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Averbach B., Chein O. Ч Problem solving through recreational mathematics
Averbach B., Chein O. Ч Problem solving through recreational mathematics



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Ќазвание: Problem solving through recreational mathematics

јвторы: Averbach B., Chein O.

јннотаци€:

Many of the most important mathematical concepts were developed from recreational problems. This book uses problems, puzzles, and games to teach students how to think critically. It emphasizes active participation in problem solving, with emphasis on logic, number and graph theory, games of strategy, and much more. Answers to Selected Problems. Index. 1980 ed.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1980

 оличество страниц: 473

ƒобавлена в каталог: 04.12.2013

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$Greek$ $Anthology$      70 95
$Journal$ $of$ $Recreational$ $Mathematics$      320
$Ladies$ $Diary$      102
$Rhind$ $Papyrus$      95
$Sphinx$      1 156
Additivity      343
Age problems      see Problems age
Algebra      70Ч84
Algebraic techniques      321Ч331
Alphametic      157
Analyzing a game, frontal assault      233Ч234
Analyzing a game, frontal assault, limiting factors      234Ч239 241
Analyzing a game, working backward      230Ч232 246Ч247
Ancient problems      see Problems ancient
Andersson, G.      263
Antecedent      44
Appel, K.      198
Argument      38 55Ч60 377
Argument, form of      38 56 57 58 59
Argument, valid      56Ч57 58 59Ч60
Aristotle      38
assumptions      9 12Ч13 15Ч17
Assumptions, secondary      14
Axiom      137
Bachet, de M$\acute{e}$ziriac      1 151
Bachet, de M$\acute{e}$ziriac, weight problem      146 151Ч153
Ball, W. W. R.      276
Base      125 146 148Ч156 165Ч168 172
Base, addition and multiplication      153Ч155
Base, conversion      148Ч150
Base, ten      see Decimal notation
Base, two      see Binary system
Bergholt, E.      288
Biconditional statement      45 44Ч46 48
Binary system      151Ч152 165Ч166 246 247-249
Binomial coefficient      350
Binomial theorem      350 350Ч351
Bipartite graph      177 402 403
Birdcage      372
Bishop, reflecting      252
BishopТs move      203Ч204 207
Blackjack      370
Boole, G.      38
Boss Puzzle      see Fifteen Puzzle
Bouton, C. L.      247
Boxing Tournament Problem      2 4
Branch      17 19 176
Branch point      17
Bridg-it      224 262 269
calendar      144
Cancellation law      128
Cardano      337
Carroll, L.      37 38 317
Case analysis      16Ч17
Casting out nines      125Ч127
Chance      215Ч216 218
Checkerboard games      214 215 263Ч265 266 269Ч270
Chess      213 217 221 251 252
Chevalier de Mere      337
Chinese Rings      414
Chuckluck      372
Chuquet, N.      95 96
Circuit      178
Circuit, Eulerian      178 182Ч184 186 190 192Ч193 203-205
Circuit, Hamiltonian      192Ч193 194 205Ч208 401
Clavius, C.      95 96
Coefficient      350
Colored cubes      275 299Ч304 311Ч312
Colored cubes, Instant Insanity      299
Coloring      282Ч284 285 286Ч287 298Ч299 312 404 416
Coloring, of graphs      200
Coloring, of maps      see Map coloring
Combination      348 348Ч349
Common divisor      116
Complement of a graph      402 403
Complement of an event      340
Complete bipartite graph      177 403
Complete graph      177 403
Composite number      106
Conclusion      55Ч56 417 418
Conditional probability      352Ч353 370Ч371
Conditional statement      44 46 48
Congruence      121 120Ч131 132 134Ч137
Conjecture      198 202
Conjecture, FermatТs      100Ч101 104n. 202
Conjecture, Four Color      198
Conjunction      42Ч43 48
Connected graph      see Graph connected
Connectives      41
Connectives, biconditional      45 44Ч46 48
Connectives, binary      41
Connectives, conditional      44 44Ч46 48
Connectives, conjunction      42Ч43 48
Connectives, negation      41 42 48
Connectives, unary      41
Consequent      44
Contradiction      9 12 13 48
Contrapositive      54
Conway, J. H.      265
Counting      343Ч349 366Ч370
Cram      263Ч264
Craps      338 354Ч355 362Ч363 370
Cross-cram      263
Crossing problems      see Problems crossing
Cryptarithmetic      156Ч162 169Ч172
D$\acute{e}$j$\grave{a}$ vu      241 252
De Morgan, A.      38
Decanting      117Ч118
Decimal notation      125Ч126 146 163Ч165
Decimation      313Ч315
Deficient number      100
Definition      137
Degree of a vertex      180 186 199
Degree of a vertex, even      180 199
Degree of a vertex, in-degree      190
Degree of a vertex, odd      180Ч186
Degree of a vertex, out-degree      190
Dependent events      352
Dependent experiments      351
Dice      337 338 353 356 361
Dicircuit      190
Dicircuit, Eulerian      190
Dicube      308
digit      147
Digital root      125Ч127
Digraph      see Graph directed
Dimensional consistency      80
Diophantine equations      103Ч104 115 117
Diophantine equations, linear      115 117 119 131Ч137
Diophantus      70 95 96 103 104
Dipath      191
Dipath, Eulerian      191
Directed graph      190
Disjoint events      343 344
Disjunction      43Ч44 48
Dissection Problems      279Ч282 306Ч307
Dividend      120 160
