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51(075.3) Matemáticas-Libros de texto para la enseñanza secundariaDocumentos en la biblioteca con la clasificación 51 (3221)
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Título : 103 Trigonometry Problems : From the Training of the USA IMO Team Tipo de documento: documento electrónico Autores: Titu Andreescu ; SpringerLink (Online service) ; Feng, Zuming Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2005 Número de páginas: XII, 214 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4432-1 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Geometry Mathematics, general Clasificación: 51 Matemáticas Resumen: 103 Trigonometry Problems contains highly-selected problems and solutions used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Though many problems may initially appear impenetrable to the novice, most can be solved using only elementary high school mathematics techniques. Key features: * Gradual progression in problem difficulty builds and strengthens mathematical skills and techniques * Basic topics include trigonometric formulas and identities, their applications in the geometry of the triangle, trigonometric equations and inequalities, and substitutions involving trigonometric functions * Problem-solving tactics and strategies, along with practical test-taking techniques, provide in-depth enrichment and preparation for possible participation in various mathematical competitions * Comprehensive introduction (first chapter) to trigonometric functions, their relations and functional properties, and their applications in the Euclidean plane and solid geometry expose advanced students to college level material 103 Trigonometry Problems is a cogent problem-solving resource for advanced high school students, undergraduates, and mathematics teachers engaged in competition training. Other books by the authors include 102 Combinatorial Problems: From the Training of the USA IMO Team (0-8176-4317-6, 2003) and A Path to Combinatorics for Undergraduates: Counting Strategies (0-8176-4288-9, 2004) Nota de contenido: Trigonometric Fundamentals -- Introductory Problems -- Advanced Problems -- Solutions to Introductory Problems -- Solutions to Advanced Problems En línea: http://dx.doi.org/10.1007/b139082 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35188 103 Trigonometry Problems : From the Training of the USA IMO Team [documento electrónico] / Titu Andreescu ; SpringerLink (Online service) ; Feng, Zuming . - Boston, MA : Birkhäuser Boston, 2005 . - XII, 214 p : online resource.
ISBN : 978-0-8176-4432-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Geometry Mathematics, general Clasificación: 51 Matemáticas Resumen: 103 Trigonometry Problems contains highly-selected problems and solutions used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Though many problems may initially appear impenetrable to the novice, most can be solved using only elementary high school mathematics techniques. Key features: * Gradual progression in problem difficulty builds and strengthens mathematical skills and techniques * Basic topics include trigonometric formulas and identities, their applications in the geometry of the triangle, trigonometric equations and inequalities, and substitutions involving trigonometric functions * Problem-solving tactics and strategies, along with practical test-taking techniques, provide in-depth enrichment and preparation for possible participation in various mathematical competitions * Comprehensive introduction (first chapter) to trigonometric functions, their relations and functional properties, and their applications in the Euclidean plane and solid geometry expose advanced students to college level material 103 Trigonometry Problems is a cogent problem-solving resource for advanced high school students, undergraduates, and mathematics teachers engaged in competition training. Other books by the authors include 102 Combinatorial Problems: From the Training of the USA IMO Team (0-8176-4317-6, 2003) and A Path to Combinatorics for Undergraduates: Counting Strategies (0-8176-4288-9, 2004) Nota de contenido: Trigonometric Fundamentals -- Introductory Problems -- Advanced Problems -- Solutions to Introductory Problems -- Solutions to Advanced Problems En línea: http://dx.doi.org/10.1007/b139082 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35188 Ejemplares
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Título : 104 Number Theory Problems : From the Training of the USA IMO Team Tipo de documento: documento electrónico Autores: Titu Andreescu ; SpringerLink (Online service) ; Dorin Andrica ; Feng, Zuming Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2007 Número de páginas: XII, 204 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4561-8 Idioma : Inglés (eng) Palabras clave: Mathematics Sequences (Mathematics) Mathematical logic Number theory Theory Sequences, Series, Summability Logic and Foundations Clasificación: 51 Matemáticas Resumen: This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas, conjectures, and conclusions in writing. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory. Key features: * Contains problems developed for various mathematical contests, including the International Mathematical Olympiad (IMO) * Builds a bridge between ordinary high school examples and exercises in number theory and more sophisticated, intricate and abstract concepts and problems * Begins by familiarizing students with typical examples that illustrate central themes, followed by numerous carefully selected problems and extensive discussions of their solutions * Combines unconventional and essay-type examples, exercises and problems, many presented in an original fashion * Engages students in creative thinking and stimulates them to express their comprehension and mastery of the material beyond the classroom 104 Number Theory Problems is a valuable resource for advanced high school students, undergraduates, instructors, and mathematics coaches preparing to participate in mathematical contests and those contemplating future research in number theory and its related areas Nota de contenido: Foundations of Number Theory -- Introductory Problems -- Advanced Problems -- Solutions to Introductory Problems -- Solutions to Advanced Problems En línea: http://dx.doi.org/10.1007/978-0-8176-4561-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34554 104 Number Theory Problems : From the Training of the USA IMO Team [documento electrónico] / Titu Andreescu ; SpringerLink (Online service) ; Dorin Andrica ; Feng, Zuming . - Boston, MA : Birkhäuser Boston, 2007 . - XII, 204 p : online resource.
