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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 ; Zuming Feng 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 ; Zuming Feng . - 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
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Título : Complex Analysis and Differential Equations Tipo de documento: documento electrónico Autores: Luis Barreira ; SpringerLink (Online service) ; Claudia Valls Editorial: London : Springer London Fecha de publicación: 2012 Colección: Springer Undergraduate Mathematics Series, ISSN 1615-2085 Número de páginas: VIII, 415 p. 37 illus Il.: online resource ISBN/ISSN/DL: 978-1-4471-4008-5 Idioma : Inglés (eng) Palabras clave: Mathematics Fourier analysis Functions of complex variables Differential equations Partial differential Sequences (Mathematics) Analysis a Complex Variable Ordinary Equations Sequences, Series, Summability Clasificación: 51 Matemáticas Resumen: This text provides an accessible, self-contained and rigorous introduction to complex analysis and differential equations. Topics covered include holomorphic functions, Fourier series, ordinary and partial differential equations. The text is divided into two parts: part one focuses on complex analysis and part two on differential equations. Each part can be read independently, so in essence this text offers two books in one. In the second part of the book, some emphasis is given to the application of complex analysis to differential equations. Half of the book consists of approximately 200 worked out problems, carefully prepared for each part of theory, plus 200 exercises of variable levels of difficulty. Tailored to any course giving the first introduction to complex analysis or differential equations, this text assumes only a basic knowledge of linear algebra and differential and integral calculus. Moreover, the large number of examples, worked out problems and exercises makes this the ideal book for independent study Nota de contenido: Part 1 Complex Analysis.- Basic Notions -- Holomorphic Functions -- Sequences and Series -- Analytic Functions -- Part 2 Differential Equations.- Ordinary Differential Equations -- Solving Differential Equations -- Fourier Series -- Partial Differential Equations En línea: http://dx.doi.org/10.1007/978-1-4471-4008-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32727 Complex Analysis and Differential Equations [documento electrónico] / Luis Barreira ; SpringerLink (Online service) ; Claudia Valls . - London : Springer London, 2012 . - VIII, 415 p. 37 illus : online resource. - (Springer Undergraduate Mathematics Series, ISSN 1615-2085) .
ISBN : 978-1-4471-4008-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Fourier analysis Functions of complex variables Differential equations Partial differential Sequences (Mathematics) Analysis a Complex Variable Ordinary Equations Sequences, Series, Summability Clasificación: 51 Matemáticas Resumen: This text provides an accessible, self-contained and rigorous introduction to complex analysis and differential equations. Topics covered include holomorphic functions, Fourier series, ordinary and partial differential equations. The text is divided into two parts: part one focuses on complex analysis and part two on differential equations. Each part can be read independently, so in essence this text offers two books in one. In the second part of the book, some emphasis is given to the application of complex analysis to differential equations. Half of the book consists of approximately 200 worked out problems, carefully prepared for each part of theory, plus 200 exercises of variable levels of difficulty. Tailored to any course giving the first introduction to complex analysis or differential equations, this text assumes only a basic knowledge of linear algebra and differential and integral calculus. Moreover, the large number of examples, worked out problems and exercises makes this the ideal book for independent study Nota de contenido: Part 1 Complex Analysis.- Basic Notions -- Holomorphic Functions -- Sequences and Series -- Analytic Functions -- Part 2 Differential Equations.- Ordinary Differential Equations -- Solving Differential Equations -- Fourier Series -- Partial Differential Equations En línea: http://dx.doi.org/10.1007/978-1-4471-4008-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32727 Ejemplares
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Título : A Course in Calculus and Real Analysis Tipo de documento: documento electrónico Autores: Sudhir R. Ghorpade ; SpringerLink (Online service) ; Balmohan V. Limaye Editorial: New York, NY : Springer New York Fecha de publicación: 2006 Colección: Undergraduate Texts in Mathematics, ISSN 0172-6056 Número de páginas: X, 432 p Il.: online resource ISBN/ISSN/DL: 978-0-387-36425-4 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Functions of real variables Sequences Real Sequences, Series, Summability Clasificación: 51 Matemáticas Resumen: This book provides a self-contained and rigorous introduction to calculus of functions of one variable. The presentation and sequencing of topics emphasizes the structural development of calculus. At the same time, due importance is given to computational techniques and applications. The authors have strived to make a distinction between the intrinsic definition of a geometric notion and its analytic characterization. Throughout the book, the authors