Description |
1 online resource (xviii, 376 pages) |
Contents |
Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- Introduction -- Floor 1: LANGUAGE -- Room 1.1 Alphabet -- Room 1.2 Syntax -- Room 1.3 Semantics -- Floor 2: SETS -- Room 2.1 Sets -- Room 2.2 Subsets -- Room 2.3 Set product -- Room 2.4 Correspondences -- Room 2.5 Relations -- Room 2.6 Operators -- Room 2.7 Equinumerosity -- 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 |
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Room 3.6 Real numbers -- Section IV TUPLES -- Room 3.7 Complex numbers -- Room 3.8 Quaternions -- Floor 4: OBJECTS -- Block A ORDERED OBJECTS -- Room 4A.1 Preordered sets -- Room 4A.2 Partially ordered sets -- Room 4A.3 Special ordered sets -- Block B 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 |
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Room 4B.8 Boolean algebras -- Section III SETS WITH EXTERIOR COMPOSITION LAWS -- 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 metric spaces |
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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 MIXED STRUCTURES -- Room 5.1 Consistence of structures -- Section II TOPOLOGICAL ALGEBRAIC OBJECTS -- Room 5.2 Topological groupoids -- 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 -- Section I STRUCTURES |
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Room 6.1 Scale of sets -- Room 6.2 Structures -- Section II CATEGORIES -- Subsection 1 Categories -- Room 6.3 General categories -- Room 6.4 Non-concrete categories -- Room 6.5 Functors -- Subsection 2 Concepts -- Room 6.6 Special morphisms -- Room 6.7 Subobjects and quotient objects -- Room 6.8 Product of objects -- Room 6.9 Initial and terminal objects -- Subsection 3 Beginning -- Room 6.10 Ordered objects -- Room 6.11 Algebraic objects -- Room 6.12 Short addition -- Index |
Notes |
Simon Serovajsky is a professor of differential equations and control theory at al-Farabi Kazakh National University in Kazakhstan. He is the author of many books published in the area of optimisation and optimal control theory, modelling, philosophy and history of mathematics as well as a long list of high-quality publications in learned journals |
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Vendor-supplied metadata |
Subject |
Logic, Symbolic and mathematical.
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Mathematics -- Philosophy.
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Logic, Symbolic and mathematical
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Mathematics -- Philosophy
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Form |
Electronic book
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ISBN |
9780429470370 |
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0429470371 |
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9780429893544 |
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042989354X |
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9780429893537 |
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0429893531 |
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9780429893520 |
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0429893523 |
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