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Penney D.E. — Perspectives in Mathematics
Penney D.E. — Perspectives in Mathematics

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Название: Perspectives in Mathematics

Автор: Penney D.E.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1972

Количество страниц: 359

Добавлена в каталог: 09.01.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute value      289
Aleksandrov, A.D.      318
Alexandroff, Paul      317
American Mathematical Monthly      107
Antoine, L.      51
Approximations by continued fractions      63—65
Archimedean property      303
Area      21
Art Gallery Theorem      254
Associative law      82
Associative operations in real number system      301
Bach, J.S.      52 76
Banach, S.      21—23
Batting average      66
Beck, Anatole      318
Beet virus molecule      142
Beiler, A.H.      218 316
Benade, Arthur H.      81
Benson, R.V.      279
Bers, Lipman      317
Birkhoff, Garrett      106 316
Bleicher, Michael N.      318
Boltyanskii, V.G.      23 279
Bolyai Farkas      23—24
Bolyai Farkas, Janos      24
Bolyai — Gerwin Theorem      2 6
Borromean rings      25 see
Borromean Rings, formula      41
Borromean Rings, generalizations      29
Brunn, H.      29 51
Brunnian links      29
Brunnian links, (4,2)-links      45—46
Brunnian links, (n,k)-links      43 49
Cancellative operations      95
Cantor ternary set      312
Cantor Ternary Set, length      313
Cantor Ternary Set, number of elements      314
Cantor — Schroeder — Bernstein Theorem      164
Cantor — Schroeder — Bernstein Theorem, applications      169—172 176 181
Cantor, Georg      177 182
Cardinal numbers      179
Cardinal numbers, existence      180
Center of group      104
Cohen, Paul J.      182
Cohn-Vossen, S.      143 317
Commutative law      34
Commutative operation in group      87 94 see Abelian"
Commutator      45
Commutator, k-commutator      48
Complex number system      310
Composite numbers      185
Composite numbers, consecutive      187
Composite numbers, prime factors      186
Congruence motions of disk      90
Congruence motions of square      93
Congruence motions of tetrahedron      90
Congruence motions of triangle      83—87
Congruence motions, product      84—85
Constructions with straightedge and compass      6 19 23
Continued fractions      59—61
Continued fractions and batting averages      66—67
Continued fractions and grade distributions      67—69
Continued fractions and irrational numbers      286
Continued fractions, construction      75—76
Continued fractions, evaluation      62—63
Continuum      179
Convex hull      261
Convex hull, kernel      261
Convex hull, polyhedron in Steinitz's Theorem      116
Convex hull, sets, intersection of      258—260
Convex hull, sets, tower of      260
Convexity      255
Convexity, generalizations      276—279
Coset of subgroup      96
Coxeter, H.S.M.      143 317
Critical point      240
Cross-cancellative operation      95
Cross-cancellative operation, semigroup      105
Crowdis, David G.      318
Crowe, Donald W.      318
Crowell, R.H.      51
Curve, knotted      30
Curve, knotted on torus      30
Curve, knotted, polygonal      28
Curve, knotted, simple closed      27—30
Curve, knotted, tame      28
Curve, knotted, wild      28
Cycles in population      249
de Fermat, Pierre      184
Debrunner, H.      23 51 279 317
Decimal expansion      308—309
Dedekind Box Principle      172 175
Dedekind Box Principle, applications      177
Dedekind infinite      174
Dedekind, Richard      183
Degree of realization      230 232
Degree of realization in competing populations      234
Dehn, M.      18
Differential equations      223
Differential equations for competing populations      234 245
Differential equations in population growth      224—226
Differential equations in radioactive decay      227
Divisibility      184
divisors      184 see
Divisors, number      205
Divisors, product      189
Doerrie, Heinrich      317
Dudley, Underwood      218
Duplication of cube      18
Dynkin, E.B.      143
Equidecomposable figures      3 22 23
Equivalence relation      5 162
Equivalence relation, between nested sequences      293 295
Euclidean algorithm      92 196 197 219
Euclidean algorithm, proof      197—202
Euler's formula      108 118
Euler's formula, proof      118—122
Euler, L.      118 144
Exponent of group element      98
Factorization into primes      196 202 209—210
Fermat's theorem      218
Fifths      73
Fifths, improving      77
Five-color theorem      144
Fort, M.K.      51
Fox, R.H.      51
Fraleigh, John B.      318
frequencies      70
Frequencies of notes on piano      73
Functions      154—162
Fundamental Theorem of Arithmetic      202 204
Fundamental Theorem of Arithmetic, applications      281
Fundamental Theorem of Arithmetic, proof      202—203
Gause, G.F.      252
