Britannica Guide to The History of Mathematics
1st Edition
Published on 1. August 2010
311 pages
978-1-61530-221-5 (ISBN)
Description
The field of mathematics today represents an ongoing global effort, spanning both countries and centuries. Through this in-depth narrative, students will learn how major mathematical concepts were first derived, as well as how they evolved with the adven
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Erik Gregersen
The Britannica Guide to the History of Mathematics
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08/2010
Rosen Education Service
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Content
- Intro
- TITLE
- COPYRIGHT
- CONTENTS
- INTRODUCTION
- CHAPTER 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
- GEOMETRY IN THE 3RD CENTURY BCE
- LATER TRENDS IN GEOMETRY AND ARITHMETIC
- 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
- CHAPTER 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
- THE 18TH CENTURY
- OTHER DEVELOPMENTS
- 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
- CHAPTER 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
- SCHOLARLY REVIVAL, 11TH-13TH CENTURIES
- FALL INTO OBLIVION, 14TH-16TH CENTURIES
- MATHEMATICS IN JAPAN
- THE INTRODUCTION OF CHINESE BOOKS
- THE ELABORATION OF CHINESE METHODS
- CHAPTER 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
- CANTOR
- THE QUEST FOR RIGOUR
- FORMAL FOUNDATIONS
- CATEGORY THEORY
- CHAPTER 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
- GENERAL SOURCES
- MATHEMATICS IN ANCIENT MESOPOTAMIA
- MATHEMATICS IN ANCIENT EGYPT
- GREEK MATHEMATICS
- MATHEMATICS IN THE ISLAMIC WORLD
- EUROPEAN MATHEMATICS DURING THE MIDDLE AGES AND RENAISSANCE
- MATHEMATICS IN THE 17TH AND 18TH CENTURIES
- MATHEMATICS IN THE 19TH AND 20TH CENTURIES
- SOUTH ASIAN MATHEMATICS
- EAST ASIAN MATHEMATICS
- FOUNDATIONS OF MATHEMATICS
- PHILOSOPHY OF MATHEMATICS
- INDEX
- BACK COVER
