The Britannica Guide to the History of Mathematics (Math Explained)

TITLE......Page 4
COPYRIGHT......Page 5
CONTENTS......Page 6
INTRODUCTION......Page 13
CHAPTER 1 ANCIENT WESTERN MATHEMATICS......Page 22
ANCIENT MATHEMATICAL SOURCES......Page 23
MATHEMATICS IN ANCIENT MESOPOTAMIA......Page 24
THE NUMERAL SYSTEM AND ARITHMETIC OPERATIONS......Page 25
GEOMETRIC AND ALGEBRAIC PROBLEMS......Page 28
MATHEMATICAL ASTRONOMY......Page 30
MATHEMATICS IN ANCIENT EGYPT......Page 32
THE NUMERAL SYSTEM AND ARITHMETIC OPERATIONS......Page 33
GEOMETRY......Page 37
ASSESSMENT OF EGYPTIAN MATHEMATICS......Page 39
THE DEVELOPMENT OF PURE MATHEMATICS......Page 40
GEOMETRY IN THE 3RD CENTURY BCE......Page 52
LATER TRENDS IN GEOMETRY AND ARITHMETIC......Page 67
ORIGINS......Page 73
MATHEMATICS IN THE 9TH CENTURY......Page 75
MATHEMATICS IN THE 10TH CENTURY......Page 77
OMAR KHAYYAM......Page 80
ISLAMIC MATHEMATICS TO THE 15TH CENTURY......Page 82
EUROPEAN MATHEMATICS DURING THE MIDDLE AGES AND RENAISSANCE......Page 85
THE TRANSMISSION OF GREEK AND ARABIC LEARNING......Page 87
THE UNIVERSITIES......Page 88
THE RENAISSANCE......Page 90
THE 17TH CENTURY......Page 92
THE 18TH CENTURY......Page 113
OTHER DEVELOPMENTS......Page 121
MATHEMATICS IN THE 19TH AND 20TH CENTURIES......Page 126
PROJECTIVE GEOMETRY......Page 127
MAKING THE CALCULUS RIGOROUS......Page 130
FOURIER SERIES......Page 134
ELLIPTIC FUNCTIONS......Page 135
THE THEORY OF NUMBERS......Page 137
THE THEORY OF EQUATIONS......Page 141
GAUSS......Page 144
NON-EUCLIDEAN GEOMETRY......Page 145
RIEMANN......Page 148
RIEMANN’S INFLUENCE......Page 152
DIFFERENTIAL EQUATIONS......Page 155
LINEAR ALGEBRA......Page 157
THE FOUNDATIONS OF GEOMETRY......Page 159
THE FOUNDATIONS OF MATHEMATICS......Page 162
CANTOR......Page 163
MATHEMATICAL PHYSICS......Page 166
ALGEBRAIC TOPOLOGY......Page 170
DEVELOPMENTS IN PURE MATHEMATICS......Page 174
MATHEMATICAL PHYSICS AND THE THEORY OF GROUPS......Page 178
ANCIENT TRACES......Page 183
VEDIC NUMBER WORDS AND GEOMETRY......Page 184
THE POST-VEDIC CONTEXT......Page 185
INDIAN NUMERALS AND THE DECIMAL PLACE-VALUE SYSTEM......Page 186
THE “CLASSICAL” PERIOD......Page 187
THE ROLE OF ASTRONOMY AND ASTROLOGY......Page 188
CLASSICAL MATHEMATICAL LITERATURE......Page 190
THE CHANGING STRUCTURE OF MATHEMATICAL KNOWLEDGE......Page 192
MAHAVIRA AND BHASKARA II......Page 193
TEACHERS AND LEARNERS......Page 194
THE SCHOOL OF MADHAVA IN KERALA......Page 195
MATHEMATICS IN CHINA......Page 196
THE TEXTUAL SOURCES......Page 197
THE GREAT EARLY PERIOD, 1ST–7TH CENTURIES......Page 199
SCHOLARLY REVIVAL, 11TH–13TH CENTURIES......Page 208
FALL INTO OBLIVION, 14TH–16TH CENTURIES......Page 212
THE INTRODUCTION OF CHINESE BOOKS......Page 214
THE ELABORATION OF CHINESE METHODS......Page 215
ARITHMETIC OR GEOMETRY......Page 218
BEING VERSUS BECOMING......Page 219
UNIVERSALS......Page 222
THE AXIOMATIC METHOD......Page 223
NUMBER SYSTEMS......Page 224
THE REEXAMINATION OF INFINITY......Page 225
CALCULUS REOPENS FOUNDATIONAL QUESTIONS......Page 226
NON-EUCLIDEAN GEOMETRIES......Page 227
CANTOR......Page 230
FORMAL FOUNDATIONS......Page 231
CATEGORY THEORY......Page 245
CHAPTER 5 THE PHILOSOPHY OF MATHEMATICS......Page 257
TRADITIONAL PLATONISM......Page 259
NONTRADITIONAL VERSIONS......Page 261
REALISTIC ANTI-PLATONISM......Page 264
NOMINALISM......Page 267
LOGICISM, INTUITIONISM, AND FORMALISM......Page 271
MATHEMATICAL PLATONISM: FOR AND AGAINST......Page 273
THE FREGEAN ARGUMENT FOR PLATONISM......Page 274
THE EPISTEMOLOGICAL ARGUMENT AGAINST PLATONISM......Page 278
ONGOING IMPASSE......Page 281
GLOSSARY......Page 283
GENERAL SOURCES......Page 286
GREEK MATHEMATICS......Page 287
MATHEMATICS IN THE ISLAMIC WORLD......Page 288
MATHEMATICS IN THE 17TH AND 18TH CENTURIES......Page 289
MATHEMATICS IN THE 19TH AND 20TH CENTURIES......Page 290
EAST ASIAN MATHEMATICS......Page 291
FOUNDATIONS OF MATHEMATICS......Page 292
PHILOSOPHY OF MATHEMATICS......Page 294
INDEX......Page 295
BACK COVER......Page 311