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Book Cover
E-book
Author Serovajsky, Simon. Al-Farabi Kazakh National University, Department of Differential Equations and Control Theory, Almaty, Kazakhstan

Title Architecture of Mathematics
Edition First edition
Published [Place of publication not identified] : Chapman and Hall/CRC, 2020

Copies

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
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
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
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
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
Vendor-supplied metadata
Subject Logic, Symbolic and mathematical.
Mathematics -- Philosophy.
Logic, Symbolic and mathematical
Mathematics -- Philosophy
Form Electronic book
ISBN 9780429470370
0429470371
9780429893544
042989354X
9780429893537
0429893531
9780429893520
0429893523