Number systems: an introduction to algebra and analysis
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2015]
|
| Schriftenreihe: | Pure and applied undergraduate texts
23 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | viii, 144 Seiten Diagramme |
| ISBN: | 9781470420185 |
Internformat
MARC
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| 264 | 4 | |c © 2015 | |
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| 650 | 7 | |a Mathematics education ... Arithmetic, number theory ... Integers, rational numbers |2 msc | |
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| 650 | 4 | |a Numeration |v Textbooks | |
| 650 | 4 | |a Algebra |v Textbooks | |
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| 650 | 4 | |a Mathematics education ... Arithmetic, number theory ... Integers, rational numbers | |
| 650 | 4 | |a Mathematics education ... Arithmetic, number theory ... Real numbers, complex numbers | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-027948552 | ||
Datensatz im Suchindex
| _version_ | 1804153260932595712 |
|---|---|
| adam_text | Contents
Preface
vii
Chapter
1.
Natural Numbers
1
1.1.
Peano Systems
2
1.2.
Addition
4
1.3.
Multiplication
9
1.4.
Order
12
1.5.
Isomorphism of Peano Systems
13
1.6.
A Set-Theoretic Model
17
1.7.
Recursion
19
1.8.
Mathematical Induction
24
1.9.
Algebraic Structures
27
Notes
28
Exercises
29
Chapter
2.
Integers
37
2.1.
Definition of the Integers
37
2.2.
Addition of Integers
40
2.3.
Multiplication of Integers
44
2.4.
Order
47
2.5.
Rings and Integral Domains
49
Notes
54
Exercises
55
Chapter
3.
Rational Numbers
59
3.1.
Definition of Rational Numbers
60
vi
Contents
3.2. Addition
of
Rational
Numbers
61
3.3.
Multiplication of Rational Numbers
62
3.4.
Order
64
3.5.
Algebraic Structures on
Q
68
3.6.
Convergence in an Ordered Field
71
3.7.
Limitations of
Q
77
Notes
80
Exercises
80
Chapter
4.
Real Numbers
85
4.1.
Definition of Real Numbers
85
4.2.
Operations on
R
87
4.3.
R
as a Field
88
4.4.
R
as an Ordered Field
90
4.5.
Cauchy Completeness of
R
93
4.6.
Dedekind Completeness of
R
96
4.7.
Continuous Functions on
R
101
Notes
103
Exercises
104
Chapter
5.
Complex Numbers
107
5.1.
Definition of Complex Numbers
108
5.2.
The Field
С
of Complex Numbers
108
5.3.
С
as a Vector Space 111
5.4.
С
as a Normed Algebra
112
5.5.
Convergence in
С
113
5.6.
Roots of Complex Numbers
117
5.7.
Continuous functions
118
5.8.
The Fundamental Theorem of Algebra
120
Notes
122
Exercises
123
Appendix A. Sets, Relations, Functions
127
A.I. Sets
127
A.
2.
Operations on Sets
129
A.3. Relations
132
A.
4.
Functions and Operations
133
Notes
134
Exercises
135
Bibliography
139
Index
141
|
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| author | Ovchinnikov, Sergei 1950- |
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| callnumber-subject | QA - Mathematics |
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| dewey-full | 512.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7 |
| dewey-search | 512.7 |
| dewey-sort | 3512.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| isbn | 9781470420185 |
| language | English |
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| spelling | Ovchinnikov, Sergei 1950- Verfasser (DE-588)1029590540 aut Number systems an introduction to algebra and analysis Sergei Ovchinnikov Providence, Rhode Island American Mathematical Society [2015] © 2015 viii, 144 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Pure and applied undergraduate texts 23 The Sally series Literaturangaben Mathematics education ... Arithmetic, number theory ... Natural numbers msc Mathematics education ... Arithmetic, number theory ... Integers, rational numbers msc Mathematics education ... Arithmetic, number theory ... Real numbers, complex numbers msc Numeration Textbooks Algebra Textbooks Mathematics education ... Arithmetic, number theory ... Natural numbers Mathematics education ... Arithmetic, number theory ... Integers, rational numbers Mathematics education ... Arithmetic, number theory ... Real numbers, complex numbers Zahlenbereich (DE-588)4190464-3 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Zahlenbereich (DE-588)4190464-3 s DE-604 Pure and applied undergraduate texts 23 (DE-604)BV035489189 23 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027948552&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ovchinnikov, Sergei 1950- Number systems an introduction to algebra and analysis Pure and applied undergraduate texts Mathematics education ... Arithmetic, number theory ... Natural numbers msc Mathematics education ... Arithmetic, number theory ... Integers, rational numbers msc Mathematics education ... Arithmetic, number theory ... Real numbers, complex numbers msc Numeration Textbooks Algebra Textbooks Mathematics education ... Arithmetic, number theory ... Natural numbers Mathematics education ... Arithmetic, number theory ... Integers, rational numbers Mathematics education ... Arithmetic, number theory ... Real numbers, complex numbers Zahlenbereich (DE-588)4190464-3 gnd |
| subject_GND | (DE-588)4190464-3 (DE-588)4123623-3 |
| title | Number systems an introduction to algebra and analysis |
| title_auth | Number systems an introduction to algebra and analysis |
| title_exact_search | Number systems an introduction to algebra and analysis |
| title_full | Number systems an introduction to algebra and analysis Sergei Ovchinnikov |
| title_fullStr | Number systems an introduction to algebra and analysis Sergei Ovchinnikov |
| title_full_unstemmed | Number systems an introduction to algebra and analysis Sergei Ovchinnikov |
| title_short | Number systems |
| title_sort | number systems an introduction to algebra and analysis |
| title_sub | an introduction to algebra and analysis |
| topic | Mathematics education ... Arithmetic, number theory ... Natural numbers msc Mathematics education ... Arithmetic, number theory ... Integers, rational numbers msc Mathematics education ... Arithmetic, number theory ... Real numbers, complex numbers msc Numeration Textbooks Algebra Textbooks Mathematics education ... Arithmetic, number theory ... Natural numbers Mathematics education ... Arithmetic, number theory ... Integers, rational numbers Mathematics education ... Arithmetic, number theory ... Real numbers, complex numbers Zahlenbereich (DE-588)4190464-3 gnd |
| topic_facet | Mathematics education ... Arithmetic, number theory ... Natural numbers Mathematics education ... Arithmetic, number theory ... Integers, rational numbers Mathematics education ... Arithmetic, number theory ... Real numbers, complex numbers Numeration Textbooks Algebra Textbooks Zahlenbereich Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027948552&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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