Elements of mathematics: from Euclid to Gödel
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton ; Oxford
Princeton University Press
[2016]
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | xiv, 422 Seiten Illustrationen, Diagramme 25 cm |
| ISBN: | 9780691171685 9780691178547 |
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MARC
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| 245 | 1 | 0 | |a Elements of mathematics |b from Euclid to Gödel |c John Stillwell |
| 264 | 1 | |a Princeton ; Oxford |b Princeton University Press |c [2016] | |
| 264 | 4 | |c © 2016 | |
| 300 | |a xiv, 422 Seiten |b Illustrationen, Diagramme |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
| _version_ | 1804176440259772416 |
|---|---|
| adam_text | CONTENTS
PREFACE
XI
ELEMENTARY TOPICS
1
1.1
ARITHMETIC
2
1.2
COMPUTATION 4
1.3 ALGEBRA
7
1.4
GEOMETRY
9
1.5
CALCULUS
13
1.6
COMBINATORICS
16
1.7
PROBABILITY 20
1.8 LOGIC 22
1.9
HISTORICAL REMARKS 25
1.10
PHILOSOPHICAL REMARKS
32
2 ARITHMETIC
35
2.1
THE EUCLIDEAN ALGORITHM
36
2.2
CONTINUED FRACTIONS 38
2.3 PRIME
NUMBERS
40
2.4
FINITE ARITHMETIC 44
2.5
QUADRATIC INTEGERS
46
2.6
THE
GAUSSIAN
INTEGERS
49
2.7
EULER S
PROOF REVISITED
54
2.8
AND
THE
PELL
EQUATION
57
2.9
HISTORICAL
REMARKS
60
2.10
PHILOSOPHICAL
REMARKS
67
3
COMPUTATION
73
3.1
NUMERALS 74
3.2
ADDITION 77
3.3
MULTIPLICATION
79
3.4 DIVISION 82
3.5
EXPONENTIATION 84
IBLIOTHEK
DEUTSCHES
MUSEUM
_Y
..
VIII
CONTENTS
3.6 P
AND
NP PROBLEMS
87
3.7
TURING
MACHINES 90
3.8
*UNSOLVABLE
PROBLEMS
94
3.9
*UNIVERSAL
MACHINES
97
3.10
HISTORICAL REMARKS
98
3.11 PHILOSOPHICAL REMARKS 103
4
ALGEBRA
106
4.1
CLASSICAL ALGEBRA
107
4.2
RINGS
112
4.3
FIELDS
117
4.4
TWO THEOREMS
INVOLVING
INVERSES
120
4.5
VECTOR
SPACES
123
4.6 LINEAR
DEPENDENCE, BASIS,
AND
DIMENSION
126
4.7
RINGS
OF
POLYNOMIALS
128
4.8
ALGEBRAIC
NUMBER
FIELDS 133
4.9
NUMBER FIELDS
AS
VECTOR
SPACES
136
4.10
HISTORICAL REMARKS
139
4.11
PHILOSOPHICAL
REMARKS
143
5
GEOMETRY
148
5.1
NUMBERS
AND
GEOMETRY 149
5.2
EUCLID S THEORY
OF
ANGLES
150
5.3
EUCLID S
THEORY
OF
AREA
153
5.4
STRAIGHTEDGE
AND
COMPASS
CONSTRUCTIONS
159
5.5
GEOMETRIC
REALIZATION
OF
ALGEBRAIC
OPERATIONS
161
5.6
ALGEBRAIC
REALIZATION
OF
GEOMETRIC
CONSTRUCTIONS
164
5.7 VECTOR SPACE
GEOMETRY
168
5.8 INTRODUCING
LENGTH
VIA
THE
INNER
PRODUCT
171
5.9
CONSTRUCTIBLE NUMBER FIELDS
175
5.10 HISTORICAL REMARKS 177
5.11 PHILOSOPHICAL REMARKS
184
6
CALCULUS
193
6.1
GEOMETRIC SERIES
194
6.2
TANGENTS
AND
DIFFERENTIATION 197
CONTENTS
IX
6.3
CALCULATING
DERIVATIVES
202
6.4
CURVED AREAS
208
6.5
THE
AREA
UNDER
Y=
X
211
6.6
*THE
FUNDAMENTAL
THEOREM
OF
CALCULUS
214
6.7
POWER SERIES
FOR
THE
LOGARITHM
218
6.8
*THE
INVERSE
TANGENT
FUNCTION
AND N
226
6.9
ELEMENTARY FUNCTIONS
229
6.10
HISTORICAL REMARKS
233
6.11 PHILOSOPHICAL
REMARKS
239
7 COMBINATORICS
243
7.1
THE INFINITUDE
OF
PRIMES
244
7.2 BINOMIAL
COEFFICIENTS
AND
FERMAT S LITTLE
THEOREM
245
7.3
GENERATING FUNCTIONS
246
7.4
GRAPH
THEORY
250
7.5
TREES
252
7.6 PLANAR
GRAPHS
254
7.7
THE EULER
POLYHEDRON FORMULA 256
7.8
NONPLANAR
GRAPHS
263
7.9
*THE
KOENIG
INFINITY LEMMA
264
7.10
SPERNER S
LEMMA 268
7.11
HISTORICAL
REMARKS 272
7.12
PHILOSOPHICAL REMARKS 274
8
PROBABILITY
279
8.1
PROBABILITY
AND
COMBINATORICS
280
8.2
GAMBLER S RUIN
282
8.3
RANDOM
WALK
284
