Five-minute Mathematics

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American Mathematical Soc., Jan 1, 2008 - Mathematics - 380 pages
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This collection of one hundred short essays gives readers a grand tour through contemporary and everyday mathematics. Behrends provides classics from his newspaper column in Die Welt, expands and illustrates them, and gives readers just enough information at a time to build mastery of concepts and applications. The topics range from pure mathematics to applied math, but all essays are suspenseful and fun to read. This is a very handy tool for teachers of all levels of mathematics (even elementary school children will be able to handle some of the topics), and Behrends assumes his readership has and interest but only a minimal background in mathematics so the essays are accessible but not dumbed-down.
 

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Contents

You Cant Beat the Odds
1
Magical Mathematics The Integers
5
How Old Is the Captain?
8
Vertiginously Large Prime Numbers
11
Loss Plus Loss Equals Win
14
When It Comes to Large Numbers Intuition Fails
17
The Key for Encryption Is in the Telephone Book
22
The Village Barber Who Shaves Himself
27
The Book of Nature Is Written in the Language of Mathematics
202
The Search for Mersenne Primes
206
Berlin Eighteenth Century A Beautiful Formula Is Discovered
210
The First Really Complicated Number
213
P NP In Mathematics Is Luck Sometimes Unnecessary?
216
Happy 32nd Birthday
219
Buffons Needle
222
Running Hot and Cold Controlled Cooling Solves Optimization Problems
226

Quit While Youre Ahead?
31
Can a Monkey Create Great Literature?
34
The Birthday Paradox
37
Horror Vacui
42
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
A OneMillionDollar Prize 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
Magical Mathematics 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
Zero An Undeservedly Underrated Number
109
I Love to Count
112
Genius Autodidact The Indian Mathematician Ramanujan
118
I Hate Mathematics Because
121
The Traveling Salesman A Modern Odyssey
124
Squaring the Circle
127
A Step into the Infinite
134
Mathematics in Your CD Player
139
The Logarithm A Dying Breed
142
Prizeworthy Mathematics
145
Why Axioms of All Things?
148
Proof by Computer?
151
The Lottery 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
Who Didnt Pay?
230
What Can Statistics Tell Us?
233
Arbitrage
236
Farewell to Risk 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
Chance as Reckoner 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
The Lazy Eight 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
Index
377
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