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Stillwell J. — Mathematics and its history

Stillwell J. — Mathematics and its history

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Название: Mathematics and its history

Автор: Stillwell J.

Аннотация:

This book presents a concise unified view of mathematics and its historical development. It is aimed at senior undergraduates - or other mathematicians - who have mastered the basic topics but wish to gain a better grasp of mathematics as a whole. Reasons for the emergence of the main fields of modern mathematics are identified, and connections between them are explained, by tracing the course of a few mathematical themes from ancient times down to the 20th century.

The emphasis is on history as a method for unifying and motivating mathematics, rather than as an end in iteself, and there is more mathematical detail than in other general histories. No historical expertise is assumed, and classical mathematics is rephrased in modern terms whenever it seems desirable. Nevertheless, there are copious references to original sources, and readers wishing to explore the classics for themselves will find it a useful guide.

An advantage of the unified approach is that it ties up loose ends and fills gaps in the standard undergraudate curriculum. Thus, readers can expect to add to their mathematical knowledge as well as gaining a new perspective on what they already know.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 5-th edition

Год издания: 1989

Количество страниц: 379

Добавлена в каталог: 27.01.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Abel      58 66 159—164 166 215 218 272 278 279 290
Abel theorem      162 163 166
Abelian function      166
Abelian integral      166
Adams      171
Addition theorems      149 155—158 222 230
Adian      309
Al-Haytham (Alhazen)      77 102 255
al-Khwarizmi      48 49 52 54
Al-Kuji      21
Alberti      78 80—82 84
Algebra      48 49 73
Algebraic curves      25 67 69 92 169 171 198—200 204 231 237 240 295
Algebraic functions      120 125 126 131 154 291
Algebraic geometry      49 73 217
Algebraic topology      311
Algorithm      5 35 48 309 323
Algorithm, Euclidean      30 32 34 276
Analytic geometry      9 11 49 54 65 69 73 76 86 150
Anamorphosis      81 82
Angeli      131
Angle division      55 56 192—195
Angular defect      250 257 258
Angular excess      248 249 258 259
Anthyphairesis      32 34
Apollonius      21 24 53 65 66 169
Arc length      67 153 155 174 176 237—240
Archimedes      34 44 46 47 61 102 103 118 123 167 171
Archimedes cattle problem      34
Archimedes spiral      103 171
Archimedes, Method      38 47 103 167
Argand      196 197
Aristotle      9 37 38 46 112 168
Arithmetization of geometry      73 74
Asymptotic lines      256 257 263 264
Axiom of Choice      318—320 330
Axioms      13 324 326—328
Axioms of infinity      327 328
Babylonians      3 51 52
Bachet      28 36 140 141 144
Banach      319
Banach — Tarski theorem      319
Barrow      110 114
Bartels      252 259 273
Beeckman      71 76 176
Beltrami      218 246 258—266 271 303
Berkeley      38
Bernays      326
Bernoulli, Daniel      132 178 181 184—187 202
