Architecture of mathematics:
"Architecture of Mathematics describes the logical structure of Mathematics from its foundations to its real-world applications. It describes the many interweaving relationships between different areas of mathematics and its practical applications, and as such provides unique reading for profes...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton
CRC Press
2022
|
| Ausgabe: | First issued in paperback |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "Architecture of Mathematics describes the logical structure of Mathematics from its foundations to its real-world applications. It describes the many interweaving relationships between different areas of mathematics and its practical applications, and as such provides unique reading for professional mathematicians and nonmathematicians alike. This book can be a very important resource both for the teaching of mathematics and as a means to outline the research links between different subjects within and beyond the subject. Features All notions and properties are introduced logically and sequentially, to help the reader gradually build understanding. Focusses on illustrative examples that explain the meaning of mathematical objects and their properties. Suitable as a supplementary resource for teaching undergraduate mathematics, and as an aid to interdisciplinary research. Forming the reader's understanding of Mathematics as a unified science, the book helps to increase his general mathematical culture"-- |
| Beschreibung: | Includes index |
| Beschreibung: | xvii, 375 Seiten Illustrationen, Diagramme 25 cm |
Internformat
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| 500 | |a Includes index | ||
| 505 | 8 | |a Language -- Sets -- Numbers -- Objects -- Composites -- Synthesis | |
| 520 | |a "Architecture of Mathematics describes the logical structure of Mathematics from its foundations to its real-world applications. It describes the many interweaving relationships between different areas of mathematics and its practical applications, and as such provides unique reading for professional mathematicians and nonmathematicians alike. This book can be a very important resource both for the teaching of mathematics and as a means to outline the research links between different subjects within and beyond the subject. Features All notions and properties are introduced logically and sequentially, to help the reader gradually build understanding. Focusses on illustrative examples that explain the meaning of mathematical objects and their properties. Suitable as a supplementary resource for teaching undergraduate mathematics, and as an aid to interdisciplinary research. Forming the reader's understanding of Mathematics as a unified science, the book helps to increase his general mathematical culture"-- | ||
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| 650 | 4 | |a Mathématiques / Philosophie | |
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Datensatz im Suchindex
| _version_ | 1804184787827556352 |
|---|---|
| adam_text | Contents xi Preface Introduction xiii Floor 1 LANGUAGE 1 Room 1.1 Room 1.2 Room 1.3 Alphabet................................... Syntax......................................... Semantics................................... 2.1 2.2 2.3 2.4 2.5 2.6 2.7 Sets............................................ Subsets...................................... Set product................................ Correspondences ....................... Relations................................... Operators................................... Equinumerosity.......................... Floor 2 SETS 11 . Room Room Room Room Room Room Room Floor 3 NUMBERS Section I CARDINALITIES ................................................. Room 3.1 Zero number ............................. Room 3.2 Natural numbers....................... Section II SOLUTIONS.......................................................... Room 3.3 Integer numbers...................... Room 3.4 Rational numbers....................... Room 3.5 Algebraic numbers................... Section III CUTS....................................................................... Room 3.6 Real numbers............................. Section IV TUPLES................................................................... Room 3.7 Complex numbers................... Room 3.8 Quaternions................................ Floor 4 OBJECTS Block A 2 4 5 ORDERED OBJECTS ..................................................... Room 4A.1 Preordered sets.......................... Room 4A.2 Partially ordered sets ............. 12 19 25 27 30 34 41 47 49 49 50 56 56 64 69 71 71 77 77
79 83 85 87 99
