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Hayes D.F. (ed.), Shubin T. (ed.) — Mathematical Adventures for Students and Amateurs
Hayes D.F. (ed.), Shubin T. (ed.) — Mathematical Adventures for Students and Amateurs

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Название: Mathematical Adventures for Students and Amateurs

Авторы: Hayes D.F. (ed.), Shubin T. (ed.)

Аннотация:

How should you encode a message to an extraterrestrial? What do frogs and powers of 2 have in common? How many faces does the Stella Octangula have? Is a plane figure of constant diameter a circle, and what has this to do with NASA? 210 = 5 x 6 x 7 = 14 x 15, so just how many numbers can be the product of both two and of three consecutive integers? Is there any such thing as a truly correct map? What patterns are possible in juggling?

What do all of these questions have in common? They, and many others, are answered in this book.

The authors are distinguished mathematicians; some are bright newcomers while others have been well known in mathematical circles for decades.

This is a partial record of the Bay Area Math Adventures (BAMA), a lecture series for high school students (and incidentally their teachers, parents, and other interested adults) hosted by San Jose State and Santa Clara Universities in the San Francisco Bay Area. These lectures are aimed primarily at bright high school students, the emphasis on bright, and as a result, the mathematics in some cases is far from what one would expect to see in talks at this level. There are
serious mathematical issues addressed here.

We hope that this book will capture some of the magic of these talks that have filled auditoriums at the host schools almost monthly for several years. Join the students in sharing these mathematical adventures.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 304

