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Polya G. Ч Mathematical Discovery: On Understanding, Learning and Teaching Problem Solving Combined Edition
Polya G. Ч Mathematical Discovery: On Understanding, Learning and Teaching Problem Solving Combined Edition

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Ќазвание: Mathematical Discovery: On Understanding, Learning and Teaching Problem Solving Combined Edition

јвтор: Polya G.

јннотаци€:

Combining standard Volumes I and II into one soft cover edition, this helpful book explains how to solve mathematical problems in a clear, step-by-step progression. It shows how to think about a problem, how to look at special cases, and how to devise an effective strategy to attack and solve the problem. Covers arithemetic, algebra, geometry, and some elementary combinatorics. Includes an updated bibliography and newly expanded index.


язык: en

–убрика: ћатематика/

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

ed2k: ed2k stats

»здание: Combined edition

√од издани€: 1981

 оличество страниц: 432

ƒобавлена в каталог: 24.01.2011

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
'Blind Man's Rule', (Euler)      1 55
5-prism      2 151 154
A priori      1 119
abbreviations      1 xvii
Abel, Niels Henrik      1 188 2
Abracadabra      1 68Ч73
Abstraction      1 30 56
Adam, Charles      1 56
Aeppli, Alfred      1 xiii
Age of Reason (The)      2 60Ч61
Alexanderson, Gerald L.      1 vii xiii xvi
Algebra, for solving word problems      1 22 24
Alternating procedure      2 50Ч51
American Mathematical Monthly      2 112
Analogue, to Heron's theorem      1 45
Analogue, to Pythagoras' theorem      1 34 45
Analogy      1 13 2 52 86 124 149 H I II 27Ч28 see specialization
Analogy, binomial and polynomial coefficients      1 87Ч88
Analogy, of Heron's theorem      1 45
Analogy, of Pythagoras' theorem      1 34 45 H
Analogy, Pascal's and Leibnitz's triangles      1 88Ч90
Analogy, plane and solid geometry      1 12Ч13 50Ч51 83 2 108 H 235 I 45Ч47
Analysis      2 23 31 see
Angle, dihedral      1 12 2
Angle, trihedral      1 12
Anticipation      1 58Ч59
Aphorismen      2 99
Archimedes      1 38 44 57 98 2 163 H I 166Ч167
Area of triangle      1 34Ч35
Ariadne, The Thread of      1 148
Aristotle      2 71
Arithmetic mean      1 98
Ars Conjectandi      1 76
Ass of Buridan (The)      2 161Ч162
Auxiliary problem      1 18 2 96 H
Auxiliary problem, equivalent      2 37Ч39 H
Auxiliary problem, figures      1 14Ч15
Auxiliary problem, more, or less, ambitious      2 39Ч40 H
Auxiliary problem, remoter      2 41Ч42
Baron, Julius G.      2 202
Beckenbach, E.F.      2 175
Bernoulli, Jacob      1 76
Bernoulli, polynomials      1 62Ч68
Binomial coefficients      1 71Ч75
Binomial formula      1 63 65 67
Binomial theorem      1 75 91Ч93
Bolzano, Bernard      2 184 H
Borel, Emile      2 127
Boutroux, P. (and L.Brunschvicg)      1 67
Bradley      2 71
Bright idea      1 15 23 62 2 H
Brunschvicg, L. (and P.Boutroux)      1 67
Buridan      2 161
Butler, Samuel      2 60
Carbon atom (the)      2 188
Carroll, Lewis      1 41
Carry out your plan      2 7 31 H
Cartesian pattern      1 22Ч59
Cartesian pattern, classroom examples      1 29Ч32
Cartesian pattern, geometric examples      1 32Ч37
Cartesian pattern, wider scope      1 129Ч133
Case history      1 vi 9
Cavalieri      2 32 183
Ceteris paribus      2 93
Chains of equivalent problems      2 38Ч39
Checkmate in two moves      1 152
Choice between three plans      2 32
Circle, circumscribed      1 5
Circle, inscribed      1 5
Classroom examples of Cartesian pattern      1 29Ч32
Comparison of solutions to a word problem      1 25
Conclusion      1 121 2 H
Conclusion, how can you prove such a      2 26 34
Condition      1 4 119Ч120 129Ч133 2 78 H see data condition"
Condition, clauses      1 4 122
Condition, express by equations      see "Pattern Cartesian"
Condition, keep only a part      1 4 17 33 147 2 H
Condition, major clause      1 140
Condition, redundant      1 42Ч44 I 200Ч202
Condition, split the condition      1 5 6 19 27 129Ч133 150
Condition, sufficient, or insufficient, to determine the unknown      1 18 41Ч42 54 55 57Ч58 H I
