Ãëàâíàÿ    Ex Libris    Êíèãè    Æóðíàëû    Ñòàòüè    Ñåðèè    Êàòàëîã    Wanted    Çàãðóçêà    ÕóäËèò    Ñïðàâêà    Ïîèñê ïî èíäåêñàì    Ïîèñê    Ôîðóì   
blank
Àâòîðèçàöèÿ

       
blank
Ïîèñê ïî óêàçàòåëÿì

blank
blank
blank
Êðàñîòà
blank
Cofman J. — What to Solve? Problems and Suggestions for Young Mathematicians
Cofman J. — What to Solve? Problems and Suggestions for Young Mathematicians



Îáñóäèòå êíèãó íà íàó÷íîì ôîðóìå



Íàøëè îïå÷àòêó?
Âûäåëèòå åå ìûøêîé è íàæìèòå Ctrl+Enter


Íàçâàíèå: What to Solve? Problems and Suggestions for Young Mathematicians

Àâòîð: Cofman J.

Àííîòàöèÿ:

This book provides a wide variety of mathematical problems for teenagers and students to help stimulate interest in mathematical ideas outside of the classroom. Problems in the text vary in difficulty from the easy to the unsolved, but all will encourage independent investigation, demonstrate different approaches to problem-solving, and illustrate some of the famous dilemmas that well-known mathematicians have attempted to solve. Helpful hints and detailed discussions of solutions are included, making this book a valuable resource for schools, student teachers, and college mathematics courses, as well as for anyone fascinated by mathematical ideas.


ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1990

Êîëè÷åñòâî ñòðàíèö: 263

Äîáàâëåíà â êàòàëîã: 22.01.2014

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
blank
Ïðåäìåòíûé óêàçàòåëü
$\pi$, the number, Archimedes' algorithm for calculating      137
$\pi$, the number, Leibniz' series for      138 164
$\pi$, the number, problems      137—140
$\pi$, the number, solutions      160—166
Abel, Niels Henrik      234
Algebra, fundamental theorem of      140
Algebraic structures      144 214—218
Archimedes of Syracuse      137 146 234
Argand diagrams      220—221
Arithmetic progressions      12—13 41—43 133—134
Axioms      145
Axonometry      141—142 166—167
Binomial coefficients      38 230
Block designs      183 192—194 231 232
Block designs, balanced incomplete      231—232
Bolyai, Janos      145 234
Buffon's Needle Problem      139—140 165—166
Buffon, Comte de, Georges Louis Leclerc      139 234
Catalan's problem      149—150 172—173
Cayley, Arthur      145 235 240
Centres of gravity      131
Chameleons problem      97 115
Chessboards, generalized      22—23 74—77
Chessboards, king moves on      11 12 39—40
Chessboards, knight moves on      10—11 35—37
Chessboards, natural numbers on      91—92
Chessboards, number patterns from      11—12 37—40
Chessboards, rook moves on      11 22—23 37—38 74—77
Circles and lattice points      186 199
Circles, carrying at least three points      182—183 191—192
Circles, circumferences of      137
Circles, circumscribed about polygons      221
Circles, construction of      96 112
Circles, inscribed in polygons      221
Circles, inscribed in triangles      25—26 85—87
Circles, inversion with respect to      225—226
Circles, properties of points on      21 69—70
Circles, rolling      97 116—117
Coefficients of polynomials      213
Coefficients, binomial      38 230
Coefficients, multinomial      230
Coefficients, trinomial      40 76 230
Combinations      229
Combinatorics      149 183 229
complex numbers      208 220
Complex numbers, applications of problems      140—145
Complex numbers, applications of solutions      166—168
Composite numbers      208
Congruences      208
Contradiction, proof by      94
Contradiction, proof by, problems      99
Contradiction, proof by, solutions      127
Converses      4—5
Converses, problems      23—27
Converses, solutions      77—88
Coordinate systems      141 219—221
Coordinate systems, barycentric      107—110 220
Coordinate systems, Cartesian      70 98 103 120—121 186 219—220
Copernicus, Nicholas      97 235
Counting, the art of      149
Counting, the art of, problems      149—153
Counting, the art of, solutions      172—179
Cube numbers      41 210
Cube numbers, sum of      45
Cubes, division of      98 118—120
Cycles      105 231
de Bruijn, N.G.      183 234
de Fermat, Pierre      187 188 236
Desargues, Girard      235
Desargues, theorem of, in plane      97 113—115
Desargues, theorem of, in space      25 85
Descartes, Rene      235
Diophantine equations      203 235
Diophantus of Alexandria      235
Dirichlet's principle      184
Dirichlet, Peter Gustav Lejeune      134 235
Dodecahedra      112
Dominoes      95 99—101
Duality, principle of      171
Edges      230—231
Erdoes, Paul      181 182 183 185 235
Euclid of Alexandria      133 145 153 236
Euclid's parallel postulate      145
Euler's problem on polygon division      150—151 174
Euler, Leonhard      150 188 236
Eulerian paths      100
Exceptions and special cases      3—4
Exceptions and special cases, problems      17—19
Exceptions and special cases, solutions      55—66
Extending the field of investigation      90—91
Extending the field of investigation, problems      96—97
Extending the field of investigation, solutions      110—115
Extremal elements, use of      91—92
Extremal elements, use of, problems      97—98
Extremal elements, use of, solutions      117—118
Factors      208
Faltings, Gerd      188 236
Fermat's last theorem      187—188 201—204
Fermat's little theorem      24 81 155 157
Fibonacci numbers      15 38 48 210 236
Fibonacci numbers, properties of      8 32
Fibonacci, son of Bonaccio      236
Figurate numbers      208—210
Fox, Captain      140
Fractions      205
Fractions in simplest terms      16 53
Fractions, decimal      205—206
Fractions, successors of      16—17 53—54
Gabriel-Marie, Fr      127
Gallai, problem of Sylvester — Gallai      180—183 188—194
Gallai, Tibor      181 236
Gauss' fundamental theorem of axonometry      140—142 166—167
Gauss, Carl Friedrich      140 236
Generalizing given problems      4
Generalizing given problems, problems      19—23
Generalizing given problems, solutions      66—77
Geometry, Euclidean problems      145—146 180—183
Geometry, Euclidean solutions      168—170 188—192
Geometry, non-Euclidean      145
Geometry, non-Euclidean, problems      146—149
Geometry, non-Euclidean, solutions      170—172
graphs      230—231
Graphs, connected      104 231
Graphs, oriented      99—101 231
Gregory's arc tangent series      138—139 161—164
Gregory, James      138 237
groups      214—216
Hamilton, William Rowen      143 144 237
Hanani, Haim      183 194 232 237
Heron of Alexandria      126 237
Hexagons, regular      121
Hilbert, David      237—238 240 244
Hurwitz, Adolf      134 238
Hyperbolic geometry      145
imaginary numbers      140 207
incidence      148 170—172
Incident pairs      123 124
Induction, mathematical      94
Induction, mathematical, problems      98—99
Induction, mathematical, solutions      121—124
Infinite descent, method of      92—94
Infinite descent, method of, problems      98
Infinite descent, method of, solutions      118—121
Integers, positive      205
Integers, positive, as solutions to equations      96 97 102—104 117
Invariants of transformations, use of      91
Invariants of transformations, use of, problems      97