Bernoulli, Hydrodynamica      179 185—187
Bernoulli, James      117 124 132 154 172—174 181—184 240—242 246 318
Bernoulli, John      117 124 132 172—173 181 183—184 186 187 193 195 220 221 242 246
Bertrand      300
bessel      160 224
Betti      218
Bezout's theorem      71 72 93—96 200 205
Binomial coefficients      135—139
Binomial series      109 114
Binomial theorem      107 122
Birkhoff      312
Bolyai, F.      42 259 271 272
Bolyai, J.      66 259 260 262 266 271 272 274
Bolzano      196 197
Bombelli      36 190 191 221
Bonnet      246 247
Bonola      259
Boole      324
Borel      317 318
Borel sets      317 318
Bosse      83 96 97
Boyle      181 185
Brachistochrone      173
Brahana      296
Brahmagupta      34 48 51 52
Branching      125 210 211
Briggs      123
Bring      58
Brouncker      31 34 107
Brunelleschi      78
Calculus      54 100—110 167 170 183 237
Calculus of variations      174 183
Cantor      179 314—316 320 321
Cardano      54 57 59—62 189 190
Cardano formula      55—57 189—191
Cardinality      315
Cartesian parabola      71
Cassini      24 179
Cassini ovals      24
Catenary      171—173 183 240 242
Cauchy      29 163 181 223 225 234—236 279 289 290
Cauchy integral theorem      224—226 236
Cauchy — Riemann equations      222
Cavalieri      102 103 131
Cayley      262 279 280 285
Cayley theorem      280
Celestial mechanics      169—171 234 311
Chain rule      107
Chinese remainder theorem      135
Choice function      318 319
Chord and tangent construction      35 49 147 230 279
Christina of Sweden      76
Church      323
Cicero      46 47
Circular functions      56 108 109 120 131 152 154 221 258
Cissoid      22 23 67
Clairaut      179 180 202
Clebsch      147
Closed form      110 116 154
Cohen      316 320 330
Combinatorics      101 116 126 136
Complex functions      73 181 220—232 269
complex numbers      56 57 59 72 90 131 153 159 222
Complex numbers in algebra      188—220
Complex numbers, geometric interpretation      191 192 196—198
Composition of forces      169
Composition of functions      275
Computable      321—323
Computable functions      321—323
Computable real numbers      321
Computable set of defining relations      323
Condorcet      203 234
Conformal mapping      223 224 254
Congruence      284 319
Conic sections      20 24 65 66 69 73 83 86 88—90 95 98
Connelly      236
Construction of equations      71 72
Continued fractions      34 106 107 289
Continuity      169 179 196 197 198 200 292 317
Continuum Hypothesis      316 318 319 330
Convergence of series      131 228
Copernicus      169
Costruzione legittima      80
Cotes      194 195 221
Countable additivity      318 319
Countable sets      314—320
Counting board      50
Coverings      210 212 302—308
Coverings, universal      302—308
Cramer      50 72 279
Cramer rule      50
Crelle      163
Cross-ratio      83—85
Cryptography      62 64 112 138
cube      15 16 282
Cube, duplication of      18 20 23 53 54
Cubic curves      67 69 90 114 144—149 152 153 213 230 231
Cubic curves, Newton's classification      69—71 90 114 115 147 230
Cubic curves, projective equivalence      231
Cubic equations      54—56 58 189—191
Curvature      100 114 217 241—246 253 297—301 306