Condition, the clause to begin with      1 138Ч142 148Ч149 151Ч153
Condition, using the whole      see "Did you use all of the data?"
Conjecture      see "Guess"
Consistence, Independence and      1 57Ч58
Constructions, geometric      1 20
Constructions, ruler and compass      1 3 20 32
Contained in, sets      1 20
Continuous transition      1 10 37 2
Could you solve part of the problem?      1 40 45
Counterexample      2 49Ч51 H
Courant, Richard      1 20 32
Critique of Pure Reason      1 99
Crossword puzzle      1 32Ч33 131 138Ч139 2
cube      2 151 154
Cuboctahedron      2 205
Curvilinear quadrilateral      1 44
Dante      2 54 I
DATA      1 3 119Ч120 127Ч128 2 H see data condition"
Data, derive something useful from      1 7 2 H
Data, to determine this kind of unknown      2 85Ч86
Data, variation of      1 10 31 101 H
de Montaigne, Michel      2 102
Decimals, periodic      2 164Ч165
Decisions      2 65Ч66
Definition      2 81 83 H
Denk, Franz      2 138 207
Descartes, on polyhedra      2 154 I
Descartes, Rene      1 1 22 23 27Ч28 55Ч59 61 115 129 2 12 36 77 78 126Ч127 149Ч158 184 H II 142
Descartes, Rules for the Direction of the Mind      1 22 26Ч28 55Ч56 58Ч59 2
Descriptive geometry      2 12
Deus ex machina      1 64 2 II
Diagram      2 68Ч71
Did you use all the data (the whole condition, the whole hypothesis)?      1 17 102 2 H 152 II 162Ч163
Difference equations, homogeneous      1 108
Differential equations      1 96
Differential equations, homogeneous linear      1 108
Dihedral angle      1 12 2
Diophantine problem      1 55
Diophantus      2 187
Discipline of the mind      2 12 77Ч88
Discovery, Story of a Little      1 60Ч62
Do not commit yourself      2 34
Do you know a related problem?      2 80 H
dodecahedron      2 153Ч154
Dodecahedron, rhombic      2 205
Dodgson, Charles      1 41
Dudeney, H.E.      1 207
Duncan, Isadora      2 134
Duncker, Karl      2 65 67 72 H
Economy      2 91Ч92 96
Egyptian Problem, An      1 48
Einstein      2 102
Elwes, R.H.H.      2 134
Empty set      1 20
Equal sets      1 20
Equations, as many as unknowns      1 54
Equations, differential      1 96
Equations, fewer than unknowns      1 55
Equations, homogeneous linear difference      1 108
Equations, homogeneous linear differential      1 108
Equations, incompatible      1 58
Equations, inconsistent system of      1 58
Equations, more than unknowns      1 54
Equations, n in n unknowns      1 142Ч145
Equations, self-contradictory system of      1 58
Equations, setting up      1 26
Equations, system of      1 28 2
Equations, system of four      1 129Ч130
Equivalent problems      1 125 2
Euclid      1 3 43 104 118 122 127 2 36 85Ч86 152 184 I
Euclidean constructions      1 3 20 32
Euler, 'Blind Man's Rule'      1 55
Euler, Leonhard (1707Ч1783)      1 46Ч48 55 72 2 I 9 18Ч22 30Ч34 90Ч102 106Ч107 121 II 95Ч96
Euler, line      2 48
Euler, on polyhedra      2 149Ч158 176 I 52Ч58
Example, from a puzzle      1 39Ч40
Example, from physics      1 37Ч39
Example, pattern      1 4Ч6
Example, puzzling (cartesian)      1 41Ч44
Expanding pattern      1 40
Exploring the neighborhood      2 194
Extrapolation      1 100
Extreme case      1 10
Fact and conjecture      2 168
Fejes-Toth, L.      2 164
Fibonacci, (Leonardo of Pisa)      1 49
Fibonacci, numbers      1 109 2
Fibonacci, numbers (Binet formulas for)      1 196Ч197
flexibility      2 35 II
Folding, cardboard      1 12Ч13
France, Anatole      2 142
Frustum (of a right pyramid)      2 2Ч10
Function      1 99Ч100
Galileo      1 109 2 I 194Ч196
Galois, Evariste      2 88
Gauss, Carl Friedrich      1 60Ч62 2 I
Generalization      1 25 48 53 62 64 77 81 83 88 92 111 112 175 2 152 H I 22Ч23 II
Generalization and specialization      2 51Ч52
Generalization, general formulation advantageous      1 69
Generalization, letters for numbers      1 25 44 162 H
Generalization, observe and generalize      1 76 84 2 152 H I
Generalization, specialization, and analogy      2 53 80 124 I
Genetic principle      2 132Ч133
Genius, the expert, and the beginner      2 97
Geometric constructions      1 3Ч4 20
Geometric mean      1 98
