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Daepp U., Gorkin P. — Reading, writing and proving. Close look at mathematics
Daepp U., Gorkin P. — Reading, writing and proving. Close look at mathematics

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Название: Reading, writing and proving. Close look at mathematics

Авторы: Daepp U., Gorkin P.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 406

Добавлена в каталог: 18.11.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute value      56
Absolute value, function      151 237
Adleman, L.M.      338 371
Algebraic number      368
Antecedent      20
Archimedean property      134
Associative property      379
Associative property, compound statement      32
Associative property, sets      83
asymmetric      143
Axiom      134
Axiom of infinity      351
Ball, open      297
Ball, unit      297
Barber problem      72
Bernoulli's inequality      216
Bernoulli, Joh.      158
Bijective      163
Binomial coefficient      220
Binomial theorem      220
Birthday calendar      329
Bounded sequence      225
Bounded sequence, above      225
Bounded sequence, below      225
Bounded set      130
Bounded set, above      130
Bounded set, below      130
Caesar cipher      10
Cantor diagonalization argument      277
Cantor set      362
Cantor, G.      271 278 369
Cardinality      265
Cartesian product      98 106
Cauchy sequence      250
Cauchy sequence, metric space      295
Cauchy — Bunyakovsky — Schwarz inequality      367
Characteristic function      159
Cipher      3
Clock arithmetic      313
Closed set      302
Closed set, closed interval      40
Closed set, not closed      309
Closed set, unbounded interval      40
Closure      312
Cocks, C.      338
Code      334 371
Codomain      148
Commutative property      379
Commutative property, compound statements      32
Commutative property, sets      83
Complement      69
Completeness axiom of $\mathbb{R}$      134
Completeness axiom of $\mathbb{R}$, infimum version      134 140
complex numbers      40
Composite function      175
Composite number      349
composition      175
Conclusion      20
Congruence modulo n      314
Conjecture      57
Conjunction      20
Connectives      18
Contained      65
Contradiction      22
Contrapositive      32
Convergent sequence      237
Convergent sequence, metric space      287
Convergent sequence, proving convergence      240
Convergent sequence, theorems      244 249
CONVERSE      34
Convex set      218
Convex set, $\mathbb{R}^{n}$      367
Countable set      271
Countably infinite set      271
Counterexample      58
Counterfeit coin problem      13
de Fermat, last theorem      58
de Fermat, little theorem      332
de Fermat, P.      58 331
Decreasing sequence      227
Dedekind, R.      158
DeMorgan's laws      31 83 93
Diffie, W.      338 371
Dirichlet drawer principle      262
Dirichlet function      157
Dirichlet pigeonhole principle      261
Dirichlet principle      200 262
Dirichlet problem      199
Dirichlet, P.G.L.      157 262
Discrete metric      285
Disjoint      69
Disjoint, pairwise      96
Disjunction      19
Distance      237 283
Distributive property      380
Distributive property, compound statements      31
Distributive property, sets      80 83 95
Divergent sequence      238 242
Divergent sequence, diverges to $\infty$      250
divides      54 313
Division algorithm      315
Domain      148
Double Negation      31
Element      39 63
Ellis, J.      338
Empty set      63 68
Equivalence of statements      21
Equivalence relation      110—111 122
Equivalence relation, classes      111
Equivalent sets      252
Equivalent statement      22
Equivalent statement forms      22
Euclid      58
Euclid, Elements      58 317 327 350
Euclidean algorithm      317 327—328
Euclidean metric      285
Euclidean n-space      40
Euler $\phi$-function      332
Euler theorem      333 371
Euler, L.      58 157 158 331 358
Factorial      220 229
Family of set      90
fibonacci      229
Fibonacci numbers      230 248
Fibonacci sequence      230
Field      380
Field, ordered      380
Finite set      253
Fourier, J.      158
Frenicle de Bessy, B.      331
Function      147 157
Function, defined in cases      149
Function, equality      152
Function, notation      148
Function, preserves distance      311
Function, recursively defined      229
