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Historical Encyclopedia of Natural and Mathematical Sciences
Bearbeitet vonAri Ben-Menahem
1. Auflage 2009. Buch. clxii, 5983 S. HardcoverISBN 978 3 540 68831 0
Format (B x L): 20,3 x 27,6 cm
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Contents
Part I
Pre-Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1. Origins – Splendor of the Simple
(4200 bce–529 ce) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
• Calendars, or the Conquest of Time
• Wheels and Numerals
• Papyri and Clay
• Birth of Science in Ionia
• Blossom in Alexandria
General Bibliography
Name Index
Subject Index
2. Slumber and Awakening (529–1583) . . . . . . . . . . . 497
• In the Womb of Asia
• Diffusion of Greco-Hindu Lore into Western Europe
• Rise of the Universities
• Renaissance
• The Scientific Revolution
• Voyagers and Explorers
General Bibliography
Name Index
Subject Index
xx Contents
Part II
3. The Clockwork Universe (1583–1819) . . . . . . . . . . 911
• Beyond the Greeks
• Infinitesimals and Infinities
• Rise of Mechanics
• The New Astronomy
• Enlightenment
• Social Revolutions and Industrialization
• Algebraization of Geometry and Exploitation of the
Calculus:
Analytic and Projective GeometryAnalytical MechanicsPartial Differential EquationsThe Calculus of Variations
• Emergence of the Theories of Numbers, Probability and
Statistics
• From Alchemy to Chemistry
• Evolution of the Steam Engine
General Bibliography
Name Index
Subject Index
4. Abstraction and Unification (1820–1894) . . . . 1733
• Emergence of Algebraic Structures and the Rise of Ab-
stract Algebras:
Fields, Groups, Matrices, Vectors, QuaternionsInvariants and Quadratic FormsSymbolic Algebra
• Breakaway from Euclidean Geometry
Non-Euclidean GeometriesDifferential Geometry of Surfaces; Riemannian Geometry
Contents xxi
Topology; Algebraic GeometryTensor Calculus
• The Arithmetization of Analysis:
Limits and Convergence of Infinite Series; Fourier SeriesRigorization of the Real Number System; Set Theory
• Complex Analysis; Differential and Integral Equations
• Advent of Electromagnetism: Unification of Optics,
Electricity and Magnetism
• Quantification of Thermal Phenomena: Thermodynam-
ics and Statistical Physics
• The Periodic Table of the Elements
• Organic Chemistry and Cell Theory
• The Theory of Biological Evolution
• Alternating Current Technology; Discovery of Photo-
conductivity
• Oceanography – The Conquest of Inner Space
• Emergence of World Communication: Telephone, Tele-
graph, Facsimile
General Bibliography
Name Index
Subject Index
Part III
5. Demise of the Dogmatic Universe
(1895–1950) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2801
• Maturation of Abstract Algebra and the Grand Fusion
of Geometry, Algebra, Arithmetic and Topology:
Lie Groups and Algebras; Modular Groups: Noether RingsTopological SpacesSpinors; Fiber Bundles; CategoriesModular Functions and Analytic Number Theory
xxii Contents
Exterior Calculus, Homology, and Genera
• Logic, Set Theory, Foundations of Mathematics and the
Genesis of Computer Science
• Modern Analysis:
Functional Analysis and Infinite-Dimensional SpacesNon-Archimedean Analysis (p-adics)
• Electrons, Atoms, Nuclei and Quanta
• Einstein’s Relativity and the Geometrization of Grav-
ity; The Expanding Universe
• Preliminary Attempts to Geometrize Non-Gravitational
Interactions; Kaluza – Klein Models With Compactified
Dimensions
• Subatomic Physics: Quantum Mechanics and Quantum
Electrodynamics; Nuclear and Particle Physics
• Reduction of Chemistry to Physics; Condensed Matter
Physics; The 4th
State of Matter
• The Conquest of Distance by Automobile, Aircraft and
Wireless Communications; Cinematography
• The ‘Flaming Sword’: Antibiotics and Nuclear Weapons
• Unfolding Basic Biostructures: Chromosomes, Genes,
Hormones, Enzymes and Viruses; Proteins and Amino
Acids
• Electromagnetic Technology: Early Laser Theory;
Holography; Magnetic Recording and Vacuum Tubes; In-
vention of the Transistor
• ‘Big Science’: Accelerators; The Manhattan Project
General Bibliography
Name Index
Subject Index
6. Deep Principles – Complex Structures
(1950–2008) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5081
• Continuation of Abstraction and Unification of Pure
Mathematics
Contents xxiii
• Discrete Mathematics and the Ubiquitous Algorithm;
Computation Beyond Algorithms
• Nonlinearity, Stochasticity and the Science of Com-
plexity; Adding Noise to Deterministic Evolution
• Mathematization of the Biological, Environmental and
Social Sciences
• Abstract Algebra and Group Theory in Modern Theo-
retical Physics
• Particle Physics and the Coming of Gauge
• The New Cosmology: Whence, Whither and Why?
• General Relativity meets Quantum Mechanics and Par-
ticle Physics
• Quantum Technology
• RF Engineering and Particle-Accelerator Technology
• Worldwide Communications and Information Technol-
ogy
• Modern Microscopy and Telescopy
• Material Science
• Computer Technology; Computer Simulation – the
Third mode of Science
• Molecular Biology, Genetics and Biochemistry
• Biotechnology of Nature and Man
• Big Science
Appendices
Bibliography
Name Index