Introduction to analysis and abstract algebra:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia [u.a.]
Saunders
1967
|
| Series: | Saunders mathematics books
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 344 S. |
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Record in the Search Index
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|---|---|
| adam_text | CHAPTER I
INTRODUCTION 1
1. Logic and Proofs 1
2. Axiomatic Systems 3
3. The Language of Sets 4
chapter II
THE ORDERED FIELD OF REAL NUMBERS 8
1. Preliminaries 8
2. The Axioms for Addition 9
3. The Axioms for Multiplication 12
4. The Distributive Axiom 14
5. The Axioms of Order 17
chapter III
THE NATURAL NUMBERS 23
1. Introduction 23
2. Inductive Sets 24
3. The General Associative and Commutative Laws 35
chapter IV
THE INTEGERS AND THE RATIONALS 40
1. The Integers 40
2. The Integers as Exponents 41
ix
x I Contents
3. Elementary Number Theory 43
4. The Rationals 56
CHAPTER V
THE COMPLETE ORDERED FIELD OF REAL NUMBERS 61
1. Introduction 61
2. The Axiom of Completeness 62
3. The Archimedean Property 68
4. Irrational Numbers 70
5. Denumerable and Nondenumerable Sets 74
CHAPTER VI
SETS AND RELATIONS 81
1. The Composition of Sets 81
2. Ordered Pairs and Product Sets 87
3. Relations 89
4. Equivalence Relations and Partitions 91
CHAPTER VII
MAPPINGS AND OPERATIONS 96
1. Mappings Into 96
2. Mappings Onto 99
3. One to One Mappings 100
4. Operations and Mathematical Systems 106
CHAPTER VIII
GROUPS Ill
1. Definitions and Examples Ill
2. Sources of Groups 116
3. Elementary Properties 125
4. Isomorphisms 127
5. Cyclic Groups 131
6. Subgroups 136
7. Cayley s Theorem 140
Contents / xi
chapter IX
RINGS, INTEGRAL DOMAINS AND FIELDS 142
1. Definition of a Ring; Examples 142
2. Integral Domains 145
3. The Integers 148
4. Fields 151
CHAPTER X
CONSTRUCTIVE APPROACH TO THE REAL NUMBERS 159
1. Introduction 159
2. The Construction of the Integers 161
3. Construction of the Rationals 173
4. Construction of the Real Numbers 176
chapter XI
SEQUENCES AND POINT SETS 199
1. Definition of a Sequence; Convergence 199
2. Monotonic Sequences 208
3. Point Sets 212
4. Cauchy Sequences 221
chapter XII
LIMITS AND CONTINUITY 227
1. The Limit of a Function 227
2. Continuity 236
3. Functions Continuous on a Closed Interval 240
4. Differentiable Functions 246
5. Elementary Functions 259
CHAPTER XIII
INTEGRATION 264
1. The Area Problem 264
2. The Integral of a Bounded Function 269
3. More on Elementary Functions 294
xii I Contents
CHAPTER XIV
THE ROLE OF POLYNOMIALS IN THE CLASS OF CONTIN¬
UOUS FUNCTIONS 314
1. Normed Linear Spaces 314
2. Approximations by Polynomials 318
3. Interpolation 326
4. Least Square Approximation 329
5. Conclusion 339
INDEX 341
|
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| indexdate | 2024-07-09T15:53:39Z |
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| language | English |
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| physical | XII, 344 S. |
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| publishDate | 1967 |
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| publishDateSort | 1967 |
| publisher | Saunders |
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| series2 | Saunders mathematics books |
| spelling | Hafstrom, John E. Verfasser aut Introduction to analysis and abstract algebra Philadelphia [u.a.] Saunders 1967 XII, 344 S. txt rdacontent n rdamedia nc rdacarrier Saunders mathematics books Algèbre abstraite Analyse mathématique Analyse mathématique ram Algebra, Abstract Mathematical analysis Algebra (DE-588)4001156-2 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Algebra (DE-588)4001156-2 s Analysis (DE-588)4001865-9 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001945613&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hafstrom, John E. Introduction to analysis and abstract algebra Algèbre abstraite Analyse mathématique Analyse mathématique ram Algebra, Abstract Mathematical analysis Algebra (DE-588)4001156-2 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4001156-2 (DE-588)4001865-9 |
| title | Introduction to analysis and abstract algebra |
| title_auth | Introduction to analysis and abstract algebra |
| title_exact_search | Introduction to analysis and abstract algebra |
| title_full | Introduction to analysis and abstract algebra |
| title_fullStr | Introduction to analysis and abstract algebra |
| title_full_unstemmed | Introduction to analysis and abstract algebra |
| title_short | Introduction to analysis and abstract algebra |
| title_sort | introduction to analysis and abstract algebra |
| topic | Algèbre abstraite Analyse mathématique Analyse mathématique ram Algebra, Abstract Mathematical analysis Algebra (DE-588)4001156-2 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Algèbre abstraite Analyse mathématique Algebra, Abstract Mathematical analysis Algebra Analysis |
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