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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

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.

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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
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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