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Books > Science & Mathematics > Mathematics > Combinatorics & graph theory
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Inevitable Randomness in Discrete Mathematics (Paperback, New ed.)
Loot Price: R1,342
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Inevitable Randomness in Discrete Mathematics (Paperback, New ed.)
Series: University Lecture Series
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Mathematics has been called the science of order. The subject is
remarkably good for generalizing specific cases to create abstract
theories. However, mathematics has little to say when faced with
highly complex systems, where disorder reigns. This disorder can be
found in pure mathematical arenas, such as the distribution of
primes, the 3n 1 conjecture, and class field theory. The purpose of
this book is to provide examples - and rigorous proofs - of the
complexity law: discrete systems are either simple or they exhibit
advanced pseudorandomness; a priori probabilities often exist even
when there is no intrinsic symmetry. Part of the difficulty in
achieving this purpose is in trying to clarify these vague
statements. The examples turn out to be fascinating instances of
deep or mysterious results in number theory and combinatorics. This
book considers randomness and complexity. The traditional approach
to complexity - computational complexity theory - is to study very
general complexity classes, such as P, NP and PSPACE. What Beck
does is very different: he studies interesting concrete systems,
which can give new insights into the mystery of complexity. The
book is divided into three parts. Part A is mostly an essay on the
big picture. Part B is partly new results and partly a survey of
real game theory. Part C contains new results about graph games,
supporting the main conjecture. To make it accessible to a wide
audience, the book is mostly self-contained.
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