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LecturesonStochasticProgramming:ModelingandTheory(MPS-SIAMSeriesonOptimization)

LecturesonStochasticProgramming:ModelingandTheory(MPS-SIAMSeriesonOptimization)

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作者: Alexander Shapiro 著 , Darinka Dentcheva 著 , Andrzej Ruszczynski 著

出版社: SIAM-SocietyforIndustrialandAppliedMathematics

出版时间: 2009-09

ISBN: 9780898716870

定价: 874.10

装帧: 平装

页数: 452页

正文语种: 英语

分类: 外文古旧书>英文书>自然科学

Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. For the first time in a text, this book uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common phenomena and advancing to a precise specification of the nature of Categories of Sets. Set theory as the algebra of mappings is introduced and developed as a unifying basis for advanced mathematical subjects such as algebra, geometry, analysis, and combinatorics. The formal study evolves from general axioms which express universal properties of sums, products, mapping sets, and natural number recursion. The distinctive features of Cantorian abstract sets, as contrasted with the variable and cohesive sets of geometry and analysis, are made explicit and taken as special axioms. Functor categories are introduced in order to model the variable sets used in geometry, and to illustrate the failure of the axiom of choice. An appendix provides an explicit introduction to necessary concepts from logic, and an extensive glossary provides a window to the mathematical landscape. Alexander Shapiro is a Professor in the School of Industrial and Systems Engineering at Georgia Institute of Technology. He has published more than 100 articles in peer-reviewed journals and is the coauthor of several books. Darinka Dentcheva is a Professor of Mathematics at Stevens Institute of Technology. She works in the areas of decisions under uncertainty, convex analysis, and stability of optimization problems. Andrzej Ruszczynski is a Professor in the Department of Operations Research at Rutgers University. His research is devoted to the theory and methods of optimization under uncertainty and risk.
内容简介:
Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. For the first time in a text, this book uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common phenomena and advancing to a precise specification of the nature of Categories of Sets. Set theory as the algebra of mappings is introduced and developed as a unifying basis for advanced mathematical subjects such as algebra, geometry, analysis, and combinatorics. The formal study evolves from general axioms which express universal properties of sums, products, mapping sets, and natural number recursion. The distinctive features of Cantorian abstract sets, as contrasted with the variable and cohesive sets of geometry and analysis, are made explicit and taken as special axioms. Functor categories are introduced in order to model the variable sets used in geometry, and to illustrate the failure of the axiom of choice. An appendix provides an explicit introduction to necessary concepts from logic, and an extensive glossary provides a window to the mathematical landscape.
作者简介:
Alexander Shapiro is a Professor in the School of Industrial and Systems Engineering at Georgia Institute of Technology. He has published more than 100 articles in peer-reviewed journals and is the coauthor of several books. Darinka Dentcheva is a Professor of Mathematics at Stevens Institute of Technology. She works in the areas of decisions under uncertainty, convex analysis, and stability of optimization problems. Andrzej Ruszczynski is a Professor in the Department of Operations Research at Rutgers University. His research is devoted to the theory and methods of optimization under uncertainty and risk.

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