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Título : Advanced Calculus : A Geometric View Tipo de documento: documento electrónico Autores: Callahan, James J ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2010 Colección: Undergraduate Texts in Mathematics, ISSN 0172-6056 Número de páginas: XVI, 526 p Il.: online resource ISBN/ISSN/DL: 978-1-4419-7332-0 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Approximation theory Functions of real variables Applied mathematics Engineering Real Applications Approximations and Expansions Clasificación: 51 Matemáticas Resumen: With a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus. Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse's lemma and the Poincaré lemma. The ideas behind most topics can be understood with just two or three variables. This invites geometric visualization; the book incorporates modern computational tools to give visualization real power. Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps, such as the role of the derivative as the local linear approximation to a map and its role in the change of variables formula for multiple integrals. The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books. Advanced Calculus: A Geometric View is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics. Prerequisites are an introduction to linear algebra and multivariable calculus. There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry. It avoids duplicating the material of real analysis. The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study Nota de contenido: Starting Points -- Geometry of Linear Maps -- Approximations -- The Derivative -- Inverses -- Implicit Functions -- Critical Points -- Double Integrals -- Evaluating Double Integrals -- Surface Integrals -- Stokes’ Theorem En línea: http://dx.doi.org/10.1007/978-1-4419-7332-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33645 Advanced Calculus : A Geometric View [documento electrónico] / Callahan, James J ; SpringerLink (Online service) . - New York, NY : Springer New York, 2010 . - XVI, 526 p : online resource. - (Undergraduate Texts in Mathematics, ISSN 0172-6056) .
ISBN : 978-1-4419-7332-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Approximation theory Functions of real variables Applied mathematics Engineering Real Applications Approximations and Expansions Clasificación: 51 Matemáticas Resumen: With a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus. Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse's lemma and the Poincaré lemma. The ideas behind most topics can be understood with just two or three variables. This invites geometric visualization; the book incorporates modern computational tools to give visualization real power. Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps, such as the role of the derivative as the local linear approximation to a map and its role in the change of variables formula for multiple integrals. The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books. Advanced Calculus: A Geometric View is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics. Prerequisites are an introduction to linear algebra and multivariable calculus. There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry. It avoids duplicating the material of real analysis. The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study Nota de contenido: Starting Points -- Geometry of Linear Maps -- Approximations -- The Derivative -- Inverses -- Implicit Functions -- Critical Points -- Double Integrals -- Evaluating Double Integrals -- Surface Integrals -- Stokes’ Theorem En línea: http://dx.doi.org/10.1007/978-1-4419-7332-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33645 Ejemplares
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Título : Algebraic Combinatorics : Walks, Trees, Tableaux, and More Tipo de documento: documento electrónico Autores: Stanley, Richard P ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Undergraduate Texts in Mathematics, ISSN 0172-6056 Número de páginas: XII, 223 p Il.: online resource ISBN/ISSN/DL: 978-1-4614-6998-8 Idioma : Inglés (eng) Palabras clave: Mathematics Combinatorics Graph theory Theory Clasificación: 51 Matemáticas Resumen: Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and rudiments of group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix–Tree Theorem, de Bruijn sequences, the Erdos-Moser conjecture, electrical networks, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Pólya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhäuser Nota de contenido: Preface -- Notation.- 1. Walks in graphs -- 2. Cubes and the Radon transform -- 3. Random walks -- 4. The Sperner property -- 5. Group actions on boolean algebras -- 6. Young diagrams and q-binomial coefficients -- 7. Enumeration under group action -- 8. A glimpse of Young tableaux -- Appendix. The RSK algorithm -- Appendix. Plane partitions -- 9. The Matrix–Tree Theorem -- Appendix. Three elegant combinatorial proofs -- 10. Eulerian diagraphs and oriented trees -- 11. Cycles, bonds, and electrical networks -- 12. Miscellaneous gems of algebraic combinatorics -- Hints -- References En línea: http://dx.doi.org/10.1007/978-1-4614-6998-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32332 Algebraic Combinatorics : Walks, Trees, Tableaux, and More [documento electrónico] / Stanley, Richard P ; SpringerLink (Online service) . - New York, NY : Springer New York : Imprint: Springer, 2013 . - XII, 223 p : online resource. - (Undergraduate Texts in Mathematics, ISSN 0172-6056) .