Function, well-defined      147
Fundamental Theorem of Arithmetic      218
Gauss, C.F.      209
GCHQ      338
Gelfond — Schneider theorem      376
Gelfond, A.O.      376
Geometric series      356 365
Golden ratio      248
Greatest common divisor      315
Greatest lower bound      133
Greatest lower bound, sequence      226
Green, G.      200
Halmos, P.R.      106 115
Hardy, G.H.      55 58 356
Harmonic series      216
Heine, H.E.      158
Hellman, M.      338 371
Hermite, C.      376
Hilbert, D.      200 251 278 374
Hotel Infinity      251
Identity      379 380
Identity function      180
Image      191
Image theorems      195
Implication      20
Increasing sequence      227
Index set      90
Indexed family      90 161
Induction      208 221 352
Induction, second principle      218
Infimum      133 199
Infimum sequence      226
Infimum uniqueness      133 143
Infinite set      253
Injective      163
Integers      40
Integers, modulo n      314
Integers, positive      40
Interior point      311
Intersection      69 91
Intersection, family of sets      91
Intersection, finitely many sets      89
Intersection, infinitely many sets      90
Inverse      177 379 380
Inverse image      192
Inverse image theorems      195
Inverse, composition      181
Inverse, uniqueness      180
Irrational number      48 353—358
Josephus problem      223
Kronecker, L.      278
Lacroix, S.-F.      158
Lambert, J.H.      358
Least common multiple      324
Least upper bound      131
Least upper bound, sequence      227
Lemma      121
LIMIT      238
Limit point      311
Limit, inferior      249
Limit, superior      249
Limit, uniqueness      243
Lindemann, F.      376
linear combination      316
Lower bound, sequence      225
Lower bound, set      130 133
Lower triangle inequality      61
Lucas sequence      235
MAP      147
Max metric      286
Maximum      130
Member      39 63
Merkle, R.      338
Metric      284
Metric space      284
Metric, bounded associated      293
Metric, definiteness      284
Metric, discrete      285
Metric, Euclidean      285
Metric, max      286
Metric, nonnegativity      284
Metric, symmetry      284
Metric, taxicab      286
Metric, triangle inequality      284
Metric, usual      284
Minimum      130 199
Minkowski, H.      278
Monotone sequence      250
Natural numbers      40
Negation      19 22—23 42—45
Negation of implication      22
Negation of quantifier      42
Niven, I.      355 358
NSA      338
One-to-one      163
One-to-one, not one-to-one      169
Onto      163
Onto, not onto      169
Open set      299
Open set, ball      297
Open set, ball, unit ball      297
Open set, not open      301
Open set, open interval      40
Open set, unbounded interval      40
Ordered pair      98 106
Pairwise disjoint      96
Paradox      72
Partial order      142
Partition      119 122
Pascal, B.      360
Pascal, triangle      360
Peano axioms      352
Perfect number      349—350
Pigeonhole Principle      261 263
Pisano, L.      229
Plaintext      373
Plane      40 76
Poincare, H.      278
Polya, the list      2 11 382
Polynomial      115
Polynomial degree      115
Polynomial root      61
Positive definite      284
Power set      97
Primality testing      374
Prime number      35 59 349
Product notation      211
Proof in cases      53 56—57 79
Proof, contradiction      53—56
Proof, direct      53—54
Proof, if and only if      82
Proof, reductio ad absurdum      54
Proof, top down, bottom up      66 80
Proof, uniqueness      131—132
Proof, working backwards      152 240 288
Proper divisor      349
Proper subset      65
Prym, F.      200
Public key encryption      335
Pythagorean Theorem      346
Quantifier, existential      41
Quantifier, universal      41
RANGE      152
Rational numbers      40 353—355
Rational numbers, closed under addition      353
Rational numbers, closed under multiplication      353
Real numbers      40
Real numbers, positive      380
Reciprocal modulo n      322
Recursion      229
Reflexive      109 142
Relation      101 109
Relation from X to Y      101
Relation on X      101
Relation, equivalence      110
Relatively prime      315
Restriction      188 255
Riemann, G.F.B.      200
Rivest, R.      338 371
RSA-key      371
Russell, B.      72 278
Schneider, T.      376
SEQUENCE      224
Sequence, bounded      225
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