Foundations and fundamental concepts of mathematics:
Gespeichert in:
| Vorheriger Titel: | Eves, Howard An introduction to the foundations and fundamental concept of mathematics |
|---|---|
| 1. Verfasser: | |
| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
Boston, Mass.
PWS-Kent Publ. Co.
1990
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | The Prindle, Weber & Schmidt series in advanced mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 344 S. graph. Darst. |
| ISBN: | 0534921639 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV026090733 | ||
| 003 | DE-604 | ||
| 005 | 20110228 | ||
| 007 | t | ||
| 008 | 110326s1990 d||| |||| 00||| und d | ||
| 020 | |a 0534921639 |9 0-534-92163-9 | ||
| 035 | |a (OCoLC)636351063 | ||
| 035 | |a (DE-599)BVBBV026090733 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | |a und | ||
| 049 | |a DE-188 | ||
| 100 | 1 | |a Eves, Howard |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Foundations and fundamental concepts of mathematics |c Howard Eves |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Boston, Mass. |b PWS-Kent Publ. Co. |c 1990 | |
| 300 | |a XVII, 344 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a The Prindle, Weber & Schmidt series in advanced mathematics | |
| 648 | 7 | |a Geschichte |2 gnd |9 rswk-swf | |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Grundlage |0 (DE-588)4158388-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Mathematik |0 (DE-588)4037944-9 |D s |
| 689 | 0 | 1 | |a Geschichte |A z |
| 689 | 0 | |5 DE-188 | |
| 689 | 1 | 0 | |a Mathematik |0 (DE-588)4037944-9 |D s |
| 689 | 1 | 1 | |a Grundlage |0 (DE-588)4158388-7 |D s |
| 689 | 1 | |5 DE-188 | |
| 780 | 0 | 0 | |i Früher u.d.T. |a Eves, Howard |t An introduction to the foundations and fundamental concept of mathematics |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021685180&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-021685180 | ||
Datensatz im Suchindex
| _version_ | 1804144522368647168 |
|---|---|
| adam_text | Titel: Foundations and fundamental concepts of mathematics
Autor: Eves, Howard Whitley
Jahr: 1990
CONTENTS i i 1 Mathematics Before Euclid 1 I 1.1 The Empirical Nature of pre-Hellenic Mathematics 1 1.2 Induction Versus Deduction 5 1.3 Early Greek Mathematics and the Introduction of Deductive Procedures 9 1.4 Material Axiomatics 13 1.5 The Origin of the Axiomatic Method 15 Problems 17 i l 2 Euclid s Elements 26 i ~~1 2.1 The Importance and Formal Nature of Euclid’s Elements 26 2.2 Aristotle and Proclus on the Axiomatic Method 29 2.3 Euclid’s Definitions, Axioms, and Postulates 32 2.4 Some Logical Shortcomings of Euclid’s Elements 37 2.5 The End of the Greek Period and the Transition to Modern Times 41 Problems 45 I I 3 Non-Euclidean Geometry 51 i I 3.1 Euclid’s Fifth Postulate 51 3.2 Saccheri and the Reductio ad Absurdum Method 54 3.3 The Work of Lambert and Legendre 58 3.4 The Discovery of Non-Euclidean Geometry 60 3.5 The Consistency and the Significance of Non-Euclidean Geometry 65 Problems 70 XV
XVI CONTENTS i ... ... J 4 Hilbert s Grundlagen 79 i i 4.1 The Work of Pasch, Peano, and Pieri 79 4.2 Hilbert’s Grundlagen der Geometrie 82 4.3 Poincare’s Model and the Consistency of Lobachevskian Geometry 88 4.4 Analytic Geometry 92 4.5 Projective Geometry and the Principle of Duality 98 Problems 104 i i 5 Algebraic Structure 113 i i 5.1 Emergence of Algebraic Structure 113 5.2 The Liberation of Algebra 118 5.3 Groups 124 5.4 The Significance of Groups in Algebra and Geometry 128 5.5 Relations 132 Problems 136 i ~i 6 Formal Axiomatics 147 i ~i 6.1 Statement of the Modern Axiomatic Method 147 6.2 A Simple Example of a Branch of Pure Mathematics 150 6.3 Properties of Postulate Sets—Equivalence and Consistency 154 6.4 Properties of Postulate Sets—Independence, Completeness, and Categoricalness 158 6.5 Miscellaneous Comments 162 Problems 166 l i 7 The Real Number System 173 i i 7.1 Significance of the Real Number System for the Foundations of Analysis 173 7.2 The Postulational Approach to the Real Number System 179 7.3 The Natural Numbers and the Principle of Mathematical Induction 183 7.4 The Integers and the Rational Numbers 191 7.5 The Real Numbers and the Complex Numbers 196 Problems 202 I =1 8 Sets 212 l~ ----- — - 1 8.1 Sets and Their Basic Relations and Operations 212 8.2 Boolean Algebra 216 8.3 Sets and the Foundations of Mathematics 221 8.4 Infinite Sets and Transfinite Numbers 224 8.5 Sets and the Fundamental Concepts of Mathematics 229 Problems 236
CONTENTS XVII ] 9 Logic and Philosophy 243 C 9.1 Symbolic Logic 243 9.2 The Calculus of Propositions 250 9.3 Other Logics 257 9.4 Crises in the Foundations of Mathematics 9.5 Philosophies of Mathematics Problems 271 266 Appendix 275 A.l The First Twenty-Eight Propositions of Euclid 275 A.2 Euclidean Constructions 276 A.3 Removal of Some Redundancies 284 A.4 Membership Tables 289 A. 5 A Constructive Proof of the Existence of Transcendental Numbers 290 A.6 The Eudoxian Resolution of the First Crisis in the Foundations of Mathematics 292 A.7 Nonstandard Analysis 294 A.8 The Axiom of Choice 296 A.9 A Note on Godel’s Incompleteness Theorem 299 Bibliography 303 Solution Suggestions for Selected Problems 316 Index 329