ISBN : 978-0-8176-4561-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Sequences (Mathematics) Mathematical logic Number theory Theory Sequences, Series, Summability Logic and Foundations Clasificación: 51 Matemáticas Resumen: This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas, conjectures, and conclusions in writing. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory. Key features: * Contains problems developed for various mathematical contests, including the International Mathematical Olympiad (IMO) * Builds a bridge between ordinary high school examples and exercises in number theory and more sophisticated, intricate and abstract concepts and problems * Begins by familiarizing students with typical examples that illustrate central themes, followed by numerous carefully selected problems and extensive discussions of their solutions * Combines unconventional and essay-type examples, exercises and problems, many presented in an original fashion * Engages students in creative thinking and stimulates them to express their comprehension and mastery of the material beyond the classroom 104 Number Theory Problems is a valuable resource for advanced high school students, undergraduates, instructors, and mathematics coaches preparing to participate in mathematical contests and those contemplating future research in number theory and its related areas Nota de contenido: Foundations of Number Theory -- Introductory Problems -- Advanced Problems -- Solutions to Introductory Problems -- Solutions to Advanced Problems En línea: http://dx.doi.org/10.1007/978-0-8176-4561-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34554 Ejemplares
Signatura Medio Ubicación Sección Estado ningún ejemplar 18 Unconventional Essays on the Nature of Mathematics / SpringerLink (Online service) ; Hersh, Reuben (2006)
Título : 18 Unconventional Essays on the Nature of Mathematics Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Hersh, Reuben Editorial: New York, NY : Springer New York Fecha de publicación: 2006 Número de páginas: XXII, 326 p. 10 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-29831-3 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical logic Mathematics, general Logic and Foundations Clasificación: 51 Matemáticas Resumen: Advance praise for 18 Unconventional Essays on the Nature of Mathematics: "I was pleasantly surprised to find that this book does not treat mathematics as dessicated formal logic but as a living organism, immediately recognizable to any working mathematician." - Sir Michael Atiyah, University of Edinburgh "A wonderful collection of essays on the philosophy of mathematics, some by mathematicians, others by philosophers, and all having significant things to say. Most readers will be informed, some will be infuriated, but all will be stimulated." - John H. Conway, John von Neumann Distinguished Professor of Mathematics, Princeton University This startling new collection of essays edited by Reuben Hersh contains frank facts and opinions from leading mathematicians, philosophers, sociologists, cognitive scientists, and even an anthropologist. Each essay provides a challenging and thought-provoking look at recent advances in the philosophy of mathematics, demonstrating the possibilities of thinking fresh, sticking close to actual practice, and fearlessly letting go of standard shibboleths. The following essays are included: * Alfred Renyi: Socratic Dialogue * Carlo Cellucci: Filosofia e Matematica, introduction * William Thurston: On Proof and Progress in Mathematics * Andrew Aberdein: The Informal Logic of Mathematical Proof * Yehuda Rav: Philosophical Problems of Mathematics in Light of Evolutionary Epistemology * Brian Rotman: Towards a Semiotics of Mathematics * Donald Mackenzie: Computers and the Sociology of Mathematical Proof * Terry Stanway: From G.H.H. and Littlewood to XML and Maple: Changing Needs and Expectations in Mathematical Knowledge Management * Rafael Nunez: Do Numbers Really Move? * Timothy Gowers: Does Mathematics Need a Philosophy? * Jody Azzouni: How and Why Mathematics is a Social Practice * Gian-Carlo