Geometry, descriptive      1 12
Geometry, plane      1 48
Geometry, solid      1 34 50Ч51 2
Gestalt      2 68
Given      1 3
Go back to definitions      2 194
Goldbach, Christian      1 121 I
Gothic tracery      1 17 32Ч33 44
Graphic time table      1 52Ч54
Guess      1 34 46 79 95 2 105 124 143Ч168 I II
Guess, examine your guess      2 156Ч157 168 H see "Induction"
Hadamard, Jacques      1 113 2 184 H 199
Haeckel, Ernest      2 133
Harmonic mean      1 98
Harmonic triangle      1 88Ч89
Hartkopf, Werner      1 ix 2 184
Have you seen it before?      1 147
Heath, T.L.      1 98
Hermite, Charles      2 143
Heron's (also Hero's) theorem      1 34Ч35 2 158 see
Heron's (also Hero's) theorem, analogue to      1 45
Heuristic      2 10
Heuristic, rat's maze      2 74
Hilbert, David      2 127
Hilgard, E.R.      2 100
Hilton, Peter      1 vii xvi 2
Hobbes, Thomas      2 22
Homothetic figures      1 9
How can you get THIS kind of thing (unknown, conclusion)?      1 34 36 110 2 6 29Ч30 79 86 see or kind "Theorem or
Hypothesis      1 121
Hypothesis and conclusion      1 121 125 127 2 78 94 H
Hypothesis to derive this conclusion      2 85Ч86
icosahedron      2 153Ч154
If you cannot solve the proposed problem      1 10 69 24 H
Incompatible equations      1 58
Inconsistent system of equations      1 58
Independence and consistence      1 57Ч58
Indeterminate problem      1 99Ч101
Indeterminate system of equations      1 58
Induction      1 91Ч92 183 2 H I I II see observe
Induction, fundamental inductive pattern (heuristic syllogism)      H 186Ч190 II
Induction, mathematical      1 73Ч75
Induction, observe and explain regularities      1 94 189 190 2 181 H I
Induction, verification (in particular cases, of consequences)      1 92 2 153 154 H
Inequality      1 51
Inside help, outside help      2 135Ч137 H
Interpolation      1 99Ч101
Interpretation      1 30 44
Interpretation, mechanical      1 146Ч148
Interpretation, optical      1 142Ч146
Interpretation, reinterpretation      1 149Ч155
Intersection, of sets      1 21
Inversion of a power series      1 95
Is there a solution?      2 79 H see sufficient or to
Isolation and combination      2 68Ч69
Isoperimetric problem      2 144Ч145
James, William      1 117 2 H
Kant, Immanuel      2 99 103
Keep part of the condition      1 33
Kepler, Johannes      2 123 181 I 196Ч198
Key facts      2 81 85
Key figure      1 167
Keynes, J.M.      2 161
Klein, Felix      2 126
Kohler, Wolfgang      2 36 H
Krauss, F.      2 184 H
Lagrange, interpolation formula      1 101Ч104
Lagrange, Joseph      1 104 195
Lakatos, Imre      2 51 127 184
Language, algebraic (mathematical)      1 24 2 124 H
Language, algebraic (mathematical), of geometric figures      2 85 124Ч125
Lattice point      1 202
leap years      2 194
Learning, Three principles of      2 102Ч104
Leibnitz's Harmonic Triangle      1 88Ч89
Leonardo of Pisa (Fibonacci)      1 49
Lichtenberg, Georg      2 61 99 103
Lighthouses, Three      1 16Ч17
Lindemann, Ferdinand      1 126
linear combination      1 106Ч107
Listening posts, three      1 19
Loci, patterns of      1 3Ч21
Loci, two for a function      1 140Ч142
Locus      1 4 5 133
Loewner, Charles      1 xv 2
Logothetti, Dave      1 xvi
Look at the unknown      2 87 H see or kind
Mach, Ernst      2 184 H I
Magic square      1 149
Maps      2 129Ч132
Mariotte      2 62
Mathematical induction      1 73Ч75 82 H I
Mathematische Schriften      2 99
Maxwell, James Clerk      2 133
Mean, arithmetic      I 98
Mean, geometric      1 98
Mean, harmonic      1 98
Medians of a triangle      1 11
Meiklejohn, J.M.D.      2 99
Mental inertia      I 63
metaphors      2 1Ч2
method      see also "Pattern" "Result
Method of successive approximations      1 26
Method of undetermined coefficients      1 93Ч94
Mice and men      2 75Ч76
Mobilization and organization      1 57 2 66Ч67 73 H
Mobilization and organization, diagram (How we think)      2 69
Modus operandi      1 122
Monroe, Marilyn      2 134
Morphological structure      2 155
Mozart, Wolfgang      2 102
Multiplicity of approaches      1 75 83 109
n-double-pyramid      2 153Ч154
1 2
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