The Resource Limits, Limits Everywhere : the Tools of Mathematical Analysis, David Applebaum
Limits, Limits Everywhere : the Tools of Mathematical Analysis, David Applebaum
Resource Information
The item Limits, Limits Everywhere : the Tools of Mathematical Analysis, David Applebaum represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Limits, Limits Everywhere : the Tools of Mathematical Analysis, David Applebaum represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 A quantity can be made smaller and smaller without it ever vanishing. This fact has profound consequences for science, technology, and even the way we think about numbers. In this book, we will explore this idea by moving at an easy pace through an account of elementary real analysis and, in particular, will focus on numbers, sequences, and series. Almost all textbooks on introductory analysis assume some background in calculus. This book doesn't and, instead, the emphasis is on the application of analysis to number theory. The book is split into two parts. Part 1 follows a standard university
 Language
 eng
 Extent
 1 online resource (217 pages)
 Contents

 Cover; Contents; PART I: APPROACHING LIMITS; 1. A Whole Lot of Numbers; 1.1 Natural Numbers; 1.2 Prime Numbers; 1.3 The Integers; 1.4 Exercises for Chapter 1; 2. Let's Get Real; 2.1 The Rational Numbers; 2.2 Irrational Numbers; 2.3 The Real Numbers; 2.4 A First Look at Infinity; 2.5 Exercises for Chapter 2; 3. The Joy of Inequality; 3.1 Greater or Less?; 3.2 Intervals; 3.3 The Modulus of a Number; 3.4 Maxima and Minima; 3.5 The Theorem of the Means; 3.6 Getting Closer; 3.7 Exercises for Chapter 3; 4. Where Do You Go To, My Lovely?; 4.1 Limits; 4.2 Bounded Sequences; 4.3 The Algebra of Limits
 4.4 Fibonacci Numbers and the Golden Section4.5 Exercises for Chapter 4; 5. Bounds for Glory; 5.1 Bounded Sequences Revisited; 5.2 Monotone Sequences; 5.3 An Old Friend Returns; 5.4 Finding Square Roots; 5.5 Exercises for Chapter 5; 6. You Cannot be Series; 6.1 What are Series?; 6.2 The Sigma Notation; 6.3 Convergence of Series; 6.4 Nonnegative Series; 6.5 The Comparison Test; 6.6 Geometric Series; 6.7 The Ratio Test; 6.8 General Infinite Series; 6.9 Conditional Convergence; 6.10 Regrouping and Rearrangements; 6.11 Real Numbers and Decimal Expansions; 6.12 Exercises for Chapter 6
 PART II: EXPLORING LIMITS7. Wonderful Numbers  e, p and?; 7.1 The Number e; 7.2 The Number p; 7.3 The Number?; 8. Infinite Products; 8.1 Convergence of Infinite Products; 8.2 Infinite Products and Prime Numbers; 8.3 Diversion  Complex Numbers and the Riemann Hypothesis; 9. Continued Fractions; 9.1 Euclid's Algorithm; 9.2 Rational and Irrational Numbers as Continued Fractions; 10. How Infinite Can You Get?; 11. Constructing the Real Numbers; 11.1 Dedekind Cuts; 11.2 Cauchy Sequences; 11.3 Completeness; 12. Where to Next in Analysis? The Calculus; 12.1 Functions; 12.2 Limits and Continuity
 12.3 Differentiation12.4 Integration; 13. Some Brief Remarks About the History of Analysis; Further Reading; Appendices; Appendix 1: The Binomial Theorem; Appendix 2: The Language of Set Theory; Appendix 3: Proof by Mathematical Induction; Appendix 4: The Algebra of Numbers; Hints and Solutions to Selected Exercise; Index; A; B; C; D; E; F; G; H; I; J; K; L; M; N; O; P; Q; R; S; T; U; V; W; Z
 Isbn
 9780191627866
 Label
 Limits, Limits Everywhere : the Tools of Mathematical Analysis
 Title
 Limits, Limits Everywhere
 Title remainder
 the Tools of Mathematical Analysis
 Statement of responsibility
 David Applebaum
 Language
 eng
 Summary
 A quantity can be made smaller and smaller without it ever vanishing. This fact has profound consequences for science, technology, and even the way we think about numbers. In this book, we will explore this idea by moving at an easy pace through an account of elementary real analysis and, in particular, will focus on numbers, sequences, and series. Almost all textbooks on introductory analysis assume some background in calculus. This book doesn't and, instead, the emphasis is on the application of analysis to number theory. The book is split into two parts. Part 1 follows a standard university
 Cataloging source
 EBLCP
 http://library.link/vocab/creatorDate
 1956
 http://library.link/vocab/creatorName
 Applebaum, David
 Dewey number
 515
 Index
 no index present
 LC call number
 QA300
 LC item number
 .A67 2012eb
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/subjectName

 Mathematical analysis
 MATHEMATICS
 MATHEMATICS
 Mathematical analysis
 Label
 Limits, Limits Everywhere : the Tools of Mathematical Analysis, David Applebaum
 Antecedent source
 unknown