Divisibility      104Ч105
Divisibility, properties of      105
Divisibility, tests for      351Ч352 395
Divisibility, transitivity of      105
Division algorithm      120
Divisor      104 111Ч113 116 120 160
Divisor, greatest common      116 128
Divisor, number of      112
Dominating set (of vertices)      211 404
Dominoes      205 274 281 282Ч283 308
Dots      261Ч262 268Ч269
Drawing strategy      see Strategy drawing
Dual map      199
Dudeney, H. E.      102
Dwarfs and Giant      267
EDGE      176
Edge-disjoint path      187Ч189
Elimination, method of      77Ч78 326Ч327
End position problems      253 268Ч272
Entertainment value      365
Entrapment, games of      266Ч268
Equally likely outcomes      339 342
Eratosthenes      107
Euclid      100 106 119
Euclidean algorithm      119
Euler diagrams      417Ч418
Euler, L.      173 175
Eulerian circuit      see Circuit Eulerian
Eulerian dicircuit      190
Eulerian dipath      191
Eulerian path      see Path Eulerian
Even vertex      see Vertex even
Event      339
Eves, H.      70
Expectation      362 361Ч364 372Ч373
expected payoff      361
Expected value      362 372Ч373
Experiment      338
Extraneous solution      83
Factor      105
Factorial      139 334 346
Factoring, integers      83
Factoring, quadratic polynomials      325
Fair coin      340 363
Fair game      363
Fair odds      362
Favorable game      363
Favorable outcomes      338
Fermat, P.      100 101 104n. 337
Fermat, УLast TheoremФ      100 104n. 202
Fibonacci sequence      418
Fifteen puzzle      274Ч275 288Ч299
Fifteen Puzzle, sliding block puzzles      311
Finiteness (of a game)      216 218
Five color theorem      199
Four color conjecture      198
Four color theorem      198 199 200 202
Fox and Geese      266Ч267
Fox and Hounds      266 270
Frege, F. L. G.      38
Fundamental Theorem of Arithmetic      109Ч110
Gale, D.      262
Gale, game of      262
Games, analysis of      see Analyzing a game
Games, bounded      217
Games, chance-free      215Ч216 218
Games, checkerboard      see Checkerboard games
Games, entrapment      266Ч268
Games, finite      216Ч217 218
Games, join of      405
Games, length of      217 218Ч221 413
Games, matchstick      see Matchstick games
Games, mis$\grave{e}$re form      252 254 255
Games, of perfect information      216 218
Games, regular form      254 255
Games, state of      224Ч225 228
Games, two-person      213 218
Games, variations of      251Ч252
Gardner, M.      1 213 253 264 320
Gauss, C. F.      122
Golomb, S.      281 308
Graph      176 175Ч212 303Ч304
Graph, bipartite      177 402 403
Graph, coloring      200
Graph, complement of      402 403
Graph, complete      177 403
Graph, complete bipartite      177 403
Graph, connected      179 182 185 187 190 193
Graph, directed      190
Graph, nonplanar      177
Graph, planar      177
Graph, traceable      178
Grasshopper      252
Greatest common divisor      116 128 130 131Ч132
GrundyТs Game      256
Guthrie, F.      198
Haken, W.      198
Hamilton, W. R.      192
Hamiltonian circuit      see Circuit Hamiltonian
Hamiltonian path      see Path Hamiltonian
Hein, P.      223 260 262 285
HEX      223 222Ч224 262 269
Hexapawn      264 269 270
Hexominoes      308
Hi Q      see Peg Solitaire
Highway inspectorТs problem      187Ч189
Hip      264Ч265
Honest die      340
Hunter, J. A.      157
Impossible event      340
incidence      180
Independence      351 352 353 370Ч371
Independent events      352 353
Independent experiments      351
Independent vertices      212 404
Inductive reasoning      332
Inference problems      see Problems inference
Instant Insanity      see Colored cubes
Integers, positive      100 104
Intersection      344
inversion      291 292
Join of games      405
Josephus problem      313
K$\ddot{o}$nigsberg bridge problem      173Ч174 175 181Ч182 186Ч187 201-202
Kalah      312
Kayles      255
Khowarizmi, al      70
KnightТs move      194
KnightТs tour      194Ч195 207
KnightТs tour, reentrant      194 195 207 312
Labyrinth      4Ч5
Leibnitz, G. W.      38
Length of a game      217
Length of a game, example of      218Ч221 413
Linear equations      322 325Ч330
Linear equations, dependence of      326n. 327n.
Linear equations, inconsistent      326n. 327n.
Linear equations, systems of      325Ч329
Linear inequality      323
Listing order      290Ч291 294
Logic      37
Logic problems      see Problems inference
Logical equivalence      54
Logical implication      54
Loop      176
Lottery      373
Loyd, S.      288 289 294
Luck      see Chance
MacMahon, P. A.      311
Mah$\bar{a}$v$\bar{\imath}$ra      95 96
Mancala      312
Map, coloring      198Ч201 335 418 20
Map, dual      199
Map, planar      198 199
Matching problems      see Problems matching
Matchstick games, more than one pile      214Ч215 246Ч249 255
Matchstick games, one pile      3 20Ч22 214 218Ч221 227Ч228 230Ч232 254 256
Mathematical induction      152 153 218Ч220 278 332Ч335 418-420
Metrodorus      1 70 95
Mis$\grave{e}$re form (of a game)      252 254 255
Modulus (modulo)      120 121 128
Monochromatic triangle      403
MooreТs Nim      255
1 2
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