ISBN : 978-1-4614-6998-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Combinatorics Graph theory Theory Clasificación: 51 Matemáticas Resumen: Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and rudiments of group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix–Tree Theorem, de Bruijn sequences, the Erdos-Moser conjecture, electrical networks, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Pólya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhäuser Nota de contenido: Preface -- Notation.- 1. Walks in graphs -- 2. Cubes and the Radon transform -- 3. Random walks -- 4. The Sperner property -- 5. Group actions on boolean algebras -- 6. Young diagrams and q-binomial coefficients -- 7. Enumeration under group action -- 8. A glimpse of Young tableaux -- Appendix. The RSK algorithm -- Appendix. Plane partitions -- 9. The Matrix–Tree Theorem -- Appendix. Three elegant combinatorial proofs -- 10. Eulerian diagraphs and oriented trees -- 11. Cycles, bonds, and electrical networks -- 12. Miscellaneous gems of algebraic combinatorics -- Hints -- References En línea: http://dx.doi.org/10.1007/978-1-4614-6998-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32332 Ejemplares
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Título : An Introduction to Difference Equations Tipo de documento: documento electrónico Autores: Elaydi, Saber ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2005 Colección: Undergraduate Texts in Mathematics, ISSN 0172-6056 Número de páginas: XXII, 540 p Il.: online resource ISBN/ISSN/DL: 978-0-387-27602-1 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Difference equations Functional and Equations Clasificación: 51 Matemáticas Resumen: The book integrates both classical and modern treatments of difference equations. It contains the most updated and comprehensive material, yet the presentation is simple enough for the book to be used by advanced undergraduate and beginning graduate students. This third edition includes more proofs, more graphs, and more applications. The author has also updated the contents by adding a new chapter on Higher Order Scalar Difference Equations, along with recent results on local and global stability of one-dimensional maps, a new section on the various notions of asymptoticity of solutions, a detailed proof of Levin-May Theorem, and the latest results on the LPA flour-beetle model. Saber Elaydi is Professor of Mathematics at Trinity University. He is also the author of Discrete Chaos (1999), and the Editor-In-Chief of the Journal of Difference Equations and Applications. About the Second Edition: The book is a valuable reference for anyone who models discrete systems. Dynamicists have the long-awaited discrete counterpart to standard textbooks such as Hirsch and Smale ('Differential Equations, Dynamical Systems, and Linear Algebra'). It is so well written and well designed, and the contents are so interesting to me, that I had a difficult time putting it down. - Shandelle Henson, Journal of Difference Equations and Applications Among the few introductory texts to difference equations this book is one of the very best ones. It has many features that the other texts don't have, e.g., stability theory, the Z-transform method (including a study of Volterra systems), and asymptotic behavior of solutions of difference equations (including Levinson's lemma) are studied extensively. It also contains very nice examples that primarily arise in applications in a variety of disciplines, including neural networks, feedback control, biology, Markov chains, economics, and heat transfer... -Martin Bohner, University of Missouri, Rolla Nota de contenido: Dynamics of First-Order Difference Equations -- Linear Difference Equations of Higher Order -- Systems of Linear Difference Equations -- Stability Theory -- Higher-Order Scalar Difference Equations -- The Z-Transform Method and Volterra Difference Equations -- Oscillation Theory -- Asymptotic Behavior of Difference Equations -- Applications to Continued Fractions and Orthogonal Polynomials -- Control Theory En línea: http://dx.doi.org/10.1007/0-387-27602-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35126 An Introduction to Difference Equations [documento electrónico] / Elaydi, Saber ; SpringerLink (Online service) . - New York, NY : Springer New York, 2005 . - XXII, 540 p : online resource. - (Undergraduate Texts in Mathematics, ISSN 0172-6056) .