Rota: The Pernicious Influence of Mathematics Upon Philosophy * Jack Schwartz: The Pernicious Influence of Mathematics on Science * Alfonso Avila del Palacio: What is Philosophy of Mathematics Looking For? * Andrew Pickering: Concepts and the Mangle of Practice: Constructing Quaternions * Eduard Glas: Mathematics as Objective Knowledge and as Human Practice * Leslie White: The Locus of Mathematical Reality: An Anthropological Footnote * Reuben Hersh: Inner Vision, Outer Truth Nota de contenido: A Socratic Dialogue on Mathematics -- “Introduction” to Filosofia e matematica -- On Proof and Progress in Mathematics -- The Informal Logic of Mathematical Proof -- Philosophical Problems of Mathematics in the Light of Evolutionary Epistemology -- Towards a Semiotics of Mathematics -- Computers and the Sociology of Mathematical Proof -- From G.H.H. and Littlewood to XML and Maple: Changing Needs and Expectations in Mathematical Knowledge Management -- Do Real Numbers Really Move? Language, Thought, and Gesture: The Embodied Cognitive Foundations of Mathematics -- Does Mathematics Need a Philosophy? -- How and Why Mathematics Is Unique as a Social Practice -- The Pernicious Influence of Mathematics upon Philosophy -- The Pernicious Influence of Mathematics on Science -- What Is Philosophy of Mathematics Looking for? -- Concepts and the Mangle of Practice Constructing Quaternions -- Mathematics as Objective Knowledge and as Human Practice -- The Locus of Mathematical Reality: An Anthropological Footnote -- Inner Vision, Outer Truth En línea: http://dx.doi.org/10.1007/0-387-29831-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34764 18 Unconventional Essays on the Nature of Mathematics [documento electrónico] / SpringerLink (Online service) ; Hersh, Reuben . - New York, NY : Springer New York, 2006 . - XXII, 326 p. 10 illus : online resource.
ISBN : 978-0-387-29831-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical logic Mathematics, general Logic and Foundations Clasificación: 51 Matemáticas Resumen: Advance praise for 18 Unconventional Essays on the Nature of Mathematics: "I was pleasantly surprised to find that this book does not treat mathematics as dessicated formal logic but as a living organism, immediately recognizable to any working mathematician." - Sir Michael Atiyah, University of Edinburgh "A wonderful collection of essays on the philosophy of mathematics, some by mathematicians, others by philosophers, and all having significant things to say. Most readers will be informed, some will be infuriated, but all will be stimulated." - John H. Conway, John von Neumann Distinguished Professor of Mathematics, Princeton University This startling new collection of essays edited by Reuben Hersh contains frank facts and opinions from leading mathematicians, philosophers, sociologists, cognitive scientists, and even an anthropologist. Each essay provides a challenging and thought-provoking look at recent advances in the philosophy of mathematics, demonstrating the possibilities of thinking fresh, sticking close to actual practice, and fearlessly letting go of standard shibboleths. The following essays are included: * Alfred Renyi: Socratic Dialogue * Carlo Cellucci: Filosofia e Matematica, introduction * William Thurston: On Proof and Progress in Mathematics * Andrew Aberdein: The Informal Logic of Mathematical Proof * Yehuda Rav: Philosophical Problems of Mathematics in Light of Evolutionary Epistemology * Brian Rotman: Towards a Semiotics of Mathematics * Donald Mackenzie: Computers and the Sociology of Mathematical Proof * Terry Stanway: From G.H.H. and Littlewood to XML and Maple: Changing Needs and Expectations in Mathematical Knowledge Management * Rafael Nunez: Do Numbers Really Move? * Timothy Gowers: Does Mathematics Need a Philosophy? * Jody Azzouni: How and Why Mathematics is a Social Practice * Gian-Carlo Rota: The Pernicious Influence of Mathematics Upon Philosophy * Jack Schwartz: The Pernicious Influence of Mathematics on Science * Alfonso Avila del Palacio: What is Philosophy of Mathematics Looking For? * Andrew Pickering: Concepts and the