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### Colección Problem Books in Mathematics

- Editorial : Springer New York
- ISSN : 0941-3502

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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 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: http://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=341 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

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: http://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=341 ## Ejemplares

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Título : A Cp-Theory Problem Book : Topological and Function Spaces Tipo de documento: documento electrónico Autores: Tkachuk, Vladimir V ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Colección: Problem Books in Mathematics, ISSN 0941-3502 Número de páginas: XVI, 488 p Il.: online resource ISBN/ISSN/DL: 978-1-4419-7442-6 Idioma : Inglés Palabras clave: Mathematics Topology Algebraic topology Manifolds (Mathematics) Complex manifolds and Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: The theory of function spaces endowed with the topology of pointwise convergence, or Cp-theory, exists at the intersection of three important areas of mathematics: topological algebra, functional analysis, and general topology. Cp-theory has an important role in the classification and unification of heterogeneous results from each of these areas of research. Through over 500 carefully selected problems and exercises, this volume provides a self-contained introduction to Cp-theory and general topology. By systematically introducing each of the major topics in Cp-theory, this volume is designed to bring a dedicated reader from basic topological principles to the frontiers of modern research. Key features include: - A unique problem-based introduction to the theory of function spaces. - Detailed solutions to each of the presented problems and exercises. - A comprehensive bibliography reflecting the state-of-the-art in modern Cp-theory. - Numerous open problems and directions for further research. This volume can be used as a textbook for courses in both Cp-theory and general topology as well as a reference guide for specialists studying Cp-theory and related topics. This book also provides numerous topics for PhD specialization as well as a large variety of material suitable for graduate research Nota de contenido: Preface -- Introduction -- 1.1. Basic notions of topology and function spaces Bibliographic notes -- 1.2. Solutions of problems 1.001–1.500 -- 1.3. Bonus results: some hidden statements -- 1.4. Open problems -- 1.5. Bibliography -- 1.6. List of special symbols -- 1.7. Index En línea: http://dx.doi.org/10.1007/978-1-4419-7442-6 Link: http://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=331 A Cp-Theory Problem Book : Topological and Function Spaces [documento electrónico] / Tkachuk, Vladimir V ; SpringerLink (Online service) . - New York, NY : Springer New York, 2011 . - XVI, 488 p : online resource. - (Problem Books in Mathematics, ISSN 0941-3502) .ISBN: 978-1-4419-7442-6

Idioma : Inglés

Palabras clave: Mathematics Topology Algebraic topology Manifolds (Mathematics) Complex manifolds and Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: The theory of function spaces endowed with the topology of pointwise convergence, or Cp-theory, exists at the intersection of three important areas of mathematics: topological algebra, functional analysis, and general topology. Cp-theory has an important role in the classification and unification of heterogeneous results from each of these areas of research. Through over 500 carefully selected problems and exercises, this volume provides a self-contained introduction to Cp-theory and general topology. By systematically introducing each of the major topics in Cp-theory, this volume is designed to bring a dedicated reader from basic topological principles to the frontiers of modern research. Key features include: - A unique problem-based introduction to the theory of function spaces. - Detailed solutions to each of the presented problems and exercises. - A comprehensive bibliography reflecting the state-of-the-art in modern Cp-theory. - Numerous open problems and directions for further research. This volume can be used as a textbook for courses in both Cp-theory and general topology as well as a reference guide for specialists studying Cp-theory and related topics. This book also provides numerous topics for PhD specialization as well as a large variety of material suitable for graduate research Nota de contenido: Preface -- Introduction -- 1.1. Basic notions of topology and function spaces Bibliographic notes -- 1.2. Solutions of problems 1.001–1.500 -- 1.3. Bonus results: some hidden statements -- 1.4. Open problems -- 1.5. Bibliography -- 1.6. List of special symbols -- 1.7. Index En línea: http://dx.doi.org/10.1007/978-1-4419-7442-6 Link: http://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=331 ## Ejemplares

