Five-Minute MathematicsAmerican Mathematical Soc., 2008 - 380 páginas How much math can you cover in five minutes? Quite a bit, if you have a good guide. In this collection of one hundred short essays, Ehrhard Behrends offers a tour through contemporary and everyday mathematics. The topics range from pure mathematics to applications of mathematics to observations about the mathematics that surrounds us in daily life. Here, we read about the parable of grains of rice on a chessboard, the mathematics of the lottery, music and mathematics, intriguingparadoxes, the concept of infinity, the Poincare conjecture, quantum computers, and plenty more. |
Índice
The Integers | 5 |
Vertiginously Large Prime Numbers | 11 |
When It Comes to Large Numbers Intuition | 17 |
The Village Barber Who Shaves Himself | 27 |
Quit While Youre Ahead? | 31 |
Can a Monkey Create Great Literature? | 34 |
The Birthday Paradox | 37 |
Horror Vacui | 42 |
A Beautiful Formula Is Discovered | 210 |
The First Really Complicated Number | 213 |
In Mathematics Is Luck Sometimes Unnecessary? | 216 |
Happy 32nd Birthday | 219 |
Buffons Needle | 222 |
Controlled Cooling Solves Optimization Problems | 226 |
Who Didnt Pay? | 230 |
What Can Statistics Tell Us? | 233 |
Sufficient Difficulties with the Logic of Mathematics Are in Fact a Necessity | 45 |
To Change or Not to Change? The Monty Hall Problem | 48 |
In Hilberts Hotel There Is Always a Vacancy | 58 |
That Fascinating Number Pi | 61 |
How Random Events Become Calculable Quantities | 64 |
How Are the Prime Numbers Distributed? | 68 |
The FiveDimensional Cake | 72 |
One Night Stand | 76 |
Fly Me to the Moon | 80 |
Using Residues | 83 |
Top Secret | 86 |
Order amidst Chaos | 92 |
How Does One Approach Genius? | 96 |
On Semitones and Twelfth Roots | 101 |
Why Am I Always Standing in the Wrong Line? | 105 |
An Undeservedly Underrated Number | 109 |
I Love to Count | 112 |
The Indian Mathematician Ramanujan | 118 |
I Hate Mathematics Because | 121 |
A Modern Odyssey | 124 |
Squaring the Circle | 127 |
A Step into the Infinite | 134 |
Mathematics in Your CD Player | 139 |
A Dying Breed | 142 |
Prizeworthy Mathematics | 145 |
Why Axioms of All Things? | 148 |
Proof by Computer? | 151 |
The Small Prizes | 155 |
Formulas Concentrated Thought | 158 |
Endless Growth | 161 |
How Do Quanta Compute? | 165 |
Extremes | 169 |
Infinitely Small? | 172 |
Mathematical Observations at the Fire Department | 176 |
The First Mathematical Proof Is 2500 Years Old | 179 |
There Is Transcendence in Mathematics Though It Has Nothing to Do with Mysticism | 183 |
Is Every Even Number the Sum of Two Primes? | 188 |
Why We Invert Conditional Probabilities Incorrectly | 192 |
Millionaire or Billionaire? | 196 |
Mathematics and Chess | 199 |
The Book of Nature Is Written in the Language of Mathematics | 202 |
The Search for Mersenne Primes | 206 |
Arbitrage | 236 |
Options | 239 |
Is Mathematics a Reflection of the World? | 242 |
Mathematics That You Can Hear | 246 |
Chance as Composer | 251 |
Do Dice Have a Guilty Conscience? | 255 |
Strawberry Ice Cream Can Kill You | 258 |
Prosperity for All | 261 |
No Risk Thank You | 264 |
A Nobel Prize in Mathematics? | 268 |
Monte Carlo Methods | 272 |
Fuzzy Logic | 276 |
Secret Messages in the Bible? | 279 |
How Knotted Can a Knot Be? | 283 |
How Much Mathematics Does a Person Need? | 287 |
Big Bigger Biggest | 290 |
It Is Probably Correct | 293 |
Is the World a Crooked Place? | 296 |
Is There a Mathematical Bureau of Standards? | 299 |
The Butterfly That Fluttered By | 303 |
Guaranteed to Make You Rich | 307 |
Dont Trust Anyone over Thirty | 310 |
Equality in Mathematics | 312 |
Magical Invariants | 314 |
Mathematics Goes to the Movies | 318 |
Infinity | 320 |
Books Need Bigger Margins | 323 |
Visualizing Internal Organs with Mathematics | 327 |
A Brain in the Computer | 330 |
Cogito Ergo Sum | 335 |
Does the World Have a Hole? | 339 |
Complex Numbers Are Not So Complex as Their Name Suggests | 342 |
M C Escher and Infinity | 347 |
A One at the Beginning Is Much More Likely Than a Two | 351 |
The Leipzig Town Hall and the Sunflower | 354 |
Information Optimally Packaged | 360 |
Four Colors Suffice | 364 |
Mathematics Makes Billionaires | 369 |
Further Reading | 373 |
| 377 | |
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Palavras e frases frequentes
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