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| D'Angelo J.P., West D.B. — Mathematical Thinking: Problem-Solving and Proofs |
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| Предметный указатель |
Absolute value 4 11 19 21 88 93 259 279 305 312 326 329 351 362 3 368 370
Addition 3 11 16 7 51 74 86 98 131 133 143 149 50 258 296 361—2 369 371 83
Additive identity 16 102 144 195 380
Additive inverse 3 16 144 149 50 375 381
Adjacency relation 208 11 228
Adjacent vertices 208 219 20
AGM inequality 5 12 22 3 29 43 258 268 274 291 359 398
Algebraic closure 368
Algorithm 126
Alternating series 279 291
Analysis by cases 18 20 37 189 193
Andre, Antoine Desire 173
Antiderivative 345
Antipodal points 293 301
Antisymmetric property 17 141
Appel, Kenneth 223
Approximation 264 5 284 5 307—13 318 22 338 353 396
Archimedean property 258 9 263 265 269 70
Archimedes 258
Area 20 1 42 163 174 185 298 307 314 337 48 351 1 358 360 397
Arguments 272 6 279 290
Arithmetic mean (average) 5 165 257
Arithmetic properties x, xi 3 16 7 51 2 76 7 139 142 1 149 164— 5 257 8 273 4 361 371 9 382-3
Arrangement 101 4 107 111 154 182 3 185 187 201 253
Art Gallery Problem 203 227 8 231
Associative property 16 86 112 150 369 373 5 383
Average value 337 346
Average xix 5 38 156 165 177 8 181 184 186 9 192 308 320 391
Axioms x xiii 2 15 8 51 2 160 256— 8 267 270 276 373 377 9 382-3
Babylonian problem 2 3 15 21 24
Ballot list 187
Ballot path 244
Ballot problem xi 170 172 3 182 185 187 206 244 391
Barnett, A. 177
Base q representation x 76 8 80 94 96 137 269
Baseball problems xx 168 170 184 186 7 198 281 335
Basis step 52 54 64 70 124 5 234
Bayes’ formula 176 186 391
Bell numbers 252
Bernoulli trials 170 175 179 80
Bernoulli, Jakob 170
Bernoulli, John 317
Bertrand, Joseph Louis 172 173
Bertrand’s paradox 174 185
Biconditional 32 6 48
Bijection 80 98 102 5 111 2 115—7 121 2 144 5 147 155 173 187—8 196 208 11 240 251 4 266 347— 9 353 358 373 4 382 3 386-93
Billiard problem 156 158 162
Binary, encoding 82 3 103 105
Binary, expansion 166 264 6 278 288 394
Binary, list (n-tuple) 82 103 105 109 116 120 188 206 215 217 239 10
Binary, operation 131 143 150 155 252 296 373
Binary, representation 77 96 139 144 149
Binomial coefficients 102 10 113 22 135 6 171 3 175 178 182 187—8 195 7 201 210 222 227 230 237 244 5 247 52 254 281 309 333
Binomial distribution 178 179 182
Binomial theorem 96 104 106 109 120 136 178 183 188 196 201 292 309 316 369
Bipartite graph 215 9 225 231
Bipartition 215 9 231
Bisection method 278 300 306 7 319
Block-walking 106 109 188 240
Bolzano — Weierstrass theorem xi 277 9 289 302 304 306 365
Boundary 15 188 223 7 231 393
Bounded, function 12 13 24 31 269 303 305 310 312 326 7 332 45 357 366—7
Bounded, interval 302 3 313 335
Bounded, region 49 224 8 231 338
Bounded, sequence 258 261 2 267 70 274 9 284 287 92 300 302 305 360
Bounded, set 12 258 268 270 302 352 365 8 378 381 2
breakpoints 339 343 357 8
Butterfly effect 293
Calculus x-xvi 68 69 87 94 118 271 287 307 60 397 100
Canonical expansion 263 6 269 278
Canonical representation 158 263
Cantor, Georg 266
Card problems 89 100 103 4 115 118 9 138 171 200 252 316 387
Cardinality xii 76 87 92 98 270
Carmichael numbers 149
Cartesian coordinates 9
Cartesian Plane 361
Cartesian product 9 23 87 90 98 101 247 8
Casting out nines 144
Catalan numbers 173 244 5 249 54
Catalan recurrence 245 249 253 394
Catalan, Eugene Charles 244
Cauchy Convergence Crit 276 9 363
Cauchy mean value theorem 316 7 321 332 3
Cauchy sequence xi xii xvi 276 9 282 3 291 304 326 7 363 369 378 80 383
Cauchy, Augustin 276
Ceiling function 126 135 138 252 389
Census problem 22
Chain rule 312 3 319 323 330 4 349 51 356 358 396—7
Chairperson Identity 108 117 8
Change of variables 94 168 344 347 8 353
Checkerboard problems xvii 48 50 58 192 251 386
Chess-player problem 192 3
Chessboard 75 167
Chinese remainder theorem xi 139 145 6 154 390
Chord 174 185 228 306 391
Chromatic number 219 22 231
Chromatic polynomial 221 2 231 253