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Título : Exercises in Modules and Rings Tipo de documento: documento electrónico Autores: Lam, T. Y ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2007 Colección: Problem Books in Mathematics, ISSN 0941-3502 Número de páginas: XVIII, 414 p Il.: online resource ISBN/ISSN/DL: 978-0-387-48899-8 Idioma : Inglés Palabras clave: Mathematics Algebra Associative rings Rings (Algebra) and Algebras Clasificación: 51 Matemáticas Resumen: For the Backcover This Problem Book offers a compendium of 639 exercises of varying degrees of difficulty in the subject of modules and rings at the graduate level. The material covered includes projective, injective, and flat modules, homological and uniform dimensions, noncommutative localizations and Goldie’s theorems, maximal rings of quotients, Frobenius and quasi-Frobenius rings, as well as Morita’s classical theory of category dualities and equivalences. Each of the nineteen sections begins with an introduction giving the general background and the theoretical basis for the problems that follow. All exercises are solved in full detail; many are accompanied by pertinent historical and bibliographical information, or a commentary on possible improvements, generalizations, and latent connections to other problems. This volume is designed as a problem book for the author’s Lectures on Modules and Rings (Springer GTM, Vol. 189), from which the majority of the exercises were taken. Some forty new exercises have been added to further broaden the coverage. As a result, this book is ideal both as a companion volume to Lectures, and as a source for independent study. For students and researchers alike, this book will also serve as a handy reference for a copious amount of information in algebra and ring theory otherwise unavailable from textbooks. An outgrowth of the author’s lecture courses and seminars over the years at the University of California at Berkeley, this book and its predecessor Exercises in Classical Ring Theory (Springer, 2003) offer to the mathematics community the fullest and most comprehensive reference to date for problem solving in the theory of modules and rings Nota de contenido: Free Modules, Projective, and Injective Modules -- Flat Modules and Homological Dimensions -- More Theory of Modules -- Rings of Quotients -- More Rings of Quotients -- Frobenius and Quasi-Frobenius Rings -- Matrix Rings, Categories of Modules and Morita Theory En línea: http://dx.doi.org/10.1007/978-0-387-48899-8 Link: http://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=344 Exercises in Modules and Rings [documento electrónico] / Lam, T. Y ; SpringerLink (Online service) . - New York, NY : Springer New York, 2007 . - XVIII, 414 p : online resource. - (Problem Books in Mathematics, ISSN 0941-3502) .ISBN: 978-0-387-48899-8

Idioma : Inglés

Palabras clave: Mathematics Algebra Associative rings Rings (Algebra) and Algebras Clasificación: 51 Matemáticas Resumen: For the Backcover This Problem Book offers a compendium of 639 exercises of varying degrees of difficulty in the subject of modules and rings at the graduate level. The material covered includes projective, injective, and flat modules, homological and uniform dimensions, noncommutative localizations and Goldie’s theorems, maximal rings of quotients, Frobenius and quasi-Frobenius rings, as well as Morita’s classical theory of category dualities and equivalences. Each of the nineteen sections begins with an introduction giving the general background and the theoretical basis for the problems that follow. All exercises are solved in full detail; many are accompanied by pertinent historical and bibliographical information, or a commentary on possible improvements, generalizations, and latent connections to other problems. This volume is designed as a problem book for the author’s Lectures on Modules and Rings (Springer GTM, Vol. 189), from which the majority of the exercises were taken. Some forty new exercises have been added to further broaden the coverage. As a result, this book is ideal both as a companion volume to Lectures, and as a source for independent study. For students and researchers alike, this book will also serve as a handy reference for a copious amount of information in algebra and ring theory otherwise unavailable from textbooks. An outgrowth of the author’s lecture courses and seminars over the years at the University of California at Berkeley, this book and its predecessor Exercises in Classical Ring Theory (Springer, 2003) offer to the mathematics community the fullest and most comprehensive reference to date for problem solving in the theory of modules and rings Nota de contenido: Free Modules, Projective, and Injective Modules -- Flat Modules and Homological Dimensions -- More Theory of Modules -- Rings of Quotients -- More Rings of Quotients -- Frobenius and Quasi-Frobenius Rings -- Matrix Rings, Categories of Modules and Morita Theory En línea: http://dx.doi.org/10.1007/978-0-387-48899-8 Link: http://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=344 ## Ejemplares