Curvature of surfaces      243—246
Curvature, centre of      241
Curvature, constant      244—246 258 260 301
Curvature, Gaussian      244—248 250 254
Curvature, geodesic      246—248
Curvature, negative      245—247 258 261 301
Curvature, principal      244
Curvature, radius of      241
Cusp      23 67 70 71 90
Cycloid      99 171 173 174 240 242
D'Alembert      69 177 180 196—203 222 223 233
D'Alembert lemma      197 199
De la Hire      97
De Moivre      57 109 113 126 127 192—195 220
de Moivre formula      57 193 221
Decimals      48 107
Dedekind      9 38 40 217 218 254
Dedekind cut      40 197 314
Degen      162
Degree of a curve      22 67
Dehn      43 295 308
del Ferro, Scipione      54 59
Desargues      81—83 86 88 92 95—97 250
Desargues theorem      83
Descartes      14 22 49 58 66—68 71 73—77 86 103 104 107 112 171 181 271 293 297—300
Descartes factor theorem      59 124 195
Descartes folium      67 68 104 145—147
Descartes, La geometrie      66 71 77 104 171
Descriptive geometry      82
Diagonal argument      320—325
Dichotomy of Zeno      37 38 118
Diderot      203
Differentiability      169 178 223 224 226
Differential equations      170 174 270 311
Differential equations, partial      176 177
Differential geometry      73 114 164 217 218 237—250 259 260
Differentiation      100 103 107 110 169 237
Differentiation, partial      183
Diocles      22
Diophantine equations      5 27 31 48 144 147
Diophantus      4 27 28 35 36 49 135 140 141 144 147 189
Dirichlet      140 165 179 217 218 317 320
Dirichlet function      317 320
Dirichlet principle      217 224
Distance      see also "Metric"
Distance, definition of      9 11
Distance, Euclidean      9 11 266
Distance, hyperbolic      261 262 264—266 306
Divergence of series      119
Division of stakes      137 138
dodecahedron      15 17 282
Donaldson      293
Double periodicity      159 160 217 226—228 230
du Bois-Reymond      321
Duerer      78
Duplication of the cube      18—20 23 53 54
Dyck      285 287
Einstein's equations      330
Eisenstein      217 227 228 254
Elastic curve (elastica)      154 171 174 175
Elementary functions      154
Elimination      49—50 72
ellipse      20 21 88 89 114 154 170 174
Elliptic curves      154 228—231
Elliptic functions      66 110 147—149 152—161 164—166 214 217 226—230 279 302 311
Elliptic integrals      153—155 158 159 174
Empty set      315
Epicycles      24 25 97 169—171
Equiangular spiral      237—241
Equidistant curve      263 264 266
Euclid      3 25 26 42 44 53 82 250 257
Euclid, Elements      3 13 14 25 26 29 30 39 40 46 52 53 61 73 113 116 255—257 262 316
Euclidean algorithm      30 32 33 276
Euclidean geometry      73 246 255 260 266 272 273 301 306
Eudoxus      25 39 40 44 47
Euler      27 29 31 69 72 107 124 128 129 132—134 139 140 144 147 149 157 158 161 162 164 166 170 174 184 186 193 194 202 215 221—223 227 228 233 236 244 246 252 276 293 295 312
Euler characteristic      293—297 300—304 306 307
Euler pentagonal number theorem      29 134
Euler Polyhedron Formula      293 294 300 301
Euler, algebra      134 191
Exhaustion      see "Method of exhaustion"
Exponential function      108 109 120 154 184 221 222
Exponential function, complex      193 221 222
Extreme Value Theorem      197 198
Fagnano      147 149 157 161 174
Faltings      141
Fermat      5 27 28 35 36 49 66 71 76 103 104 140 141 143 144 147 149—151 236 276
Fermat last theorem      19 140 141 144
Fermat little theorem      138—140 276 277
Ferrari      54 57 59 60 62
fibonacci      53 126
Fibonacci sequence      126—128
Fields      279
Fior, Antonio Maria      54
Folium of Descartes      67 104 145—147
FOURIER      179 316 317
Fourier series      176 179 217 314 316 317
Frege      324
Fuchs      310 311
Fuchsian functions      311
Fuertwangler      329
Function      110 123 125 178 179 222 234
Function, many-valued      125
Fundamental group      307—309 311
Fundamental theorem of algebra      110 195—200 205 206 252
Fundamental Theorem of Arithmetic      31
Fundamental theorem of calculus      110 131
Galileo      76 168 169 172
Galois      19 58 278 279 288—291
Galois theory      16 58 279 291
Gauss      19 27 58 106 159—164 174 196—200 206 208 216—218 221 224 225 244 246—250 252—254 258—260 268 270 271—274 291 297—300 306
Gauss — Bonnet theorem      247—250 258 297—302 306
Gauss, curvature      244—250 254 298—302 306
Gauss, sphere      208
Generating functions      126 137
Genus      141 144—147 162 208 215 217 297
Geodesic      246 247 260 306
Geodesic curvature      246—248
Geometric series      44 46 108 118 120 127 129 183
Goedel      316 321 323—331
Goedel Incompleteness Theorem      324—328 330 331
Goedel second theorem      326—328
Golden ratio      128
Golden rectangle      16
Goursat      226
Gravity      114 241
Green      225 226
Gregory      107 114 116 121—123 130—132 161
Gregory — Newton interpolation formula      121—123
groups      232 275—288
Groups of permutations      277—279
Groups of rigid motions      271 284
Groups of transformations      232 276 284
Groups, definition      275
Groups, finite      280
Groups, fundamental      307—309 311
Groups, isomorphism problem      309
Groups, polyhedral      280—284
Groups, presentation by generators and relations      283 285—288
Groups, word problem      323
hadamard      194
Hahn      329
Halley      114 170
Halting problem      322 323
Hamilton      283
Harnack      317 318
Harrington      327
Harriot      123 223 237—239 249—252 257 294 300
Hausdorff      319
Heath      141 143

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