Mangle of Practice: Constructing Quaternions * Eduard Glas: Mathematics as Objective Knowledge and as Human Practice * Leslie White: The Locus of Mathematical Reality: An Anthropological Footnote * Reuben Hersh: Inner Vision, Outer Truth Nota de contenido: A Socratic Dialogue on Mathematics -- “Introduction” to Filosofia e matematica -- On Proof and Progress in Mathematics -- The Informal Logic of Mathematical Proof -- Philosophical Problems of Mathematics in the Light of Evolutionary Epistemology -- Towards a Semiotics of Mathematics -- Computers and the Sociology of Mathematical Proof -- From G.H.H. and Littlewood to XML and Maple: Changing Needs and Expectations in Mathematical Knowledge Management -- Do Real Numbers Really Move? Language, Thought, and Gesture: The Embodied Cognitive Foundations of Mathematics -- Does Mathematics Need a Philosophy? -- How and Why Mathematics Is Unique as a Social Practice -- The Pernicious Influence of Mathematics upon Philosophy -- The Pernicious Influence of Mathematics on Science -- What Is Philosophy of Mathematics Looking for? -- Concepts and the Mangle of Practice Constructing Quaternions -- Mathematics as Objective Knowledge and as Human Practice -- The Locus of Mathematical Reality: An Anthropological Footnote -- Inner Vision, Outer Truth En línea: http://dx.doi.org/10.1007/0-387-29831-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34764 Ejemplares
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Título : 40 Puzzles and Problems in Probability and Mathematical Statistics Tipo de documento: documento electrónico Autores: Schwarz, Wolfgang ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2008 Colección: Problem Books in Mathematics, ISSN 0941-3502 Número de páginas: XII, 124 p. 29 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-73512-2 Idioma : Inglés (eng) Palabras clave: Mathematics Probabilities Probability Theory and Stochastic Processes Clasificación: 51 Matemáticas Resumen: "40 Puzzles and Problems in Probability and Mathematical Statistics" is intended to teach the reader to think probabilistically by solving challenging, non-standard probability problems. The motivation for this clearly written collection lies in the belief that challenging problems help to develop, and to sharpen, our probabilistic intuition much better than plain-style deductions from abstract concepts. The selected problems fall into two broad categories. Problems related to probability theory come first, followed by problems related to the application of probability to the field of mathematical statistics. All problems seek to convey a non-standard aspect or an approach which is not immediately obvious. The word puzzles in the title refers to questions in which some qualitative, non-technical insight is most important. Ideally, puzzles can teach a productive new way of framing or representing a given situation. Although the border between the two is not always clearly defined, problems tend to require a more systematic application of formal tools, and to stress more technical aspects. Thus, a major aim of the present collection is to bridge the gap between introductory texts and rigorous state-of-the-art books. Anyone with a basic knowledge of probability, calculus and statistics will benefit from this book; however, many of the problems collected require little more than elementary probability and straight logical reasoning. To assist anyone using this book for self-study, the author has included very detailed step-for-step solutions of all problems and also short hints which point the reader in the appropriate direction Nota de contenido: Preface -- Notation and Terminology -- Problems -- Hints -- Solutions -- References -- Index En línea: http://dx.doi.org/10.1007/978-0-387-73512-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34181 40 Puzzles and Problems in Probability and Mathematical Statistics [documento electrónico] / Schwarz, Wolfgang ; SpringerLink (Online service) . - New York, NY : Springer New York, 2008 . - XII, 124 p. 29 illus : online resource. - (Problem Books in Mathematics, ISSN 0941-3502) .