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Título : Functional Equations and How to Solve Them Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Small, Christopher G Editorial: New York, NY : Springer New York Fecha de publicación: 2007 Colección: Problem Books in Mathematics, ISSN 0941-3502 Número de páginas: XII, 131 p Il.: online resource ISBN/ISSN/DL: 978-0-387-48901-8 Idioma : Inglés Palabras clave: Mathematics Difference equations Functional Numerical analysis and Equations Analysis Clasificación: 51 Matemáticas Resumen: This book covers topics in the theory and practice of functional equations. Special emphasis is given to methods for solving functional equations that appear in mathematics contests, such as the Putnam competition and the International Mathematical Olympiad. This book will be of particular interest to university students studying for the Putnam competition, and to high school students working to improve their skills on mathematics competitions at the national and international level. Mathematics educators who train students for these competitions will find a wealth of material for training on functional equations problems. The book also provides a number of brief biographical sketches of some of the mathematicians who pioneered the theory of functional equations. The work of Oresme, Cauchy, Babbage, and others, is explained within the context of the mathematical problems of interest at the time. Christopher Small is a Professor in the Department of Statistics and Actuarial Science at the University of Waterloo. He has served as the co-coach on the Canadian team at the IMO (1997, 1998, 2000, 2001, and 2004), as well as the Waterloo Putnam team for the William Lowell Putnam Competition (1986-2004). His previous books include Numerical Methods for Nonlinear Estimating Equations (Oxford 2003), The Statistical Theory of Shape (Springer 1996), Hilbert Space Methods in Probability and Statistical Inference (Wiley 1994). From the reviews: Functional Equations and How to Solve Them fills a need and is a valuable contribution to the literature of problem solving. - Henry Ricardo, MAA Reviews The main purpose and merits of the book...are the many solved, unsolved, partially solved problems and hints about several particular functional equations. - Janos Aczel, Zentralblatt Nota de contenido: An historical introduction -- Functional equations with two variables -- Functional equations with one variable -- Miscellaneous methods for functional equations -- Some closing heuristics -- Appendix: Hamel bases -- Hints and partial solutions to problems En línea: http://dx.doi.org/10.1007/978-0-387-48901-8 Link: http://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=344 Functional Equations and How to Solve Them [documento electrónico] / SpringerLink (Online service) ; Small, Christopher G . - New York, NY : Springer New York, 2007 . - XII, 131 p : online resource. - (Problem Books in Mathematics, ISSN 0941-3502) .ISBN: 978-0-387-48901-8

Idioma : Inglés

Palabras clave: Mathematics Difference equations Functional Numerical analysis and Equations Analysis Clasificación: 51 Matemáticas Resumen: This book covers topics in the theory and practice of functional equations. Special emphasis is given to methods for solving functional equations that appear in mathematics contests, such as the Putnam competition and the International Mathematical Olympiad. This book will be of particular interest to university students studying for the Putnam competition, and to high school students working to improve their skills on mathematics competitions at the national and international level. Mathematics educators who train students for these competitions will find a wealth of material for training on functional equations problems. The book also provides a number of brief biographical sketches of some of the mathematicians who pioneered the theory of functional equations. The work of Oresme, Cauchy, Babbage, and others, is explained within the context of the mathematical problems of interest at the time. Christopher Small is a Professor in the Department of Statistics and Actuarial Science at the University of Waterloo. He has served as the co-coach on the Canadian team at the IMO (1997, 1998, 2000, 2001, and 2004), as well as the Waterloo Putnam team for the William Lowell Putnam Competition (1986-2004). His previous books include Numerical Methods for Nonlinear Estimating Equations (Oxford 2003), The Statistical Theory of Shape (Springer 1996), Hilbert Space Methods in Probability and Statistical Inference (Wiley 1994). From the reviews: Functional Equations and How to Solve Them fills a need and is a valuable contribution to the literature of problem solving. - Henry Ricardo, MAA Reviews The main purpose and merits of the book...are the many solved, unsolved, partially solved problems and hints about several particular functional equations. - Janos Aczel, Zentralblatt Nota de contenido: An historical introduction -- Functional equations with two variables -- Functional equations with one variable -- Miscellaneous methods for functional equations -- Some closing heuristics -- Appendix: Hamel bases -- Hints and partial solutions to problems En línea: http://dx.doi.org/10.1007/978-0-387-48901-8 Link: http://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=344 ## Ejemplares