Room 4A.3 Special ordered sets ...... Block В ALGEBRAIC OBJECTS ..................................... ’ ... . Section I OPERATIONS........................................................ Room 4B.1 Operations ............................... Section II SETS WITH INTERIOR COMPOSITION LAWS Subsection 1 Groupoids............................................... Room 4B.2 Groupoids.................................. Room 4B.3 Monoids..................................... Room 4B.4 Groups ..................................... Subsection 2 Rings......................................................... Room 4B.5 Rings ........................................ Room 4B.6 Bodies and fields...................... Subsection 3 Lattices..................................................... Room 4B.7 Lattices..................................... Room 4B.8 Boolean algebras...................... Section III SETS WITH EXTERIOR COMPOSITION LAWS.................................................................... 164 Subsection 1 Groups with operators......................... Room 4B.9 Modules..................................... Room 4B.10 Vector spaces............................ Subsection 2 Rings with operators............................ Room 4B.11 Algebras..................................... Section IV UNIVERSAL ALGEBRAS .................................. Room 4B.12 Universal algebras................... Block C TOPOLOGICAL OBJECTS ........................................... Section I TOPOLOGICAL SPACES..................................... Room 4C.1 General topological spaces ... Room 4C.2
Determination of topological spaces................ Room 4C.3 Special topological spaces . . . Section II METRIC SPACES...................................... Room 4C.4 General metric spaces............ Room 4C.5 Special metricspaces................. Block D MEASURABLE OBJECTS.............................................. Section I MEASURABLE SPACES................................ Room 4D.1 Measurable spaces................... Section II MEASURE SPACES ................................... Room 4D.2 Measures .................................. Room 4D.3 Integrals..................................... Floor 5 COMPOSITES Section I Section II MIXED STRUCTURES................................. Room 5.1 Consistence of structures . . . TOPOLOGICAL ALGEBRAIC OBJECTS ... Room 5.2 Topological groupoids............ 107 113 114 114 117 118 118 129 133 148 148 154 158 158 161 165 165 166 179 179 181 181 187 189 190 199 206 220 220 226 232 233 233 238 238 253 261 262 262 266 268
Room 5.3 Topological groups.................... Room 5.4 Topological vector spaces . . . Room 5.5 Normed vector spaces............. Room 5.6 Banach spaces .......................... Room 5.7 Hilbert spaces............................. Section III APPLICATIONS.................................................... Room 5.8 Derivatives................................ Floor 6 SYNTHESIS 270 272 275 277 280 284 284 289 Section I STRUCTURES....................................................... 290 Room 6.1 Scale of sets................................ 290 Room 6.2 Structures................................... 294 Section II CATEGORIES....................................................... 307 Subsection 1 Categories................................................ 309 Room 6.3 General categories.............. 309 Room 6.4 Non-concrete categories .... 315 Room 6.5 Functors................................ 319 Subsection 2 Concepts.................................................. 331 Room 6.6 Special morphisms.............. 333 Room 6.7 Subobjects and quotientobjects 337 Room 6.8 Product of objects.............. 342 Room 6.9 Initial and terminal objects . . 345 Subsection 3 Beginning ............................................... 348 Room 6.10 Ordered objects.................... 348 Room 6.11 Algebraic objects................. 354 Room 6.12 Short addition .......................... 359 Index 361
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| adam_txt |
Contents xi Preface Introduction xiii Floor 1 LANGUAGE 1 Room 1.1 Room 1.2 Room 1.3 Alphabet. Syntax. Semantics. 2.1 2.2 2.3 2.4 2.5 2.6 2.7 Sets. Subsets. Set product. Correspondences . Relations. Operators. Equinumerosity. Floor 2 SETS 11 . Room Room Room Room Room Room Room Floor 3 NUMBERS Section I CARDINALITIES . Room 3.1 Zero number . Room 3.2 Natural numbers. Section II SOLUTIONS. Room 3.3 Integer numbers. Room 3.4 Rational numbers. Room 3.5 Algebraic numbers. Section III CUTS. Room 3.6 Real numbers. Section IV TUPLES. Room 3.7 Complex numbers. Room 3.8 Quaternions. Floor 4 OBJECTS Block A 2 4 5 ORDERED OBJECTS . Room 4A.1 Preordered sets. Room 4A.2 Partially ordered sets . 12 19 25 27 30 34 41 47 49 49 50 56 56 64 69 71 71 77 77
79 83 85 87 99
Room 4A.3 Special ordered sets . Block В ALGEBRAIC OBJECTS . ’ . . Section I OPERATIONS. Room 4B.1 Operations . Section II SETS WITH INTERIOR COMPOSITION LAWS Subsection 1 Groupoids. Room 4B.2 Groupoids. Room 4B.3 Monoids. Room 4B.4 Groups . Subsection 2 Rings. Room 4B.5 Rings . Room 4B.6 Bodies and fields. Subsection 3 Lattices. Room 4B.7 Lattices. Room 4B.8 Boolean algebras. Section III SETS WITH EXTERIOR COMPOSITION LAWS. 164 Subsection 1 Groups with operators. Room 4B.9 Modules. Room 4B.10 Vector spaces. Subsection 2 Rings with operators. Room 4B.11 Algebras. Section IV UNIVERSAL ALGEBRAS . Room 4B.12 Universal algebras. Block C TOPOLOGICAL OBJECTS . Section I TOPOLOGICAL SPACES. Room 4C.1 General topological spaces . Room 4C.2
Determination of topological spaces. Room 4C.3 Special topological spaces . . . Section II METRIC SPACES. Room 4C.4 General metric spaces. Room 4C.5 Special metricspaces. Block D MEASURABLE OBJECTS. Section I MEASURABLE SPACES. Room 4D.1 Measurable spaces. Section II MEASURE SPACES . Room 4D.2 Measures . Room 4D.3 Integrals. Floor 5 COMPOSITES Section I Section II MIXED STRUCTURES. Room 5.1 Consistence of structures . . . TOPOLOGICAL ALGEBRAIC OBJECTS . Room 5.2 Topological groupoids. 107 113 114 114 117 118 118 129 133 148 148 154 158 158 161 165 165 166 179 179 181 181 187 189 190 199 206 220 220 226 232 233 233 238 238 253 261 262 262 266 268