ISBN : 978-0-387-27602-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Difference equations Functional and Equations Clasificación: 51 Matemáticas Resumen: The book integrates both classical and modern treatments of difference equations. It contains the most updated and comprehensive material, yet the presentation is simple enough for the book to be used by advanced undergraduate and beginning graduate students. This third edition includes more proofs, more graphs, and more applications. The author has also updated the contents by adding a new chapter on Higher Order Scalar Difference Equations, along with recent results on local and global stability of one-dimensional maps, a new section on the various notions of asymptoticity of solutions, a detailed proof of Levin-May Theorem, and the latest results on the LPA flour-beetle model. Saber Elaydi is Professor of Mathematics at Trinity University. He is also the author of Discrete Chaos (1999), and the Editor-In-Chief of the Journal of Difference Equations and Applications. About the Second Edition: The book is a valuable reference for anyone who models discrete systems. Dynamicists have the long-awaited discrete counterpart to standard textbooks such as Hirsch and Smale ('Differential Equations, Dynamical Systems, and Linear Algebra'). It is so well written and well designed, and the contents are so interesting to me, that I had a difficult time putting it down. - Shandelle Henson, Journal of Difference Equations and Applications Among the few introductory texts to difference equations this book is one of the very best ones. It has many features that the other texts don't have, e.g., stability theory, the Z-transform method (including a study of Volterra systems), and asymptotic behavior of solutions of difference equations (including Levinson's lemma) are studied extensively. It also contains very nice examples that primarily arise in applications in a variety of disciplines, including neural networks, feedback control, biology, Markov chains, economics, and heat transfer... -Martin Bohner, University of Missouri, Rolla Nota de contenido: Dynamics of First-Order Difference Equations -- Linear Difference Equations of Higher Order -- Systems of Linear Difference Equations -- Stability Theory -- Higher-Order Scalar Difference Equations -- The Z-Transform Method and Volterra Difference Equations -- Oscillation Theory -- Asymptotic Behavior of Difference Equations -- Applications to Continued Fractions and Orthogonal Polynomials -- Control Theory En línea: http://dx.doi.org/10.1007/0-387-27602-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35126 Ejemplares
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Título : An Introduction to Mathematical Cryptography Tipo de documento: documento electrónico Autores: Silverman, J.H ; SpringerLink (Online service) ; Pipher, Jill ; Hoffstein, Jeffrey Editorial: New York, NY : Springer New York Fecha de publicación: 2008 Colección: Undergraduate Texts in Mathematics, ISSN 0172-6056 Número de páginas: XVI, 524 p. 29 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-77994-2 Idioma : Inglés (eng) Palabras clave: Mathematics Data structures (Computer science) encryption Coding theory Algebra Ordered algebraic Information Number Theory and Structures, Cryptology Encryption Communication, Circuits Order, Lattices, Algebraic Structures Clasificación: 51 Matemáticas Resumen: This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: * classical cryptographic constructions, such as Diffie-Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; * fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms; * an in-depth treatment of important recent cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem. This book is an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online Nota de contenido: An Introduction to Cryptography -- Discrete Logarithms and Diffie Hellman -- Integer Factorization and RSA -- Combinatorics, Probability and Information Theory -- Elliptic Curves and Cryptography -- Lattices and Cryptography -- Digital Signatures -- Additional Topics in Cryptography En línea: http://dx.doi.org/10.1007/978-0-387-77993-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34241 An Introduction to Mathematical Cryptography [documento electrónico] / Silverman, J.H ; SpringerLink (Online service) ; Pipher, Jill ; Hoffstein, Jeffrey . - New York, NY : Springer New York, 2008 . - XVI, 524 p. 29 illus : online resource. - (Undergraduate Texts in Mathematics, ISSN 0172-6056) .
ISBN : 978-0-387-77994-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Data structures (Computer science) encryption Coding theory Algebra Ordered algebraic Information Number Theory and Structures, Cryptology Encryption Communication, Circuits Order, Lattices, Algebraic Structures Clasificación: 51 Matemáticas Resumen: This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: * classical cryptographic constructions, such as Diffie-Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; * fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms; * an in-depth treatment of important recent cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem. This book is an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online Nota de contenido: An Introduction to Cryptography -- Discrete Logarithms and Diffie Hellman -- Integer Factorization and RSA -- Combinatorics, Probability and Information Theory -- Elliptic Curves and Cryptography -- Lattices and Cryptography -- Digital Signatures -- Additional Topics in Cryptography En línea: http://dx.doi.org/10.1007/978-0-387-77993-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34241 Ejemplares