circle xix 14 45 49 159 174 185 188 220 1 227 236 250 1 307 323 1 337 351 3 364 369—70
Circuit 205 212
clock 22 143 198
Closed 17 131 375 377 379 383
Closed, curve 203 223 224 228
Closed, interval 9 73 98 268 270 294 297 302 1 313
Closed, set 365 8 370 375 377 379
Closed, trail 205 206 210 212
Closure property 16 150 164 368 377
Coconuts problem 137 389
Coefficients (also binomial coefficients) in equation 25 6 124 128 237—8
Coefficients (also binomial coefficients) in expansion 264 266 270
Coefficients (also binomial coefficients) in polynomials 11 41 46 59 60 69 87 122 131 2 155 160 2 166—7 231 234 361 367
Coefficients (also binomial coefficients) in power series 247 9
Coefficients (also binomial coefficients) in recurrence 234 241 3 252
Coefficients (also binomial coefficients), multinomial 170 183 188
Coin problems xvii xviii 8 45 50 63 4 75 96 100 103 108 118 135 137 175 178 186 200 251 254
Coloring 154 219 23 227—8
Combinatorial proof xii 104 8 115 22 188 230 248 332 388
Commutative property 16 86 150 369 373 5 381 383
Compact set 302 365 6 368 370
Comparison Test 282 3 286 7 291—2
Complement 9 185 193 4 210 224 229 365 370 398
Complete bipartite graph 225
Complete graph 216 220 230 392
Complete ordered field 15 258 372 82
Completeness axiom 17 54 160 256 8 267 270 1 276 284 299 302 340 378 381 2
Complex function 366 7 370
complex numbers 168 324 361 70
Component of graph 212 3 216 222
composition 85 8 97 8 112 150 155 277 295 298 310 312 3 356 368 370 1 374
compound statements 31 3
Compounding 337 350 357
Compounding on an interval 296 9 302 6 315—6 327 9 336 344 7 357
Compounding, function 165 223 296 306 311—3 315 320 327 36 344 60
Conclusion (of conditional) 32 40
Condensation test 292
Conditional 291
Conditional of sequences 256 259 65 268 274 92 279 295 8 302 304 318 22 343 3 350 363 70 378—80
Conditional of series 279 84 288 290 2 324 351 353 363 4
Conditional probability 170 174 7 186
Conditional statement 32 49 56 58—9
Congruence xii 142 55 190 199 390
Congruent modulo n 142
Conjugate (complex numbers) 362 369
Conjunction 32 5 37 48—9
Connected graph 212 6 224 5 228—30
Connection relation 212 3
Constant, coefficients 236 8 241 3 249—52
Constant, function 131 3 141 241 301 304—5 315 6 340 346 349 351 358-9
Constant, sequence 259 261 283 381
Constant, term 3 97 180 238 243 387
| containment 6 7 23 49 212
Continuous (see uniform.) at a point 296 8 302 5 311 2 317— 9 327 332 346 359
Continuously differentiable 318 9 333 346 8 355
Contradiction, proof by 26 7 35 40 43 48 9 130 161 190 3 262 267 286 7 366—8
Contrapositive 35 8 40 43 64 83 92 130 136 148 190 205 215 299 304 386 389 392 3 395
Convergence at a point 294 8 324—6
Convergence, absolute 282 291 363 4 370
CONVERSE 32 34 7 42 44 66 141 155 159 271 276 279 282 290 366
Convex function xi 233 253 320 2 334 5 397
Convex polygon 245
Corollary 39
Cosine xi 69 94 96 319 324 350 3 364 369 398
Countable set 89 92 4 98 161 167 256 266 8 270 290 387
Countably infinite 89
Counterexample 24 37 8 65 155 161 166 177 184
Counting 23 48 79 80 101 10 116— 22 136 139 154 172 194 7 201 221 2 228 31 232 54 386 9 393
Counting two ways 53 103 5 108 115 117 120 1 178 202
Coupon Collector Problem 170 180
Crossing edges 223
Cube (graph) 206 209 212 215 229
Cube (object) 73 4 119 20 203 226
Cube root 23 27 83 93 162 331 369
Cubic equation 168
Cubic polynomial 11 74 97 332
Curvature 307 322 4 336
Curve 14 159 167 203 1 223 1 228 307 323 4 342 353
CYCLE 27 91 170 184 187
Cycle description 114
Cycle in graph 211 7 220 1 224 31 392
Cycle in permutation 113 5 121 2 147
Cyclic shift 155
Dart Board Problem xviii 123 129 31 137 202
de Morgan, Augustus 33
de Morgan’s laws 33 35 49
December 31
Decimal expansion 162 166 256 263 71 280 286 289 90 330 353 395
Decimal representation xx 76 7
deck of cards 100 103 118 9 171 200
Decreasing function 12 95
Decreasing sequence 167 274 292
Defined on 10
Degree (polynomial) 11 21 59 60 74 82 87 108 10 122 132 134 155 168 187 237 8 241 3 249 253 288 292 306 334 367 8 392—3
Degree (vertex) 204 15 222 226 31