Добавлена в каталог: 11.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel, Niels Henrik      246 257
Ahlfors' "five islands" theorem      255
Ahlfors, Lars V.      255—257
Aleksandrov, A.D.      214
Alexanderson, Gerald L.      34
Algebraic integer      58
Analytic continuation      78
Appel, Kenneth      17
Archimedes      219 221—225 227 228 230 231
Arecibo Message      5
Aristaeus      219
Armstrong, Neil      9
Asymptote      168 174 181 191 231 275
Babylonians      53 54 164
Banach's matchbox problem      145
Banach, Stefan      145 146
Bayesian probability distribution      139 153
Benford's law      47
Berra, Yogi      27
Bertrand's paradox      150 151
Beukers, Frits      61
Bijection      91 101 103 108 109 111 116 see
Binary operation      168
Binet formulas      97
Binomial coefficient      106 107 110
Birch and Swinnerton — Dyer conjecture      61 78—80
Birthday problem      138
Bloch's constant      254 256
Bloch's principle      254
Bloch's theorem      254—56
Bloch, Andre      254 257
Boethius      52
Bonk and Eremenko theorem      256
Bonk, Mario      256 257
Boole, George      278
Brianchon's theorem      173 174 179—183
Bryant, Robert      7
Buffon Needle Problem      138 149 153
Cardioid      186
Carroll, Lewis      259 261 271 275 278 280 see
Cartan — Hadamard theorem      202—203 208 211 212
Cartan — Hadamard — Gromov theorem      208
Cauchy — Riemann equations      246—248
Centroid      221 223 228—231
Challenger (Space shuttle)      7 10 11 16
Check digit      27 33 34 38
Chromatic polynomial      114 116
Coates and Wiles theorem      79
Coates, John H.      79 80
Cole, Frank Nelson      20
Collinear      165 166 168 173—176 178—182
Complex cosine      253
complex derivative      247 248
Complex exponential      248 250
Complex function      247 248 250 252 255
Complex logarithm      249 250 254
Complex number      78 246—248 250 251
Complex plane      246—248 251 252
Complex sine      253
Complex variable      78 233 251
Conformality      233 244—246 248—250 252—256
Conic section      157 165 166 181
Conjecture      74
Connolly, Robert      144 145
Contractibility      205—208 211 212
Convergence      56 78 136 138 247 248
Convex polygon      120 171
Convex polyhedron      120 121
Copernicus, Nicolaus      38
Coprime      58
Coram, Marc      152 153
Cubical complex      202 209—211 214
cuboid      51 61 62
Curvature      201 202 205 206 257
Curvature, Gaussian      201 202 206 209
Curvature, nonpositive      202—212 214 215
Curve of constant width      11 13 see
Cusp      185—189 191 194 197 198
Cycloid      185 188
D'Alembert, Jean le Rond      247
Darwin, Charles      38
de Fermat, Pierre      74
de Morgan, Augustus      269 278
De Morgan, William      269
Defect      253
Degree of a polynomial equation      246
density      44 143 152 186 197 219 221—225 227—231 252
Desargues' theorem      173 175—177 183
Developable surface      250
Diaconis, Perci      139 153
Differential      244 245 248 256
Directed ratio      173
DNA      5
dodecahedron      120 122—124 128—132
Dodgson, Charles Lutwidge      259—262 265 267—280 see
Doyle, Peter      116
Drake's equation      6
Drake, Frank      4 6
Dual statement      180
Duality      122
Egyptians, ancient      157
Eilenberg — MacLane theorem      212
Einstein, Albert      38 51
ellipse      165 166 181 186—189 191 241—243 250 256
Elliptic curve      60 61 63 65 66 69 71 73 75—77 79 80 253
Enigma code      17
Equidistribution      44—48
Eremenko, Alexandre      256 257
Error, correction      32
Error, detection      27 33 38
Euclid      121 184 219 259 272—275 279
Euclid's Elements      273
Euclidean distance      203 204 209
Euclidean geometry      183 184
Euclidean plane      204 208 247
Euclidean space      209
Euclidean triangle      204—206 210
Eudoxus      273
Euler's theorem      234 236 250
Euler, Leonhard      20 53 58 60 62 63 234 247 257
Evolute      186 187 191
Extended complex plane      252
Fake circle      11 14—16 see
Feller, William      141 144 153
Fermat's last theorem      25 61 65
Feynman, Richard      9 10 16
Fields medal      255
Flat torus      206—209 214
Four Vertex Theorem      187
Four-color theorem      17 18 25 114 267
Freshman sum      84
Freudenthal, Hans      3 6
Function, analytic      247 248 252—255
Function, complex      247 248 250 252 255
Function, entire      247 248 251—255
Function, linear      158—160
Function, meromorphic      251—257
Function, multiple-valued      250
Function, rational      251 252
Fundamental theorem of algebra      247 248 250 251
Galilei, Galileo      38
Gallian, Kristin      32
Gardner, Martin      136 144 153
Gauss' theorema egregium      250
Gauss, Carl Friedrich      55 56 246 247 250 257
Generator      166 212—214
Geodesic path      203—206 208—210
Geodesic space      203 205—209 212—214
Gladstone, William Ewart      274
Graham, Ronald L.      44
Graph      114—116
Graph, coloring      114 115
Graph, incomparability      114 115
Greeks, ancient      19 51 52