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Título : An Invitation to Abstract Mathematics Tipo de documento: documento electrónico Autores: Béla Bajnok ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Undergraduate Texts in Mathematics, ISSN 0172-6056 Número de páginas: XIV, 406 p Il.: online resource ISBN/ISSN/DL: 978-1-4614-6636-9 Idioma : Inglés (eng) Palabras clave: Mathematics History Mathematical logic Mathematics, general of Sciences Logic and Foundations Clasificación: 51 Matemáticas Resumen: This undergraduate textbook is intended primarily for a transition course into higher mathematics, although it is written with a broader audience in mind. The heart and soul of this book is problem solving, where each problem is carefully chosen to clarify a concept, demonstrate a technique, or to enthuse. The exercises require relatively extensive arguments, creative approaches, or both, thus providing motivation for the reader. With a unified approach to a diverse collection of topics, this text points out connections, similarities, and differences among subjects whenever possible. This book shows students that mathematics is a vibrant and dynamic human enterprise by including historical perspectives and notes on the giants of mathematics, by mentioning current activity in the mathematical community, and by discussing many famous and less well-known questions that remain open for future mathematicians. Ideally, this text should be used for a two semester course, where the first course has no prerequisites and the second is a more challenging course for math majors; yet, the flexible structure of the book allows it to be used in a variety of settings, including as a source of various independent-study and research projects Nota de contenido: Preface to Instructors -- Preface to Students -- Acknowledgments -- I What's Mathematics -- 1 Let's Play a Game! -- 2 What's the Name of the Game? -- 3 How to Make a Statement?- 4 What's True in Mathematics? -- 5 Famous Classical Theorems -- 6 Recent Progress in Mathematics -- II How to Solve It? -- 7 Let's be Logical! -- 8 Setting Examples -- 9 Quantifier Mechanics -- 10 Mathematical Structures -- 11 Working in the Fields (and Other Structures) -- 12 Universal Proofs -- 13 The Domino Effect -- 14 More Domino Games -- 15 Existential Proofs -- 16 A Cornucopia of Famous Problems -- III Advanced Math for Beginners -- 17 Good Relations -- 18 Order, Please! -- 19 Let's be Functional! -- 20 Now That's the Limit! -- 21 Sizing It Up -- 22 Infinite Delights -- 23 Number Systems Systematically -- 24 Games Are Valuable! -- IV. Appendices -- A. Famous Conjectures in Mathematics -- B The Foundations of Set Theory -- C All Games Considered -- D Top 40 List of Math Theorems. - Index En línea: http://dx.doi.org/10.1007/978-1-4614-6636-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32311 An Invitation to Abstract Mathematics [documento electrónico] / Béla Bajnok ; SpringerLink (Online service) . - New York, NY : Springer New York : Imprint: Springer, 2013 . - XIV, 406 p : online resource. - (Undergraduate Texts in Mathematics, ISSN 0172-6056) .
ISBN : 978-1-4614-6636-9
Idioma : Inglés (eng)
Palabras clave: Mathematics History Mathematical logic Mathematics, general of Sciences Logic and Foundations Clasificación: 51 Matemáticas Resumen: This undergraduate textbook is intended primarily for a transition course into higher mathematics, although it is written with a broader audience in mind. The heart and soul of this book is problem solving, where each problem is carefully chosen to clarify a concept, demonstrate a technique, or to enthuse. The exercises require relatively extensive arguments, creative approaches, or both, thus providing motivation for the reader. With a unified approach to a diverse collection of topics, this text points out connections, similarities, and differences among subjects whenever possible. This book shows students that mathematics is a vibrant and dynamic human enterprise by including historical perspectives and notes on the giants of mathematics, by mentioning current activity in the mathematical community, and by discussing many famous and less well-known questions that remain open for future mathematicians. Ideally, this text should be used for a two semester course, where the first course has no prerequisites and the second is a more challenging course for math majors; yet, the flexible structure of the book allows it to be used in a variety of settings, including as a source of various independent-study and research projects Nota de contenido: Preface to Instructors -- Preface to Students -- Acknowledgments -- I What's Mathematics -- 1 Let's Play a Game! -- 2 What's the Name of the Game? -- 3 How to Make a Statement?- 4 What's True in Mathematics? -- 5 Famous Classical Theorems -- 6 Recent Progress in Mathematics -- II How to Solve It? -- 7 Let's be Logical! -- 8 Setting Examples -- 9 Quantifier Mechanics -- 10 Mathematical Structures -- 11 Working in the Fields (and Other Structures) -- 12 Universal Proofs -- 13 The Domino Effect -- 14 More Domino Games -- 15 Existential Proofs -- 16 A Cornucopia of Famous Problems -- III Advanced Math for Beginners -- 17 Good Relations -- 18 Order, Please! -- 19 Let's be Functional! -- 20 Now That's the Limit! -- 21 Sizing It Up -- 22 Infinite Delights -- 23 Number Systems Systematically -- 24 Games Are Valuable! -- IV. Appendices -- A. Famous Conjectures in Mathematics -- B The Foundations of Set Theory -- C All Games Considered -- D Top 40 List of Math Theorems. - Index En línea: http://dx.doi.org/10.1007/978-1-4614-6636-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32311 Ejemplares
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