By Ivars Peterson
"Peterson's wisdom of and affection for arithmetic comes via with each word."--San Diego Union Tribune."Peterson is, briefly, the maths instructor every person needs that they had in excessive school."--Publishers Weekly."Peterson has honed his explanatory abilities finely. he's a readable advisor during the tangles of chance and random likelihood. The Jungles of Randomness will supply a few perception into the most fruitful parts the place math meets sensible living."--Christian technology Monitor.The pleasant trek throughout the unique and robust international of randomness.Popular math writer Ivars Peterson leads readers on an exhilarating foray into the wilds of randomness, introducing interesting new discoveries--from hidden principles governing video games of probability to how the 1st molecules of lifestyles shaped and the way random numbers can guard delicate info on the net. alongside the best way, he charts the ambiguous boundary among order and chaos, revealing the dazzling styles so frequently hidden in obvious randomness in addition to the startling randomness usually embedded in obvious order.Ivars Peterson (Washington, D.C.) is the maths and physics editor at technological know-how information and the writer of 4 prior exchange books, together with The Mathematical vacationer and Islands of fact: A Mathematical secret Cruise.
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25); and three tosses have eight (2x2x2) possible outcomes. In general, the number of possible outcomes can be found by multiplying together as many 2s as there are tosses. One can readily investigate the likelihood that certain patterns will appear in large numbers of consecutive tosses. For example, if a coin is tossed, say, 250 times, what's the longest run of consecutive heads that's likely to arise? A simple argument gives us a rough estimate. Except on the first toss, a run of heads can begin only after a toss showing tails.
So, if there are more pigeons than holes, some of the pigeons have to double up. Expressed mathematically, the so-called pigeonhole principle is a handy idea for proving theorems, and it often comes up in Ramsey theory to demonstrate the inevitability of the presence of certain patterns. Perhaps the simplest possible application of the pigeonhole principle concerns groups of men and women. If there are three people present in a gathering, at least two must be men or at least two must be women. The same principle can be applied to any allocation of a given type of object, whether it is balls dropped into boxes, people slotted into certain categories, or numbers meeting particular criteria.
Often, we use the word random loosely to describe something that is disordered, irregular, patternless, or unpredictable. We link it with chance, probability, luck, and coincidence. However, when we examine what we mean by random in various contexts, ambiguities and uncertainties inevitably arise. Tackling the subtleties of randomness allows us to go to the root of what we can understand of the universe we inhabit and helps us to define the limits of what we can know with certainty. We think of flipping a coin as a way of making a blind choice, yet in the hands of a skilled magician the outcome may be perfectly predictable.