highlight the fact that calculus provides a firm foundation to several concepts and results that are generally encountered in high school and accepted on faith. For example, one can find here a proof of the classical result that the ratio of the circumference of a circle to its diameter is the same for all circles. Also, this book helps students get a clear understanding of the concept of an angle and the definitions of the logarithmic, exponential and trigonometric functions together with a proof of the fact that these are not algebraic functions. A number of topics that may have been inadequately covered in calculus courses and glossed over in real analysis courses are treated here in considerable detail. As such, this book provides a unified exposition of calculus and real analysis. The only prerequisites for reading this book are topics that are normally covered in high school; however, the reader is expected to possess some mathematical maturity and an ability to understand and appreciate proofs. This book can be used as a textbook for a serious undergraduate course in calculus, while parts of the book can be used for advanced undergraduate and graduate courses in real analysis. Each chapter contains several examples and a large selection of exercises, as well as "Notes and Comments" describing salient features of the exposition, related developments and references to relevant literature Nota de contenido: Numbers and Functions -- Sequences -- Continuity and Limits -- Differentiation -- Applications of Differentiation -- Integration -- Elementary Transcendental Functions -- Applications and Approximations of Riemann Integrals -- Infinite Series and Improper Integrals En línea: http://dx.doi.org/10.1007/0-387-36425-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34830 A Course in Calculus and Real Analysis [documento electrónico] / Sudhir R. Ghorpade ; SpringerLink (Online service) ; Balmohan V. Limaye . - New York, NY : Springer New York, 2006 . - X, 432 p : online resource. - (Undergraduate Texts in Mathematics, ISSN 0172-6056) .
ISBN : 978-0-387-36425-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Functions of real variables Sequences Real Sequences, Series, Summability Clasificación: 51 Matemáticas Resumen: This book provides a self-contained and rigorous introduction to calculus of functions of one variable. The presentation and sequencing of topics emphasizes the structural development of calculus. At the same time, due importance is given to computational techniques and applications. The authors have strived to make a distinction between the intrinsic definition of a geometric notion and its analytic characterization. Throughout the book, the authors highlight the fact that calculus provides a firm foundation to several concepts and results that are generally encountered in high school and accepted on faith. For example, one can find here a proof of the classical result that the ratio of the circumference of a circle to its diameter is the same for all circles. Also, this book helps students get a clear understanding of the concept of an angle and the definitions of the logarithmic, exponential and trigonometric functions together with a proof of the fact that these are not algebraic functions. A number of topics that may have been inadequately covered in calculus courses and glossed over in real analysis courses are treated here in considerable detail. As such, this book provides a unified exposition of calculus and real analysis. The only prerequisites for reading this book are topics that are normally covered in high school; however, the reader is expected to possess some mathematical maturity and an ability to understand and appreciate proofs. This book can be used as a textbook for a serious undergraduate course in calculus, while parts of the book can be used for advanced undergraduate and graduate courses in real analysis. Each chapter contains several examples and a large selection of exercises, as well as "Notes and Comments" describing salient features of the exposition, related developments and references to relevant literature Nota de contenido: Numbers and Functions -- Sequences -- Continuity and Limits -- Differentiation -- Applications of Differentiation -- Integration -- Elementary Transcendental Functions -- Applications and Approximations of Riemann Integrals -- Infinite Series and Improper Integrals En línea: http://dx.doi.org/10.1007/0-387-36425-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34830 Ejemplares
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Título : Essays in Constructive Mathematics Tipo de documento: documento electrónico Autores: Harold M. Edwards ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2005 Número de páginas: XX, 211 p Il.: online resource ISBN/ISSN/DL: 978-0-387-27130-9 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Algebraic geometry Sequences (Mathematics) Mathematical logic Number theory Mathematics, general Geometry Sequences, Series, Summability Logic and Foundations Theory Clasificación: 51 Matemáticas Resumen: "... The exposition is not only clear, it is friendly, philosophical, and considerate even to the most naive or inexperienced reader. And it proves that the philosophical orientation of an author really can make a big difference. The mathematical content is intensely classical. ... Edwards makes it warmly accessible to any interested reader. And he is breaking fresh ground, in his rigorously