Degree-sum Formula 206 7 226—7
Deleted neighborhood 294 5 317
Denominator 157 161 165 6 249 266
Derangement 193 7 245 6 252
Derivative 308 16 319 322 330—5 346 9 355 359 396-7
Descartes, Rene 9
Diagonalization argument xvi 266 7
Dice problems 103 118 9 171 2 182 185 187 193 197 254
Dice problems of functions 60 72 300 1 315
Dice problems of sets 9 21
Differentiable 307 24 329 36 346— 51 355 6 359 397
Differential equation 350 358 397
Differentiation xi 87 307 36 345 56
Diophantine equation xii 128 9 134 137 146 389
Diophantus 128
Direct proof 36 40 43 53
Dirichlet drawer principle 189
Dirichlet, Peter G. Lejeune 153 189
Disconnected graph 212 216 227 30
Discontinuous function 298 305 333
Disjoint 9 10 88 91 2 101 109 119 151 2 171 2 215 218 9 229 231 247 387 392
Disjunction 32 5 48—9
Distance 4 5 20 88 198 259 276 284 5 299 308 329 361 2 375
Distributive law 3 16 54 5 116 125— 6 165 179 80 281 342 361 369 371 374 5 378 381 383
Divergence 279 87 291 2 355 359 364 370
Divisibility 123 39 141 148 9 151—5 162 164 168 183 190 1 387-9
Division 3 16 7 26 42 126 133 156— 8 270 296 371 388 391
Division algorithm 126 131 2 142
Divisor 123 133
dodecahedron xx 203 226
Dollars xviii xix 22 45 134 5 146 186 8 254 280 332 337
Domain 10 4 21 24 52 3 81 84—8 92 4 133 294 299 301 333 348
Drawing of graph 204 209 223 7
Drummer Problem 100 111
Dyadic rational 165 6
Dyadic rational, edge (of graph) 204 202 31 250 253
Egyptian fraction 292
Element 6 8 14 28 9 34 9
Empty set 6 9 38 9 88 125 193—7
Endpoints (edges, paths, trails) 204 8 211 214 5 222 6 231
Endpoints (intervals) 264 5 297 314
EPSILON 2
Equality of sets 6 8 23—4
Equality relation 140 213
equation 241 242 250 370 393
Equivalence class/relation xii 140 2 146 148 152 5 157 207 8 213 347 371 374 82 390
Erdos, Paul 191 199
Error function 308 13 332 346
Euclidean algorithm 126 9 131 134
Euler totient function xi 193 6 200
Euler, Leonhard 147 155 244 193 203 205 244
Eulerian graph 205 6 228
Euler’s formula 224 7 231 250
Even number 8 9 26 7 64 65 96 103 153 192 204 207 215 6 228 293
Even permutation 111
Event 171 9 185 197 200 391
Eventually periodic 290
Exclusive OR 32
Existential quantifier 28 40 44 9
Expectation 170 177 81 187 8 234 334 337 391
Expected value 178
Exponential fen 283 292 324 328 335 345 349 50 356 359 364 369
exponentiation 85 96 316 358 383
Extremality 161 202 206 213
Face 187 198 224 8 231 393
Factor 104 123 6 134 9 148 9 151 154 157 163 8 183 193 1 200 241 247 9 368
Factorial 53 102 5 111 119 21 182 193 196 7 246 283 345 360 364
Factorization xi-xii 55 59 123 125 131 133 6 149 157 161 240 331
Fermat, Pierre de 71 147 164
Fermat’s Last Theorem 164
Fermat’s Little Theorem xi 147 8 152 155 183 206 390
Fibonacci numbers xi 233 238 41 248 9 251 2 291
Field xiii 15 7 24 97 150 1 160 258 270 361 2 368 372 377 83 392
Finger Game 181 188
Finite sequence 281
Finite set 88 9 94 98 102 105 141 171 183 193 374
First difference 253
First-order recurrence 235 8 252
Fixed point 13 113 122 196 200 333
Floor fen 126 135 198 230 1 252 264
Formal power series 247 8
Forward difference 333
Four-color problem 223 227
Fourier series 324 364
Fourier, Joseph 324
FRACTION 65 74 103 157 8 161 165—6 175 6 186 7 270 280 335 353
Fractional part 198 264 330
Friday the 13
Function 10 4 59 80 98 294—360
Functional digraph 112 5 122 147 154 204 370 388
Fundamental Thm. of Algebra 367 8
Fundamental Thm. of Arithmetic 125
Fundamental Thm. of Calculus 337 345 50 355 9 397
Gambler problems 186 7 254
Game 75
Games xx 56 69 70 75 94 96 119 170 181 184 8 192 271 281 291
Gamma function 360
Gauss, Karl Friedrich 53 4 142 153
General solution 240 3 252
Generating function 247 9 254 291 336 394
Generator 132 3
Geometric mean 5
Geometric random variable 180
Geometric series 248 9 280 1 283 290 2 330 335 353 356 395
Geometric sum 55 6 73 78 9 265 335 358 9 386 397
Graph 113 154 202 31 253
Graph of function 12 5 23 4 83 97—8 260 299 300 306 8 315 318 24 329 334 6 339 41 348 354 392-7
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