Gauss, C.F.      218—219
Gelfond, A.      218
Generator of group      102
Geodesic dome      142
Geometric series      283
Goffman, Caspar      315
Golden mean      62
Greatest common divisor      205
Greatest common divisor, computation      205—206
Greek alphabet      319
Griffin, Harriett      218
Group      92
Group of prime order      102
Group, abelian      102
Group, associated with curves in space      38
Group, center      104
Group, cyclic      102
Group, examples      82—92
Group, uniqueness of identity      93
Gruenbaum, Branko      143 279
Hadwiger, H.      18 23 279 317
Half-plane      273 275
Hall, M.      106
Harmonics      70
Hausdorff, Felix      182
Helly's theorem      266 268
Helly's Theorem, applications      270—271 273 276
Herstein, I.N.      106
Hilbert, D.      143 317
Hocking, John G.      317
Homomorphism      105
Horn, Alfred      279
Image of function      155—156
Image of homomorphism      105
Induction principle      10 190
Induction Principle and well-ordering      190—193
Induction Principle, applications      10—11 49 193—195 259
Infinite series      69—70 295
Integers      184
Intermediate fractions      64
Intervals      288
Intervals, length      288
Intervals, nested sequences of      293
Intervals, sum of      297
Inverse of group element      83
Inverse of group element, uniqueness of      93
Jacobson, Nathan      106
Jakobson, Roman      317
Jeans, Sir James      81
Join of point and set      277
Kernel of homomorphism      106 see
Khinchine, A.Ya.      81
Klee, Victor      23 279 317
Kolmogorov, A.N.      318
Krasnoselskii's Theorem      254 271
Krasnoselskii, M.A.      271
Kripke, Bernard      315
Kurosh, A.G.      106
L-convexity      277
Lack, D.L.      253
Lagrange's theorem      96
Lagrange, J.L.      107
Lavrent'ev, M.A.      318
Law of quadratic reciprocity      218
Law of Small Whole Numbers      72
Least upper bound      303
Limit of sequence      65 69 284 289—291 294—295
links      30 32 see
Links, splittable      30
Lobachevsky, N.I.      24
Logarithms      53—56
Lomont, J.S.      317
Lyusternik, L.A.      143 279
MacLane, Saunders      106 316
Mansfield, M.J.      314
Map on Moebius strip      117
Map on sphere      116
Map on torus      116
Moebius strip      50 117
Moise, E.E.      23
Mordell, L.      218
n-link      30
n-link, completely splittable      32
n-link, splittable      30
n-link, sublink of      32
Natural numbers      184
Natural numbers, composite      185
Natural numbers, prime      185
Nested sequences of intervals      293
Nested sequences of intervals, equivalence of      295
Net of polyhedron      118
Niven, Ivan      218 316
Nonmeasurable set      21
Odum, Eugene      253
One-to-one correspondence      156 160—162
Order of group      96
Order of group of group element      99
Order of group, infinite      96 99
Ordered pair      159
Ore, Oystein      143
Parallelogram formed from triangle      11
Parallelogram formed from triangle, reassembled into rectangle      11
Partial quotients      62
Passman, D.S.      106
Polya, George      192 318
Polygon      2 109
Polygon, connected      109
Polygon, edge      2
Polygon, equidecomposable      3
Polygon, vertex      2
Polyhedron      113
Polyhedron, 2-connected      116
Polyhedron, edge      115
Polyhedron, face      115
Polyhedron, vertex      115
PRIMES      102 185
Pythagorean right triangles      217—218
Pythagorean Theorem      16
Rademacher, Hans      218
Radioactive decay      227
Rational numbers      280
Real numbers      297
Real numbers as nondenumerable set      178
Real numbers, Archimedean property      303
Real numbers, decimal expansions      308—309
Real numbers, order relation      302
Rectangle formed from parallelogram      11
Rectangle formed from parallelogram, reassembled into square      12—14
Regular solid      123
Rudin, Walter      314
Schoenflies theorem      110
Semigroup      104
Sets      146
Sets and Venn diagrams      151
Sets, algebra      153
Sets, cartesian product      160
Sets, convex      255
Sets, denumerable      176
Sets, descriptive definition      147
Sets, difference      154
Sets, distributive laws      152—153
Sets, element      146
Sets, empty      150
Sets, equality      148
Sets, finite      163
Sets, inclusion      149
Sets, infinite      163
Sets, intersection      150
Sets, listing      147
Sets, maximal convex      264
Sets, maximal tower      263—264
Sets, maximal with respect to a property      263
Sets, nondenumerable      177
Sets, nonlinear      263
Sets, notation      147—148
Sets, number of elements      154
Sets, subset      149
Sets, tower      260
Sets, union      149
Sierpinski, W.      23
Sigmoid curve      232
Singer, I.M.      51
Slobodkin, Lawrence B.      253
Snowflake curve      19—21
Spivak, Michael      317
Sprecher, David A.      315
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