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In the world of math, the theorem that informs how to understand the shape of the universe has defied every effort to prove it. Now, after more than a century, an eccentric Russian recluse has found the solution to one of the seven greatest math problems of the modern era.

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This work looks at polyominoes, invented by Solomon Golomb, which have contributed to the study of combinatorial geometry and tiling theory. This work takes readers on a mathematical journey through the world of the polyomino.

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This book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real numbers do in classical analysis. They have theoretical and computational uses across a broad spectrum of disciplines, including calculus, electrical enginee

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This book develops arithmetic without the induction principle, working in theories that are interpretable in Raphael Robinson's theory Q. Certain inductive formulas, the bounded ones, are interpretable in Q. A mathematically strong, but logically very weak, predicative arithmetic is constructed. Originally published in 1986. The Princeton Legacy

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Using Game Theory (a theory based on the rationale that everyone acts in their own self-interest) he can foretell and even engineer events.

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Seeks to describe the development in recent decades of sieve methods able to detect prime numbers. This work covers topics such as; primes in short intervals, the greatest prime factor of the sequence of shifted primes, Goldbach numbers in short intervals, the distribution of Gaussian primes, and the recent work of John Friedlander, and Iwaniec.

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Offers a modern and authoritative treatment of the mathematical processes that underlie performance modeling. This book looks at the fundamentals of probability theory, from the basic concepts of set-based probability, through probability distributions, to bounds, limit theorems, and the laws of large numbers.

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The description for this book, Probleme General de la Stabilite du Mouvement. (AM-17), will be forthcoming.

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The present volume reflects both the diversity of Bochner's pursuits in pure mathematics and the influence his example and thought have had upon contemporary researchers. Originally published in 1971. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguishe

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This volume contains thirty-three selected general research papers devoted to the theory and application of the mathematics of constrained optimization, including linear programming and its extensions to convex programming, general nonlinear programming, integer programming, and programming under uncertainty. Originally published in 1971. The Pri

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Through a set of lively anecdotes and essays, Nathaniel Borenstein traces the divergence between the fields of software engineering and user-centered software design, and attempts to reconcile the needs of people in both camps. Originally published in 1991. The Princeton Legacy Library uses the latest print-on-demand technology to again make avai

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Five papers by distinguished American and European mathematicians describe some current trends in mathematics in the perspective of the recent past and in terms of expectations for the future. Among the subjects discussed are algebraic groups, quadratic forms, topological aspects of global analysis, variants of the index theorem, and partial differential equations.

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This collection brings together papers by mathematicians exploring the research frontiers of topology. The book covers a wide range of topological specialities.

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Based on their relationship to exceptional algebraic groups, quadrangular algebras belong in a series together with alternative and Jordan division algebras, this book introduces a class of non-associative algebras related to exceptional algebraic groups and their associated buildings.

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Book 22 in the Princeton Mathematical Series. Originally published in 1960. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presentin