constructive or constructivist presentation. So the book will interest anyone trying to learn these major, central topics in classical algebra and algebraic number theory. Also, anyone interested in constructivism, for or against. And even anyone who can be intrigued and drawn in by a masterly exposition of beautiful mathematics." Reuben Hersh This book aims to promote constructive mathematics, not by defining it or formalizing it, but by practicing it, by basing all definitions and proofs on finite algorithms. The topics covered derive from classic works of nineteenth century mathematics---among them Galois' theory of algebraic equations, Gauss's theory of binary quadratic forms and Abel's theorem about integrals of rational differentials on algebraic curves. It is not surprising that the first two topics can be treated constructively---although the constructive treatments shed a surprising amount of light on them---but the last topic, involving integrals and differentials as it does, might seem to call for infinite processes. In this case too, however, finite algorithms suffice to define the genus of an algebraic curve, to prove that birationally equivalent curves have the same genus, and to prove the Riemann-Roch theorem. The main algorithm in this case is Newton's polygon, which is given a full treatment. Other topics covered include the fundamental theorem of algebra, the factorization of polynomials over an algebraic number field, and the spectral theorem for symmetric matrices. Harold M. Edwards is Emeritus Professor of Mathematics at New York University. His previous books are Advanced Calculus (1969, 1980, 1993), Riemann's Zeta Function (1974, 2001), Fermat's Last Theorem (1977), Galois Theory (1984), Divisor Theory (1990) and Linear Algebra (1995). Readers of his Advanced Calculus will know that his preference for constructive mathematics is not new Nota de contenido: A Fundamental Theorem -- Topics in Algebra -- Some Quadratic Problems -- The Genus of an Algebraic Curve -- Miscellany En línea: http://dx.doi.org/10.1007/b138656 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35109 Essays in Constructive Mathematics [documento electrónico] / Harold M. Edwards ; SpringerLink (Online service) . - New York, NY : Springer New York, 2005 . - XX, 211 p : online resource.
ISBN : 978-0-387-27130-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Algebraic geometry Sequences (Mathematics) Mathematical logic Number theory Mathematics, general Geometry Sequences, Series, Summability Logic and Foundations Theory Clasificación: 51 Matemáticas Resumen: "... The exposition is not only clear, it is friendly, philosophical, and considerate even to the most naive or inexperienced reader. And it proves that the philosophical orientation of an author really can make a big difference. The mathematical content is intensely classical. ... Edwards makes it warmly accessible to any interested reader. And he is breaking fresh ground, in his rigorously constructive or constructivist presentation. So the book will interest anyone trying to learn these major, central topics in classical algebra and algebraic number theory. Also, anyone interested in constructivism, for or against. And even anyone who can be intrigued and drawn in by a masterly exposition of beautiful mathematics." Reuben Hersh This book aims to promote constructive mathematics, not by defining it or formalizing it, but by practicing it, by basing all definitions and proofs on finite algorithms. The topics covered derive from classic works of nineteenth century mathematics---among them Galois' theory of algebraic equations, Gauss's theory of binary quadratic forms and Abel's theorem about integrals of rational differentials on algebraic curves. It is not surprising that the first two topics can be treated constructively---although the constructive treatments shed a surprising amount of light on them---but the last topic, involving integrals and differentials as it does, might seem to call for infinite processes. In this case too, however, finite algorithms suffice to define the genus of an algebraic curve, to prove that birationally equivalent curves have the same genus, and to prove the Riemann-Roch theorem. The main algorithm in this case is Newton's polygon, which is given a full treatment. Other topics covered include the fundamental theorem of algebra, the factorization of polynomials over an algebraic number field, and the spectral theorem for symmetric matrices. Harold M. Edwards is Emeritus Professor of Mathematics at New York University. His previous books are Advanced Calculus (1969, 1980, 1993), Riemann's Zeta Function (1974, 2001), Fermat's Last Theorem (1977), Galois Theory (1984), Divisor Theory (1990) and Linear Algebra (1995). Readers of his Advanced Calculus will know that his preference for constructive mathematics is not new Nota de contenido: A Fundamental Theorem -- Topics in Algebra -- Some Quadratic Problems -- The Genus of an Algebraic Curve -- Miscellany En línea: http://dx.doi.org/10.1007/b138656 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35109 Ejemplares