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Cover; Contents; PART I: APPROACHING LIMITS; 1. A Whole Lot of Numbers; 1.1 Natural Numbers; 1.2 Prime Numbers; 1.3 The Integers; 1.4 Exercises for Chapter 1; 2. Let's Get Real; 2.1 The Rational Numbers; 2.2 Irrational Numbers; 2.3 The Real Numbers; 2.4 A First Look at Infinity; 2.5 Exercises for Chapter 2; 3. The Joy of Inequality; 3.1 Greater or Less?; 3.2 Intervals; 3.3 The Modulus of a Number; 3.4 Maxima and Minima; 3.5 The Theorem of the Means; 3.6 Getting Closer; 3.7 Exercises for Chapter 3; 4. Where Do You Go To, My Lovely?; 4.1 Limits; 4.2 Bounded Sequences; 4.3 The Algebra of Limits
 4.4 Fibonacci Numbers and the Golden Section4.5 Exercises for Chapter 4; 5. Bounds for Glory; 5.1 Bounded Sequences Revisited; 5.2 Monotone Sequences; 5.3 An Old Friend Returns; 5.4 Finding Square Roots; 5.5 Exercises for Chapter 5; 6. You Cannot be Series; 6.1 What are Series?; 6.2 The Sigma Notation; 6.3 Convergence of Series; 6.4 Nonnegative Series; 6.5 The Comparison Test; 6.6 Geometric Series; 6.7 The Ratio Test; 6.8 General Infinite Series; 6.9 Conditional Convergence; 6.10 Regrouping and Rearrangements; 6.11 Real Numbers and Decimal Expansions; 6.12 Exercises for Chapter 6
 PART II: EXPLORING LIMITS7. Wonderful Numbers  e, p and?; 7.1 The Number e; 7.2 The Number p; 7.3 The Number?; 8. Infinite Products; 8.1 Convergence of Infinite Products; 8.2 Infinite Products and Prime Numbers; 8.3 Diversion  Complex Numbers and the Riemann Hypothesis; 9. Continued Fractions; 9.1 Euclid's Algorithm; 9.2 Rational and Irrational Numbers as Continued Fractions; 10. How Infinite Can You Get?; 11. Constructing the Real Numbers; 11.1 Dedekind Cuts; 11.2 Cauchy Sequences; 11.3 Completeness; 12. Where to Next in Analysis? The Calculus; 12.1 Functions; 12.2 Limits and Continuity
 12.3 Differentiation12.4 Integration; 13. Some Brief Remarks About the History of Analysis; Further Reading; Appendices; Appendix 1: The Binomial Theorem; Appendix 2: The Language of Set Theory; Appendix 3: Proof by Mathematical Induction; Appendix 4: The Algebra of Numbers; Hints and Solutions to Selected Exercise; Index; A; B; C; D; E; F; G; H; I; J; K; L; M; N; O; P; Q; R; S; T; U; V; W; Z
 Control code
 784886666
 Dimensions
 unknown
 Extent
 1 online resource (217 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9780191627866
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)784886666
 Label
 Limits, Limits Everywhere : the Tools of Mathematical Analysis, David Applebaum
 Antecedent source
 unknown
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Cover; Contents; PART I: APPROACHING LIMITS; 1. A Whole Lot of Numbers; 1.1 Natural Numbers; 1.2 Prime Numbers; 1.3 The Integers; 1.4 Exercises for Chapter 1; 2. Let's Get Real; 2.1 The Rational Numbers; 2.2 Irrational Numbers; 2.3 The Real Numbers; 2.4 A First Look at Infinity; 2.5 Exercises for Chapter 2; 3. The Joy of Inequality; 3.1 Greater or Less?; 3.2 Intervals; 3.3 The Modulus of a Number; 3.4 Maxima and Minima; 3.5 The Theorem of the Means; 3.6 Getting Closer; 3.7 Exercises for Chapter 3; 4. Where Do You Go To, My Lovely?; 4.1 Limits; 4.2 Bounded Sequences; 4.3 The Algebra of Limits
 4.4 Fibonacci Numbers and the Golden Section4.5 Exercises for Chapter 4; 5. Bounds for Glory; 5.1 Bounded Sequences Revisited; 5.2 Monotone Sequences; 5.3 An Old Friend Returns; 5.4 Finding Square Roots; 5.5 Exercises for Chapter 5; 6. You Cannot be Series; 6.1 What are Series?; 6.2 The Sigma Notation; 6.3 Convergence of Series; 6.4 Nonnegative Series; 6.5 The Comparison Test; 6.6 Geometric Series; 6.7 The Ratio Test; 6.8 General Infinite Series; 6.9 Conditional Convergence; 6.10 Regrouping and Rearrangements; 6.11 Real Numbers and Decimal Expansions; 6.12 Exercises for Chapter 6
 PART II: EXPLORING LIMITS7. Wonderful Numbers  e, p and?; 7.1 The Number e; 7.2 The Number p; 7.3 The Number?; 8. Infinite Products; 8.1 Convergence of Infinite Products; 8.2 Infinite Products and Prime Numbers; 8.3 Diversion  Complex Numbers and the Riemann Hypothesis; 9. Continued Fractions; 9.1 Euclid's Algorithm; 9.2 Rational and Irrational Numbers as Continued Fractions; 10. How Infinite Can You Get?; 11. Constructing the Real Numbers; 11.1 Dedekind Cuts; 11.2 Cauchy Sequences; 11.3 Completeness; 12. Where to Next in Analysis? The Calculus; 12.1 Functions; 12.2 Limits and Continuity
 12.3 Differentiation12.4 Integration; 13. Some Brief Remarks About the History of Analysis; Further Reading; Appendices; Appendix 1: The Binomial Theorem; Appendix 2: The Language of Set Theory; Appendix 3: Proof by Mathematical Induction; Appendix 4: The Algebra of Numbers; Hints and Solutions to Selected Exercise; Index; A; B; C; D; E; F; G; H; I; J; K; L; M; N; O; P; Q; R; S; T; U; V; W; Z
 Control code
 784886666
 Dimensions
 unknown
 Extent
 1 online resource (217 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9780191627866
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)784886666
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