ISBN : 978-0-387-73512-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Probabilities Probability Theory and Stochastic Processes Clasificación: 51 Matemáticas Resumen: "40 Puzzles and Problems in Probability and Mathematical Statistics" is intended to teach the reader to think probabilistically by solving challenging, non-standard probability problems. The motivation for this clearly written collection lies in the belief that challenging problems help to develop, and to sharpen, our probabilistic intuition much better than plain-style deductions from abstract concepts. The selected problems fall into two broad categories. Problems related to probability theory come first, followed by problems related to the application of probability to the field of mathematical statistics. All problems seek to convey a non-standard aspect or an approach which is not immediately obvious. The word puzzles in the title refers to questions in which some qualitative, non-technical insight is most important. Ideally, puzzles can teach a productive new way of framing or representing a given situation. Although the border between the two is not always clearly defined, problems tend to require a more systematic application of formal tools, and to stress more technical aspects. Thus, a major aim of the present collection is to bridge the gap between introductory texts and rigorous state-of-the-art books. Anyone with a basic knowledge of probability, calculus and statistics will benefit from this book; however, many of the problems collected require little more than elementary probability and straight logical reasoning. To assist anyone using this book for self-study, the author has included very detailed step-for-step solutions of all problems and also short hints which point the reader in the appropriate direction Nota de contenido: Preface -- Notation and Terminology -- Problems -- Hints -- Solutions -- References -- Index En línea: http://dx.doi.org/10.1007/978-0-387-73512-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34181 Ejemplares
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Título : 50 Years of Integer Programming 1958-2008 : From the Early Years to the State-of-the-Art Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Jünger, Michael ; Liebling, Thomas M ; Naddef, Denis ; Nemhauser, George L ; Pulleyblank, William R ; Reinelt, Gerhard ; Rinaldi, Giovanni ; Wolsey, Laurence A Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2010 Número de páginas: XX, 804 p. 151 illus., 52 illus. in color Il.: online resource ISBN/ISSN/DL: 978-3-540-68279-0 Idioma : Inglés (eng) Palabras clave: Mathematics Operations research Decision making Computer science Mathematical optimization Combinatorics Optimization Discrete in Science Operation Research/Decision Theory Clasificación: 51 Matemáticas Resumen: In 1958, Ralph E. Gomory transformed the field of integer programming when he published a short paper that described his cutting-plane algorithm for pure integer programs and announced that the method could be refined to give a finite algorithm for integer programming. In January of 2008, to commemorate the anniversary of Gomory's seminal paper, a special session celebrating fifty years of integer programming was held in Aussois, France, as part of the 12th Combinatorial Optimization Workshop. This book is based on the material presented during this session. 50 Years of Integer Programming offers an account of featured talks at the 2008 Aussois workshop, namely - Michele Conforti, Gérard Cornuéjols, and Giacomo Zambelli: Polyhedral Approaches to Mixed Integer Linear Programming - William Cook: 50+ Years of Combinatorial Integer Programming - Francois Vanderbeck and Laurence A. Wolsey: Reformulation and Decomposition of Integer Programs The book contains reprints of key historical articles together with new introductions and historical perspectives by the authors: Egon Balas, Michel Balinski, Jack Edmonds, Ralph E. Gomory, Arthur M. Geoffrion, Alan J. Hoffman & Joseph B. Kruskal, Richard M. Karp, Harold W. Kuhn, and Ailsa H. Land & Alison G. Doig. It also contains written versions of survey lectures on six of the hottest topics in the field by distinguished members of the integer programming community: - Friedrich Eisenbrand: Integer Programming and Algorithmic Geometry of Numbers - Raymond Hemmecke, Matthias Köppe, Jon Lee, and Robert Weismantel: Nonlinear Integer Programming - Andrea Lodi: Mixed Integer Programming Computation - Francois Margot: Symmetry in Integer Linear Programming - Franz Rendl: Semidefinite Relaxations for Integer Programming - Jean-Philippe P. Richard and Santanu S. Dey: The Group-Theoretic Approach to Mixed Integer Programming Integer programming holds great promise for the future, and continues to build on its foundations. Indeed, Gomory's finite cutting-plane method for the pure integer case is currently being reexamined and is showing new promise as a practical computational method. This book is a uniquely useful celebration of the past, present and future of this important and active field. Ideal for students and researchers in mathematics, computer science and operations research, it exposes mathematical optimization, in particular integer programming and combinatorial optimization, to a broad audience Nota de contenido: I The Early Years -- Solution of a Large-Scale Traveling-Salesman Problem -- The Hungarian Method for the Assignment Problem -- Integral Boundary Points of Convex Polyhedra -- Outline of an Algorithm for Integer Solutions to Linear Programs An Algorithm for the Mixed Integer Problem -- An Automatic Method for Solving Discrete Programming Problems -- Integer Programming: Methods, Uses, Computation -- Matroid Partition -- Reducibility Among Combinatorial Problems -- Lagrangian Relaxation for Integer Programming -- Disjunctive Programming -- II From the Beginnings to the State-of-the-Art -- Polyhedral Approaches to Mixed Integer Linear Programming -- Fifty-Plus Years of Combinatorial Integer Programming -- Reformulation and Decomposition of Integer Programs -- III Current Topics -- Integer Programming and Algorithmic Geometry of Numbers -- Nonlinear Integer Programming -- Mixed Integer Programming Computation -- Symmetry in Integer Linear Programming -- Semidefinite Relaxations for Integer Programming -- The Group-Theoretic Approach in Mixed Integer Programming En línea: http://dx.doi.org/10.1007/978-3-540-68279-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33695 50 Years of Integer Programming 1958-2008 : From the Early Years to the State-of-the-Art [documento electrónico] / SpringerLink (Online service) ; Jünger, Michael ; Liebling, Thomas M ; Naddef, Denis ; Nemhauser, George L ; Pulleyblank, William R ; Reinelt, Gerhard ; Rinaldi, Giovanni ; Wolsey, Laurence A . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2010 . - XX, 804 p. 151 illus., 52 illus. in color : online resource.