Gromov's lemma      211 214
Gromov, Mikhail L.      214
Group      67 69 105 116 122 123 128 131 202 203 211—215
Group presentation      212—214
Group, abelian      67 69 105 116
Group, finitely-generated      69
Group, fundamental      202 203 211—215
Group, homology      214 215
Group, symmetric      105
Group, symmetry      122 123 128 131 212
Haken, Wolfgang      17
Hall, Marshall      105 116
Halley, Edmund      245 257
Harmonia Mundi      126
Harrison, George      33
Hasse, Helmut      78
Heath, Thomas L.      219 231
Hexahedron (cube)      120 122 123 125 128
Homeomorphism      201 202 206 215
Homothety (simple scaling)      243
Homotopy      201 202 205 207 208 211 212 214
Huxley, Thomas      30
Hyperbola      166 168 174 181
icosahedron      117 120 122 123 128 131—133
Independent identically distributed sequence (HD)      141 142
Induction, mathematical      110 133 163
Infinite product      78
Infinite series      247
Invariant      201 202 214 219
inversion      180 182 183
Isometry      202 207 208
Isomorphic groups      211—214
Kepler, Johannes      126
Klein bottle      214
Klimek, Paul      99
Knuth, Donald      31 39 44
L-function      78
Lagrange, Joseph      247
Lambert's map      239 240 242 243 256
Lambert, Johann      234 257
Laplace, Pierre Simon      136 141
Law of Large Numbers      136
Legendre, Adrien Marie      273 274
Lennon, John      27 32 36
Liddell, Alice Pleasance      259 261 279
LINCOS      3 4 6
Line at infinity      168 176 177 181
Linear, approximation      244
Linear, equation      18 157 158 275 276
Linear, extension      114 115
Linear, function      158—160
Linear, map      241 244
Linear, order      115
Linear, recurrence      97 98
Linear, transformation      241 243 244 256
Link of a vertex      210 211 214
Magnusson, Bengt      99 103
Maple™      18
Markov chain      98 142
Mathemagician      83
Mathematica®      18—20
McAuliffe, Christa      7 9
McCartney, Paul      27
McNair, Ron      7 9
Menelaus' theorem      173—175 178 179 183
Mercator map (projection)      233 235 237—240 243—245 249 250
Mercator, Gerhardus      233 235 237 239 256
Mersenne Prime Search      20
Mersenne, Marin      19 20
Metric      207
Moebius inversion      111
Moebius strip      214 266
Monte Carlo simulation      149
Monty Hall problem      136
Mordell, Louis      65 69 71
National Aeronautics and Space Administration (NASA)      11 14—16
Needham, Tristan      250 257
Nevanlinna's theorem      253 255
Nevanlinna, Rolf      252 253 255—257
Newton's method      157 163 165
Newton, Sir Isaac      38
Non-Euclidean geometry      183 184
Number, complex      78 246—248 250 251
Number, congruent      73—75 77—79
Number, Eulerian      108 110 111
Number, harmonic      54—57 59 60
Number, irrational      41 42 44 46—48 97
Number, perfect      20 21
Number, prime      3—6 19—25 58 70 77 78
Number, rational      41 42 47 48 54 69 73—75
Number, triangular      52 54 55 59 60
Numbers, Fibonacci      83—85 89 90 92 97 98
Numbers, Gibonacci      92 96 97
Numbers, Lucas      89—92 96—98
O-ring      9 10
octahedron      120 122 123 126—128 132
One-to-one correspondence      87 88 94 101 107 111 112 see
Order relation      114
Pappus' theorem      173—175 182 183
parabola      160 166—168 181 185 219—221 227—231
Paraboloid      219 221 222 225 229—231
Partial order      114 115
Partially ordered set      99 113 see
Pascal's theorem      157 162 165 166 168 173 174 178 180—183
Pascal's triangle      106 110 111
Pascal, Blaise      166
Pasteur, Louis      38
Patashnik, Oren      44 116
Peirce, Benjamin      273
Permutation      99 101—116
Permutation, cyclic      103 111
Permutation, descent of      108—110 112 113 115 116
Picard's theorems      251—255
Picard, Emile      251 252 257
Picasso, Pablo      194 195
Pigeonhole Principle      41 42 44 47 48
Plimpton collection      54
Poincare disk      204 205
Point at infinity      65 66 168 176 251—253
Point, inflection      66 191
Point, integer      70 71
Point, rational      54 61—63 69 71 75—79
Poisson process      143
Pole      251 252
Polya, George      28 39 48
Polyhedron      16 117 120—124 132 133
Poncelet — Brianchon theorem      173 174 181—183
POSET      99 100 111 113—116 see
Power of point theorem      178
Power series      78 247 248 251
Price, Bartholomew      259 268 269 271 273—277 279
Prime      19—21 25
Prime factorization      19—23 25 58
Projection      152 166—168 181 197—199 207 208 235—240 242—245 249—253 256
Projection, covering      207 208
Projection, cylindrical      235—240 243 245 249
Projection, plate carree      239 240 242 256
Projection, stereographic      245 249—253 256
Projective 2—space      66
Projective geometry      66 168 175 176 181 183
Projective plane      168 176 181 265
Projective transformation      166 176 183
Pythagoras      51—54 63
Pythagorean cuboid      61 62
Pythagorean Theorem      53 73
Pythagorean triple      54 61 62
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