAN 9781461268673 - Stillwell, John
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Stillwell, John:

Numbers and Geometry | John Stillwell | Taschenbuch | Undergraduate Texts in Mathematics | Paperback | xiv | Englisch | 2012 | Springer US | EAN 9781461268673 - Paperback

2012, ISBN: 9781461268673

[ED: Taschenbuch], [PU: Springer US], A beautiful and relatively elementary account of a part of mathematics where three main fields - algebra, analysis and geometry - meet. The book prov… More...

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ISBN: 9781461268673

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… More...

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Numbers and Geometry (Undergraduate Texts in Mathematics) - Stillwell, John
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Numbers and Geometry (Undergraduate Texts in Mathematics) - Paperback

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Springer, Taschenbuch, Auflage: 1998, 360 Seiten, Publiziert: 1997-10-30T00:00:01Z, Produktgruppe: Buch, Hersteller-Nr.: black & white illustrations, 1.21 kg, Verkaufsrang: 4404, Geometri… More...

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John Stillwell:
Numbers and Geometry - Paperback

ISBN: 9781461268673

*Numbers and Geometry* - Auflage 1998 / Taschenbuch für 52.49 € / Aus dem Bereich: Bücher, Wissenschaft, Mathematik Medien > Bücher nein Buch (kartoniert) Hardcover;Naturwissenschaften, M… More...

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Details of the book
Numbers and Geometry John Stillwell Author

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.

Details of the book - Numbers and Geometry John Stillwell Author


EAN (ISBN-13): 9781461268673
ISBN (ISBN-10): 1461268672
Hardcover
Paperback
Publishing year: 2012
Publisher: Springer New York Core >1 >T

Book in our database since 2014-07-27T21:02:04+01:00 (London)
Detail page last modified on 2024-03-22T14:59:37+00:00 (London)
ISBN/EAN: 9781461268673

ISBN - alternate spelling:
1-4612-6867-2, 978-1-4612-6867-3
Alternate spelling and related search-keywords:
Book author: still, john stillwell
Book title: mathematics, numbers and geometry, undergraduate text, john stillwell, geo, number and numbers


Information from Publisher

Author: John Stillwell
Title: Undergraduate Texts in Mathematics; Numbers and Geometry
Publisher: Springer; Springer US
343 Pages
Publishing year: 2012-09-28
New York; NY; US
Printed / Made in
Language: English
52,38 € (DE)
53,85 € (AT)
75,15 CHF (CH)
POD
XIV, 343 p.

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

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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