ISBN : 978-3-540-68279-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Operations research Decision making Computer science Mathematical optimization Combinatorics Optimization Discrete in Science Operation Research/Decision Theory Clasificación: 51 Matemáticas Resumen: In 1958, Ralph E. Gomory transformed the field of integer programming when he published a short paper that described his cutting-plane algorithm for pure integer programs and announced that the method could be refined to give a finite algorithm for integer programming. In January of 2008, to commemorate the anniversary of Gomory's seminal paper, a special session celebrating fifty years of integer programming was held in Aussois, France, as part of the 12th Combinatorial Optimization Workshop. This book is based on the material presented during this session. 50 Years of Integer Programming offers an account of featured talks at the 2008 Aussois workshop, namely - Michele Conforti, Gérard Cornuéjols, and Giacomo Zambelli: Polyhedral Approaches to Mixed Integer Linear Programming - William Cook: 50+ Years of Combinatorial Integer Programming - Francois Vanderbeck and Laurence A. Wolsey: Reformulation and Decomposition of Integer Programs The book contains reprints of key historical articles together with new introductions and historical perspectives by the authors: Egon Balas, Michel Balinski, Jack Edmonds, Ralph E. Gomory, Arthur M. Geoffrion, Alan J. Hoffman & Joseph B. Kruskal, Richard M. Karp, Harold W. Kuhn, and Ailsa H. Land & Alison G. Doig. It also contains written versions of survey lectures on six of the hottest topics in the field by distinguished members of the integer programming community: - Friedrich Eisenbrand: Integer Programming and Algorithmic Geometry of Numbers - Raymond Hemmecke, Matthias Köppe, Jon Lee, and Robert Weismantel: Nonlinear Integer Programming - Andrea Lodi: Mixed Integer Programming Computation - Francois Margot: Symmetry in Integer Linear Programming - Franz Rendl: Semidefinite Relaxations for Integer Programming - Jean-Philippe P. Richard and Santanu S. Dey: The Group-Theoretic Approach to Mixed Integer Programming Integer programming holds great promise for the future, and continues to build on its foundations. Indeed, Gomory's finite cutting-plane method for the pure integer case is currently being reexamined and is showing new promise as a practical computational method. This book is a uniquely useful celebration of the past, present and future of this important and active field. Ideal for students and researchers in mathematics, computer science and operations research, it exposes mathematical optimization, in particular integer programming and combinatorial optimization, to a broad audience Nota de contenido: I The Early Years -- Solution of a Large-Scale Traveling-Salesman Problem -- The Hungarian Method for the Assignment Problem -- Integral Boundary Points of Convex Polyhedra -- Outline of an Algorithm for Integer Solutions to Linear Programs An Algorithm for the Mixed Integer Problem -- An Automatic Method for Solving Discrete Programming Problems -- Integer Programming: Methods, Uses, Computation -- Matroid Partition -- Reducibility Among Combinatorial Problems -- Lagrangian Relaxation for Integer Programming -- Disjunctive Programming -- II From the Beginnings to the State-of-the-Art -- Polyhedral Approaches to Mixed Integer Linear Programming -- Fifty-Plus Years of Combinatorial Integer Programming -- Reformulation and Decomposition of Integer Programs -- III Current Topics -- Integer Programming and Algorithmic Geometry of Numbers -- Nonlinear Integer Programming -- Mixed Integer Programming Computation -- Symmetry in Integer Linear Programming -- Semidefinite Relaxations for Integer Programming -- The Group-Theoretic Approach in Mixed Integer Programming En línea: http://dx.doi.org/10.1007/978-3-540-68279-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33695 Ejemplares
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