Invariants of transformations, use of, solutions      115—117
inversion      191 225—227
iterating      1—2
Iterating, problems      5—10
Iterating, solutions      27—37
Ladder, sliding      91
Lagrange's identity      142—144
Lagrange, Joseph Louis      134 142 238
Language, different, expressing problem in      89—90
Language, different, expressing problem, problems      95—96
Language, different, expressing problem, solutions      99—110
Lattice points      98 120—121 186—187 199—200
Leibniz' series for $\pi$      138 164
Leibniz' theorem      135 157—158
Leibniz, Gottfried Wilhelm      8 135 138 238
Light rays      126
Limits      232—233
Line segment, division of      96 107—110 122—123
Line, ideal      147 148
Lobachevsky, Nicolai Ivanovitch      145 238
Loops      231
Markoff numbers      85
Markoff, A.A.      238
Matijasevic, Jurii Vladimirovic      136 238
Matrices      21—22 73—74 212—213
Minkowski, Hermann      180 186 238
Moebius      107
Motzkin, T.S.      181 239
Mouseholes problem      18 58—59
n-gons      see "Polygons"
Natural numbers      205
Natural numbers as solutions of equations      19 63—64 187—188 201—204
Natural numbers as sums of square numbers      142—145 167—168
Natural numbers, number expressed as sum of      19 64—65
Natural numbers, odd divisors of      17 54—55
Natural numbers, prime divisors of      154—155
Natural numbers, square numbers between      110—112
Natural numbers, sum of powers of      98 121—122
Necessary conditions      4—5
News transmission problem      96 104—106
Newton, Isaac      239
Norms      144
Number sequences      232—233
Number series      7—8
Number theory, analytic      134
Operations, algebraic      214
Pappus Of Alexandria      19 146 239
parallelograms      18 19—20 48 57—58 66—67
Pascal's triangle      37 38 211 239
Pascal, Blaise      239
Paths      104—106 231
Patterns, search for      2—3
Patterns, search for, problems      11—17
Patterns, search for, solutions      37—55
Peano, Giuseppe      239
Pentagonal numbers      209
Pentagons      24 79—80
Pentagons, regular      8 30 31 98 120—121
Pentagrams      8 30 31
permutations      229 230
Permutations, zigzag      151—153 175—177
Physics, employment of      95
Physics, employment of, problems      99
Physics, employment of, solutions      125—132
Pigeon-hole principle      184 194—197
Plane, division of      21 71—72
Planes in three-dimensional space      181—183 189—191
Planes, projective      146—149
Plutarch      24
Point sets, convex      221—223
Points, ideal      147 148
Polygons (n-gons)      24 80—81 99 109—110 125 221
Polygons (n-gons), convex      18 56—57 150—151 174 221
Polygons (n-gons), regular      15 47—48 98 120—121 137 160—161
Polyhedra      19 65—66
Polynomial equations      140
Polynomials      98 121—122 134—135 155—157 213—214
Polynomials with prime number values      135—136 157—158
Positive numbers, products of      20—21 68—69
Prime numbers      24 208
Prime numbers, problems on      10 13 24 96 133—136
Prime numbers, problems on, solutions to      34 43 110 153—159
Prime numbers, relatively      15 53 208
Prime numbers, relatively, properties of      25 82 89—90 188 203—204
Probability theory      139
Projection, stereographic      112 227—228
Pyramids      20 67—68
Pythagoras of Samos      239
Pythagoras of Samos, theorem of      239
Quadrilaterals, areas of      19 61—62
Quadrilaterals, cyclic      62 129 223
Quaternions      143—144 167—168 208 225
Ramsey numbers      184—186 197—199
Ramsey, Frank Plumpton      185 239—240
Rational numbers      205 207
Real numbers      207
Rectangles      18 24 58 79
Reflection      228—229
Regions, division of plane into      21 71—72
Regions, division of space into      21 72—73
Rhombuses      15 47—48
Rotation      143 144 223—225
Scalars      216
Schoenberg, Isaac      186—187 240
Schwartz      129
sec x      151 153 178—179
Sequences, number      110—112 232—233
Series, number      7—8
Series, number, harmonic      212
Shoemaker's knife      146 168—170
Sierpiriski, Waclaw      71 154 186 240 244 246
Space, Division of      21 72—73
Sphere, cut by planes      26—27 87—88
Sphere, inversion with respect to      226—227
Sphere, properties of points on      21 70
Square numbers      19 24 42 43 62—63 209
Square numbers between terms of sequences      96 110—112
Square numbers, natural numbers as sums of      142—145 167—168
Square numbers, prime numbers as sums/differences of      136 158—159
Square, Latin      21
squares      15 18 23 48—50 58 78—79
Steinhaus, Hugo      186 240 242
Structures, algebraic      144 214—218
Sufficient conditions      4—5
Sundaram's sieve      13 43
Sylvester, James Joseph      181 240
Sylvester, problem of Sylvester — Gallai      180—183 188—194
Tan x      151 153 177—179
Tetrahedra      98—99 109 110 124 132
Tetrahedral numbers      209
transformations, geometric      223—229
Translation      228
tree diagrams      17 25 53 82—83 85
Trees      105—106
Triangle, harmonic      8 211—212
Triangle, Pascal's      37 38 211 239
Triangles, areas of      97—98 117—118
Triangles, circles inscribed in      25—26 85—87
Triangles, congruent      77 78
Triangles, construction of, problems      6—7 96 97—98 99
Triangles, construction of, solutions      29 107—108 118 125—130
Triangles, division of sides of      99 131—132
Triangles, equilateral      121
Triangles, isosceles      14 18 23 45—47 77—78
Triangles, right-angled      17—18 55—56 103—104
Triangular numbers      24 41 47 209
Tribonacci numbers      40
Trinomial coefficients      40 76 230
Triples, Pythagorean      21 210—211
tripods      141 142
Vector spaces, real      216—218
Vectors      35 69—70 216—218
Vertices      230
1 2
blank
Ðåêëàìà
blank
blank
HR
@Mail.ru
       © Ýëåêòðîííàÿ áèáëèîòåêà ïîïå÷èòåëüñêîãî ñîâåòà ìåõìàòà ÌÃÓ, 2004-2024
Ýëåêòðîííàÿ áèáëèîòåêà ìåõìàòà ÌÃÓ | Valid HTML 4.01! | Valid CSS! Î ïðîåêòå