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The Britannica Guide to the History of Mathematics



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The Britannica Guide to the History of Mathematics edited by Erik Gregerson , Associate Editor, Astronomy and Space Exploration.

The Britannica Guide to the History of Mathematics edited by Erik Gregerson cover the following topics.

  • Introduction

  • 1. Ancient Western Mathematics
    Ancient Mathematical Sources
    Mathematics in Ancient Mesopotamia
    The Numeral System and Arithmetic Operations
    Geometric and Algebraic Problems
    Mathematical Astronomy
    Mathematics in Ancient Egypt
    The Numeral System and Arithmetic Operations
    Geometry
    Assessment of Egyptian Mathematics
    Greek Mathematics
    The Development of Pure Mathematics
    The Pre-Euclidean Period
    The Elements
    The Three Classical Problems
    Geometry in the 3rd Century BCE
    Archimedes
    Apollonius
    Applied Geometry
    Later Trends in Geometry and Arithmetic
    Greek Trigonometry and Mensuration
    Number Theory
    Survival and Influence of Greek Mathematics
    Mathematics in the Islamic World (8th–15th Century)
    Origins
    Mathematics in the 9th Century
    Mathematics in the 10th Century
    Omar Khayyam
    Islamic Mathematics to the 15th Century

  • 2. European Mathematics Since the Middle Ages
    European Mathematics During the Middle Ages and Renaissance
    The Transmission of Greek and Arabic Learning
    The Universities
    The Renaissance
    Mathematics in the 17th and 18th Centuries
    The 17th Century
    Institutional Background
    Numerical Calculation
    Analytic Geometry
    The Calculus
    The 18th Century
    Institutional Background
    Analysis and Mechanics
    History of Analysis
    Other Developments
    Theory of Equations
    Foundations of Geometry
    Mathematics in the 19th and 20th Centuries
    Projective Geometry
    Making the Calculus Rigorous
    Fourier Series
    Elliptic Functions
    The Theory of Numbers
    The Theory of Equations
    Gauss
    Non-Euclidean Geometry
    Riemann
    Riemann’s Influence
    Differential Equations
    Linear Algebra
    The Foundations of Geometry
    The Foundations of Mathematics
    Cantor
    Mathematical Physics
    Algebraic Topology
    Developments in Pure Mathematics
    Mathematical Physics and the Theory of Groups

  • 3. South and East Asian Mathematics
    Ancient Traces
    Vedic Number Words and Geometry
    The Post-Vedic Context
    Indian Numerals and the Decimal Place-Value System
    The “Classical” Period
    The Role of Astronomy and Astrology
    Classical Mathematical Literature
    The Changing Structure of Mathematical Knowledge
    Mahavira and Bhaskara II
    Teachers and Learners
    The School of Madhava in Kerala
    Exchanges with Islamic and Western Mathematics
    Mathematics in China
    The Textual Sources
    The Great Early Period, 1st–7th Centuries
    The Nine Chapters
    The Commentary of Liu Hui
    The “Ten Classics”
    Scholarly Revival, 11th–13th Centuries
    Theory of Root Extraction and Equations
    The Method of the Celestial Unknown
    Chinese Remainder Theorem
    Fall into Oblivion, 14th–16th Centuries
    Mathematics in Japan
    The Introduction of Chinese Books
    The Elaboration of Chinese Methods

  • 4. The Foundations of Mathematics
    Ancient Greece to the Enlightenment
    Arithmetic or Geometry
    Being Versus Becoming
    Universals
    The Axiomatic Method
    Number Systems
    The Reexamination of Infinity
    Calculus Reopens Foundational Questions
    Non-Euclidean Geometries
    Elliptic and Hyperbolic Geometries
    Riemannian Geometry
    Cantor
    The Quest for Rigour
    Formal Foundations
    Set Theoretic Beginnings
    Foundational Logic
    Impredicative Constructions
    Nonconstructive Arguments
    Intuitionistic Logic
    Other Logics
    Formalism
    Gödel
    Recursive Definitions
    Computers and Proof
    Category Theory
    Abstraction in Mathematics
    Isomorphic Structures
    Topos Theory
    Intuitionistic Type Theories
    Internal Language
    Gödel and Category Theory
    The Search for a Distinguished Model
    Boolean Local Topoi
    One Distinguished Model or Many Models

  • 5. The Philosophy of Mathematics
    Mathematical Platonism
    Traditional Platonism
    Nontraditional Versions
    Mathematical Anti-Platonism
    Realistic Anti-Platonism
    Nominalism
    Logicism, Intuitionism, and Formalism
    Mathematical Platonism: For and Against
    The Fregean Argument for Platonism
    The Epistemological Argument Against Platonism
    Ongoing Impasse


  • Glossary

  • Bibliography

  • Index

  • Open
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