Room 5.3 Topological groups. Room 5.4 Topological vector spaces . . . Room 5.5 Normed vector spaces. Room 5.6 Banach spaces . Room 5.7 Hilbert spaces. Section III APPLICATIONS. Room 5.8 Derivatives. Floor 6 SYNTHESIS 270 272 275 277 280 284 284 289 Section I STRUCTURES. 290 Room 6.1 Scale of sets. 290 Room 6.2 Structures. 294 Section II CATEGORIES. 307 Subsection 1 Categories. 309 Room 6.3 General categories. 309 Room 6.4 Non-concrete categories . 315 Room 6.5 Functors. 319 Subsection 2 Concepts. 331 Room 6.6 Special morphisms. 333 Room 6.7 Subobjects and quotientobjects 337 Room 6.8 Product of objects. 342 Room 6.9 Initial and terminal objects . . 345 Subsection 3 Beginning . 348 Room 6.10 Ordered objects. 348 Room 6.11 Algebraic objects. 354 Room 6.12 Short addition . 359 Index 361 |
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| author | Serovajskij, Semen Jakovlevič 1954- |
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| bvnumber | BV048643423 |
| classification_rvk | SK 130 |
| contents | Language -- Sets -- Numbers -- Objects -- Composites -- Synthesis |
| ctrlnum | (OCoLC)1369568212 (DE-599)BVBBV048643423 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | First issued in paperback |
| format | Book |
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| id | DE-604.BV048643423 |
| illustrated | Illustrated |
| index_date | 2024-07-03T21:18:24Z |
| indexdate | 2024-07-10T09:44:54Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034018304 |
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| owner_facet | DE-739 DE-20 |
| physical | xvii, 375 Seiten Illustrationen, Diagramme 25 cm |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | CRC Press |
| record_format | marc |
| spelling | Serovajskij, Semen Jakovlevič 1954- Verfasser (DE-588)1147907293 aut Architecture of mathematics Simon Serovajsky First issued in paperback Boca Raton CRC Press 2022 xvii, 375 Seiten Illustrationen, Diagramme 25 cm txt rdacontent n rdamedia nc rdacarrier Includes index Language -- Sets -- Numbers -- Objects -- Composites -- Synthesis "Architecture of Mathematics describes the logical structure of Mathematics from its foundations to its real-world applications. It describes the many interweaving relationships between different areas of mathematics and its practical applications, and as such provides unique reading for professional mathematicians and nonmathematicians alike. This book can be a very important resource both for the teaching of mathematics and as a means to outline the research links between different subjects within and beyond the subject. Features All notions and properties are introduced logically and sequentially, to help the reader gradually build understanding. Focusses on illustrative examples that explain the meaning of mathematical objects and their properties. Suitable as a supplementary resource for teaching undergraduate mathematics, and as an aid to interdisciplinary research. Forming the reader's understanding of Mathematics as a unified science, the book helps to increase his general mathematical culture"-- Logic, Symbolic and mathematical Arithmetic / Foundations Mathematics / Philosophy Logique symbolique et mathématique Arithmétique / Fondements Mathématiques / Philosophie Arithmetic / Foundations fast Logic, Symbolic and mathematical fast Mathematics / Philosophy fast Metamathematik (DE-588)4074759-1 gnd rswk-swf Grundlagenforschung (DE-588)4131708-7 gnd rswk-swf Metamathematik (DE-588)4074759-1 s Grundlagenforschung (DE-588)4131708-7 s DE-604 Äquivalent Druck-Ausgabe, Hardcover 978-1-138-60105-5 Erscheint auch als Online-Ausgabe 978-0-429-47037-0 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=034018304&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Serovajskij, Semen Jakovlevič 1954- Architecture of mathematics Language -- Sets -- Numbers -- Objects -- Composites -- Synthesis Logic, Symbolic and mathematical Arithmetic / Foundations Mathematics / Philosophy Logique symbolique et mathématique Arithmétique / Fondements Mathématiques / Philosophie Arithmetic / Foundations fast Logic, Symbolic and mathematical fast Mathematics / Philosophy fast Metamathematik (DE-588)4074759-1 gnd Grundlagenforschung (DE-588)4131708-7 gnd |
| subject_GND | (DE-588)4074759-1 (DE-588)4131708-7 |
| title | Architecture of mathematics |
| title_auth | Architecture of mathematics |
| title_exact_search | Architecture of mathematics |
| title_exact_search_txtP | Architecture of mathematics |
| title_full | Architecture of mathematics Simon Serovajsky |
| title_fullStr | Architecture of mathematics Simon Serovajsky |
| title_full_unstemmed | Architecture of mathematics Simon Serovajsky |
| title_short | Architecture of mathematics |
| title_sort | architecture of mathematics |
| topic | Logic, Symbolic and mathematical Arithmetic / Foundations Mathematics / Philosophy Logique symbolique et mathématique Arithmétique / Fondements Mathématiques / Philosophie Arithmetic / Foundations fast Logic, Symbolic and mathematical fast Mathematics / Philosophy fast Metamathematik (DE-588)4074759-1 gnd Grundlagenforschung (DE-588)4131708-7 gnd |
| topic_facet | Logic, Symbolic and mathematical Arithmetic / Foundations Mathematics / Philosophy Logique symbolique et mathématique Arithmétique / Fondements Mathématiques / Philosophie Metamathematik Grundlagenforschung |
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