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Título : Limits, Series, and Fractional Part Integrals : Problems in Mathematical Analysis Tipo de documento: documento electrónico Autores: Furdui, Ovidiu ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Problem Books in Mathematics, ISSN 0941-3502 Número de páginas: XVIII, 274 p Il.: online resource ISBN/ISSN/DL: 978-1-4614-6762-5 Idioma : Inglés Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Sequences Special functions Sequences, Series, Summability Functions Clasificación: 51 Matemáticas Resumen: Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis features original problems in classical analysis that invite the reader to explore a host of strategies and mathematical tools used for solving real analysis problems. The book is designed to fascinate the novice, puzzle the expert, and trigger the imaginations of all. The text is geared toward graduate students in mathematics and engineering, researchers, and anyone who works on topics at the frontier of pure and applied mathematics. Moreover, it is the first book in mathematical literature concerning the calculation of fractional part integrals and series of various types. Most problems are neither easy nor standard and deal with modern topics of classical analysis. Each chapter has a section of open problems that may be considered as research projects for students who are taking advanced calculus classes. The intention of having these problems collected in the book is to stimulate the creativity and the discovery of new and original methods for proving known results and establishing new ones. The book is divided into three parts, each of them containing a chapter dealing with a particular type of problems. The first chapter contains problems on limits of special sequences and Riemann integrals; the second chapter deals with the calculation of special classes of integrals involving a fractional part term; and the third chapter hosts a collection of problems on the calculation of series (single or multiple) involving either a numerical or a functional term. Nota de contenido: Preface -- Notations -- 1. Limits -- 2. Fractional Part Integrals -- 3. A Bouquet of Series -- A. Elements of Classical Analysis -- B. Stolz–Cesàro Lemma -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-6762-5 Link: http://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=323 Limits, Series, and Fractional Part Integrals : Problems in Mathematical Analysis [documento electrónico] / Furdui, Ovidiu ; SpringerLink (Online service) . - New York, NY : Springer New York : [S.l.] : Imprint: Springer, 2013 . - XVIII, 274 p : online resource. - (Problem Books in Mathematics, ISSN 0941-3502) .ISBN: 978-1-4614-6762-5

Idioma : Inglés

Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Sequences Special functions Sequences, Series, Summability Functions Clasificación: 51 Matemáticas Resumen: Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis features original problems in classical analysis that invite the reader to explore a host of strategies and mathematical tools used for solving real analysis problems. The book is designed to fascinate the novice, puzzle the expert, and trigger the imaginations of all. The text is geared toward graduate students in mathematics and engineering, researchers, and anyone who works on topics at the frontier of pure and applied mathematics. Moreover, it is the first book in mathematical literature concerning the calculation of fractional part integrals and series of various types. Most problems are neither easy nor standard and deal with modern topics of classical analysis. Each chapter has a section of open problems that may be considered as research projects for students who are taking advanced calculus classes. The intention of having these problems collected in the book is to stimulate the creativity and the discovery of new and original methods for proving known results and establishing new ones. The book is divided into three parts, each of them containing a chapter dealing with a particular type of problems. The first chapter contains problems on limits of special sequences and Riemann integrals; the second chapter deals with the calculation of special classes of integrals involving a fractional part term; and the third chapter hosts a collection of problems on the calculation of series (single or multiple) involving either a numerical or a functional term. Nota de contenido: Preface -- Notations -- 1. Limits -- 2. Fractional Part Integrals -- 3. A Bouquet of Series -- A. Elements of Classical Analysis -- B. Stolz–Cesàro Lemma -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-6762-5 Link: http://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=323 ## Ejemplares

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