8.4
MEAN, VARIANCE,
AND
STANDARD DEVIATION
286
8.5
*THE
BELL
CURVE
290
8.6
HISTORICAL REMARKS
292
8.7
PHILOSOPHICAL
REMARKS
296
9
LOGIC
298
9.1
PROPOSITIONAL
LOGIC
299
9.2
TAUTOLOGIES,
IDENTITIES,
AND
SATISFIABILITY
302
X
CONTENTS
9.3 PROPERTIES,
RELATIONS,
AND
QUANTIFIERS
304
9.4
INDUCTION 307
9.5
*PEANO
ARITHMETIC 311
9.6
*THE
REAL NUMBERS
315
9.7
*INFINITY
320
9.8
*SET THEORY
324
9.9
*REVERSE
MATHEMATICS 327
9.10
HISTORICAL REMARKS 330
9.11
PHILOSOPHICAL
REMARKS 333
10
SOME ADVANCED MATHEMATICS
336
10.1
ARITHMETIC:
THE
PELL EQUATION
337
10.2
COMPUTATION:
THE
WORD
PROBLEM
344
10.3
ALGEBRA:
THE
FUNDAMENTAL
THEOREM
349
10.4
GEOMETRY:
THE
PROJECTIVE
LINE
354
10.5
CALCULUS: WALLIS S
PRODUCT
FOR
N
360
10.6
COMBINATORICS: RAMSEY
THEORY
365
10.7
PROBABILITY:
DE
MOIVRE S
DISTRIBUTION
369
10.8
LOGIC:
THE
COMPLETENESS
THEOREM
376
10.9
HISTORICAL
AND
PHILOSOPHICAL
REMARKS
381
BIBLIOGRAPHY
395
INDEX
405
|
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| author | Stillwell, John 1942- |
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| author_facet | Stillwell, John 1942- |
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| dewey-full | 510.71/1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510.71/1 |
| dewey-search | 510.71/1 |
| dewey-sort | 3510.71 11 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-10T07:32:13Z |
| institution | BVB |
| isbn | 9780691171685 9780691178547 |
| language | English |
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| physical | xiv, 422 Seiten Illustrationen, Diagramme 25 cm |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Princeton University Press |
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| spelling | Stillwell, John 1942- Verfasser (DE-588)128427264 aut Elements of mathematics from Euclid to Gödel John Stillwell Princeton ; Oxford Princeton University Press [2016] © 2016 xiv, 422 Seiten Illustrationen, Diagramme 25 cm txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematik (DE-588)4037944-9 s Mathematische Logik (DE-588)4037951-6 s DE-604 Digitalisierung Deutsches Museum application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029089245&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stillwell, John 1942- Elements of mathematics from Euclid to Gödel Mathematische Logik (DE-588)4037951-6 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4037944-9 |
| title | Elements of mathematics from Euclid to Gödel |
| title_auth | Elements of mathematics from Euclid to Gödel |
| title_exact_search | Elements of mathematics from Euclid to Gödel |
| title_full | Elements of mathematics from Euclid to Gödel John Stillwell |
| title_fullStr | Elements of mathematics from Euclid to Gödel John Stillwell |
| title_full_unstemmed | Elements of mathematics from Euclid to Gödel John Stillwell |
| title_short | Elements of mathematics |
| title_sort | elements of mathematics from euclid to godel |
| title_sub | from Euclid to Gödel |
| topic | Mathematische Logik (DE-588)4037951-6 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Mathematische Logik Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029089245&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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