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Título : From Calculus to Analysis Tipo de documento: documento electrónico Autores: Schinazi, Rinaldo B ; SpringerLink (Online service) Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2012 Otro editor: Imprint: Birkhäuser Número de páginas: X, 250 p. 7 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-8289-7 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Approximation theory Measure Sequences Sequences, Series, Summability Approximations and Expansions Integration Clasificación: 51 Matemáticas Resumen: This comprehensive textbook is intended for a two-semester sequence in analysis. The first four chapters present a practical introduction to analysis by using the tools and concepts of calculus. The last five chapters present a first course in analysis. The presentation is clear and concise, allowing students to master the calculus tools that are crucial in understanding analysis. Key features: * Contains numerous exercises; * Provides unique examples, such as many ways to estimate the number Pi; * Introduces the basic principles of analysis; * Offers a straightforward introduction to the calculus basics such as number systems, sequences, and series; * Carefully written book with a thoughtful perspective for students. From Calculus to Analysis prepares readers for their first analysis course—important because many undergraduate programs traditionally require such a course. Undergraduates and some advanced high-school seniors will find this text a useful and pleasant experience in the classroom or as a self-study guide. The only prerequisite is a standard calculus course Nota de contenido: Preface -- Ch. 1 Number Systems -- 1.1 The algebra of the reals -- 1.2 Natural numbers and integers -- .1.3 Rational numbers and real numbers -- 1.4 Power functions -- Ch. 2 Sequences and Series -- 2.1 Sequences -- 2.2 Montone sequences, Bolzano-Weirestrass theorem and operations on limits -- 2.3 Series -- 2.4 Absolute convergence -- Ch. 3 Power series and special functions.-3.1 Power series.-3.2 Tigonometric functions -- 3.3 Inverse trigonometric functions -- 3.4 Exponential and logarithmic functions -- Ch 4 Fifty Ways to Estimate the Number pi.-4.1 Power series expansions -- 4.2 Wallis' integrals, Euler's formula, and Stirling's formula.-4.3 Convergence of infinite products -- 4.4 The number pi is irrational -- Ch. 5 Continuity, Limits, and Differentiation -- 5.1 Continuity -- 5.2 Limits of functions and derivatives -- 5.3 Algebra of derivatives and mean value theorems -- 5.4 Intervals, continuity, and inverse functions -- Ch. 6 Riemann Integration -- 6.1 Construction of the integral -- 6.2 Properties of the integral -- 6.3 Uniform continuity -- Ch 7 Decimal Represenation of Numbers -- Ch 8 Countable and Uncountable Sets -- Further Readings -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-8289-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32685 From Calculus to Analysis [documento electrónico] / Schinazi, Rinaldo B ; SpringerLink (Online service) . - Boston : Birkhäuser Boston : Imprint: Birkhäuser, 2012 . - X, 250 p. 7 illus : online resource.
ISBN : 978-0-8176-8289-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Approximation theory Measure Sequences Sequences, Series, Summability Approximations and Expansions Integration Clasificación: 51 Matemáticas Resumen: This comprehensive textbook is intended for a two-semester sequence in analysis. The first four chapters present a practical introduction to analysis by using the tools and concepts of calculus. The last five chapters present a first course in analysis. The presentation is clear and concise, allowing students to master the calculus tools that are crucial in understanding analysis. Key features: * Contains numerous exercises; * Provides unique examples, such as many ways to estimate the number Pi; * Introduces the basic principles of analysis; * Offers a straightforward introduction to the calculus basics such as number systems, sequences, and series; * Carefully written book with a thoughtful perspective for students. From Calculus to Analysis prepares readers for their first analysis course—important because many undergraduate programs traditionally require such a course. Undergraduates and some advanced high-school seniors will find this text a useful and pleasant experience in the classroom or as a self-study guide. The only prerequisite is a standard calculus course Nota de contenido: Preface -- Ch. 1 Number Systems -- 1.1 The algebra of the reals -- 1.2 Natural numbers and integers -- .1.3 Rational numbers and real numbers -- 1.4 Power functions -- Ch. 2 Sequences and Series -- 2.1 Sequences -- 2.2 Montone sequences, Bolzano-Weirestrass theorem and operations on limits -- 2.3 Series -- 2.4 Absolute convergence -- Ch. 3 Power series and special functions.-3.1 Power series.-3.2 Tigonometric functions -- 3.3 Inverse trigonometric functions -- 3.4 Exponential and logarithmic functions -- Ch 4 Fifty Ways to Estimate the Number pi.-4.1 Power series expansions -- 4.2 Wallis' integrals, Euler's formula, and Stirling's formula.-4.3 Convergence of infinite products -- 4.4 The number pi is irrational -- Ch. 5 Continuity, Limits, and Differentiation -- 5.1 Continuity -- 5.2 Limits of functions and derivatives -- 5.3 Algebra of derivatives and mean value theorems -- 5.4 Intervals, continuity, and inverse functions -- Ch. 6 Riemann Integration -- 6.1 Construction of the integral -- 6.2 Properties of the integral -- 6.3 Uniform continuity -- Ch 7 Decimal Represenation of Numbers -- Ch 8 Countable and Uncountable Sets -- Further Readings -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-8289-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32685 Ejemplares
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