|
| any_adam_object | 1 |
| author | Eves, Howard |
| author_facet | Eves, Howard |
| author_role | aut |
| author_sort | Eves, Howard |
| author_variant | h e he |
| building | Verbundindex |
| bvnumber | BV026090733 |
| ctrlnum | (OCoLC)636351063 (DE-599)BVBBV026090733 |
| edition | 3. ed. |
| era | Geschichte gnd |
| era_facet | Geschichte |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01580nam a2200409 c 4500</leader><controlfield tag="001">BV026090733</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20110228 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">110326s1990 d||| |||| 00||| und d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0534921639</subfield><subfield code="9">0-534-92163-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)636351063</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV026090733</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">und</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-188</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Eves, Howard</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Foundations and fundamental concepts of mathematics</subfield><subfield code="c">Howard Eves</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">3. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boston, Mass.</subfield><subfield code="b">PWS-Kent Publ. Co.</subfield><subfield code="c">1990</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVII, 344 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">The Prindle, Weber & Schmidt series in advanced mathematics</subfield></datafield><datafield tag="648" ind1=" " ind2="7"><subfield code="a">Geschichte</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Grundlage</subfield><subfield code="0">(DE-588)4158388-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Geschichte</subfield><subfield code="A">z</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-188</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Grundlage</subfield><subfield code="0">(DE-588)4158388-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-188</subfield></datafield><datafield tag="780" ind1="0" ind2="0"><subfield code="i">Früher u.d.T.</subfield><subfield code="a">Eves, Howard</subfield><subfield code="t">An introduction to the foundations and fundamental concept of mathematics</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021685180&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-021685180</subfield></datafield></record></collection> |
| id | DE-604.BV026090733 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T23:04:54Z |
| institution | BVB |
| isbn | 0534921639 |
| language | Undetermined |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021685180 |
| oclc_num | 636351063 |
| open_access_boolean | |
| owner | DE-188 |
| owner_facet | DE-188 |
| physical | XVII, 344 S. graph. Darst. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | PWS-Kent Publ. Co. |
| record_format | marc |
| series2 | The Prindle, Weber & Schmidt series in advanced mathematics |
| spelling | Eves, Howard Verfasser aut Foundations and fundamental concepts of mathematics Howard Eves 3. ed. Boston, Mass. PWS-Kent Publ. Co. 1990 XVII, 344 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The Prindle, Weber & Schmidt series in advanced mathematics Geschichte gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Grundlage (DE-588)4158388-7 gnd rswk-swf Mathematik (DE-588)4037944-9 s Geschichte z DE-188 Grundlage (DE-588)4158388-7 s Früher u.d.T. Eves, Howard An introduction to the foundations and fundamental concept of mathematics HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021685180&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Eves, Howard Foundations and fundamental concepts of mathematics Mathematik (DE-588)4037944-9 gnd Grundlage (DE-588)4158388-7 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4158388-7 |
| title | Foundations and fundamental concepts of mathematics |
| title_auth | Foundations and fundamental concepts of mathematics |
| title_exact_search | Foundations and fundamental concepts of mathematics |
| title_full | Foundations and fundamental concepts of mathematics Howard Eves |
| title_fullStr | Foundations and fundamental concepts of mathematics Howard Eves |
| title_full_unstemmed | Foundations and fundamental concepts of mathematics Howard Eves |
| title_old | Eves, Howard An introduction to the foundations and fundamental concept of mathematics |
| title_short | Foundations and fundamental concepts of mathematics |
| title_sort | foundations and fundamental concepts of mathematics |
| topic | Mathematik (DE-588)4037944-9 gnd Grundlage (DE-588)4158388-7 gnd |
| topic_facet | Mathematik Grundlage |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021685180&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT eveshoward foundationsandfundamentalconceptsofmathematics |