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Numbers : Rational and Irrational

Author: Ivan Niven
Publisher: Cambridge : Cambridge University Press, 2012.
Series: Anneli Lax new mathematical library.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Niven, Ivan Morton.
Numbers : Rational and Irrational.
Washington : Mathematical Association of America, ©2014
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Ivan Niven
ISBN: 9780883859193 088385919X
OCLC Number: 775428797
Notes: Title from publishers bibliographic system (viewed on 30 Jan 2012).
Description: 1 online resource.
Contents: ""Front Cover""; ""Numbers: Rational and Irrational""; ""Copyright Page""; ""CONTENTS""; ""Introduction""; ""Chapter 1. Natural Numbers aud Integers""; ""1.1 Primes""; ""1.2 Unique Factorization""; ""1.3 Integers""; ""1.4 Even and Odd Integers""; ""1.5 Closure Properties""; ""1.6 A Remark on the Nature of Proof""; ""Chapter 2. Rational Numbers""; ""2.1 Definition of Rational Numbers""; ""2.2 Terminating and Non-terminating Decimals""; ""2.3 The Many Ways of Stating and Proving Propositions""; ""2.4 Periodic Decimals""; ""2.5 Terminating Decimals Written as Periodic Decimals"" ""2.6 A Summary""""Chapter 3. Real Numbers""; ""3.1 The Geometric Viewpoint""; ""3.2 Decimal Representations""; ""3.3 The Irrationality of �2""; ""3.4 The Irrationality of �3""; ""3.5 The Irrationality of v6 and v2 +�3""; ""3.6 The Words We Use""; ""3.7 An Application to Geometry""; ""3.8 A summary""; ""Chapter 4. Irrational Numbers""; ""4.1 Closure Properties""; ""4.2 Polynomial Equations""; ""4.3 Rational Roots of Polynomial Equations""; ""4.4 Further Examples""; ""4.5 A Summary""; ""Chapter 5. Trigonometric and Logarithmic Numbers"" ""5.1 Irrational Values of Trigonometric Functions""""5.2 A Chain Device""; ""5.3 Irrational Values of Common Logarithms""; ""5.4 Transcendental Numbers""; ""5.5 Three Famous Construction Problems""; ""5.6 Further Analysis of 3�2""; ""5.7 A Summary""; ""Chapter 6. The Approximation of Irrationals by Rationals""; ""6.1 Inequalities""; ""6.2 Approximation by Integers""; ""6.3 Approximation by Rationals""; ""6.4 Better Approximations""; ""6.5 Approximations to within1/n2""; ""6.6 Limitations on Approximations""; ""6.7 A Summary""; ""Chapter 7. The Existence of Transcendental Numbers"" ""7.1 Some Algebraic Preliminaries""""7.2 An Approximation to α""; ""7.3 The Plan of the Proof""; ""7.4 Properties of Polynomials""; ""7.5 The Transcendence of α""; ""7.6 A Summary""; ""Appendix A Proof That There Are Infinitely Many Prime Numbers""; ""Appendix B Proof of the Fundamental Theorem of Arithmetic""; ""Appendix C Cantor�s Proof of the Existence of Transcendental Numbers""; ""Appendix D Trigonometric Numbers""; ""Answers and Suggestions to Selected Problems""; ""Index""
Series Title: Anneli Lax new mathematical library.
Responsibility: Ivan Niven.

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