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Título : An Introduction to Mathematics of Emerging Biomedical Imaging Tipo de documento: documento electrónico Autores: Habib Ammari ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2008 Colección: Mathématiques & Applications, ISSN 1154-483X num. 62 Número de páginas: X, 198 p. 16 illus Il.: online resource ISBN/ISSN/DL: 978-3-540-79553-7 Idioma : Inglés (eng) Palabras clave: Medicine Internal medicine Differential equations Partial differential Potential theory (Mathematics) Biomathematics & Public Health Mathematical and Computational Biology Theory Equations Ordinary Clasificación: 51 Matemáticas Resumen: Biomedical imaging is a fascinating research area to applied mathematicians. Challenging imaging problems arise and they often trigger the investigation of fundamental problems in various branches of mathematics. This is the first book to highlight the most recent mathematical developments in emerging biomedical imaging techniques. The main focus is on emerging multi-physics and multi-scales imaging approaches. For such promising techniques, it provides the basic mathematical concepts and tools for image reconstruction. Further improvements in these exciting imaging techniques require continued research in the mathematical sciences, a field that has contributed greatly to biomedical imaging and will continue to do so. The volume is suitable for a graduate-level course in applied mathematics and helps prepare the reader for a deeper understanding of research areas in biomedical imaging Nota de contenido: Mathematical Tools -- Biomedical Imaging Modalities -- Preliminaries -- Layer Potential Techniques -- General Reconstruction Algorithms -- Tomographic Imaging with Non-Diffracting Sources -- Tomographic Imaging with Diffracting Sources -- Biomagnetic Source Imaging -- Anomaly Detection Algorithms -- Small Volume Expansions -- Imaging Techniques -- Hybrid Imaging Techniques -- Magnetic Resonance Electrical Impedance Tomography -- Impediography -- Magnetic Resonance Elastography En línea: http://dx.doi.org/10.1007/978-3-540-79553-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34380 An Introduction to Mathematics of Emerging Biomedical Imaging [documento electrónico] / Habib Ammari ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2008 . - X, 198 p. 16 illus : online resource. - (Mathématiques & Applications, ISSN 1154-483X; 62) .
ISBN : 978-3-540-79553-7
Idioma : Inglés (eng)
Palabras clave: Medicine Internal medicine Differential equations Partial differential Potential theory (Mathematics) Biomathematics & Public Health Mathematical and Computational Biology Theory Equations Ordinary Clasificación: 51 Matemáticas Resumen: Biomedical imaging is a fascinating research area to applied mathematicians. Challenging imaging problems arise and they often trigger the investigation of fundamental problems in various branches of mathematics. This is the first book to highlight the most recent mathematical developments in emerging biomedical imaging techniques. The main focus is on emerging multi-physics and multi-scales imaging approaches. For such promising techniques, it provides the basic mathematical concepts and tools for image reconstruction. Further improvements in these exciting imaging techniques require continued research in the mathematical sciences, a field that has contributed greatly to biomedical imaging and will continue to do so. The volume is suitable for a graduate-level course in applied mathematics and helps prepare the reader for a deeper understanding of research areas in biomedical imaging Nota de contenido: Mathematical Tools -- Biomedical Imaging Modalities -- Preliminaries -- Layer Potential Techniques -- General Reconstruction Algorithms -- Tomographic Imaging with Non-Diffracting Sources -- Tomographic Imaging with Diffracting Sources -- Biomagnetic Source Imaging -- Anomaly Detection Algorithms -- Small Volume Expansions -- Imaging Techniques -- Hybrid Imaging Techniques -- Magnetic Resonance Electrical Impedance Tomography -- Impediography -- Magnetic Resonance Elastography En línea: http://dx.doi.org/10.1007/978-3-540-79553-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34380 Ejemplares
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Título : Discovering Mathematics : A Problem-Solving Approach to Mathematical Analysis with MATHEMATICA® and Maple™ Tipo de documento: documento electrónico Autores: Gregor, Jirí ; SpringerLink (Online service) ; Tišer, Jaroslav Editorial: London : Springer London Fecha de publicación: 2011 Número de páginas: VII, 247 p. 16 illus Il.: online resource ISBN/ISSN/DL: 978-0-85729-064-9 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Clasificación: 51 Matemáticas Resumen: Discovering Mathematics: A Problem-Solving Approach to Analysis with Mathematica and Maple provides a constructive approach to mathematical discovery through innovative use of software technology. Interactive Mathematica and Maple notebooks are integral to this books’ utility as a practical tool for learning. Interrelated concepts, definitions and theorems are connected through hyperlinks, guiding the reader to a variety of structured problems and highlighting multiple avenues of mathematical reasoning. Interactivity is further enhanced through the delivery of online content (available at extras.springer.com), demonstrating the use of software and in turn increasing the scope of learning for both students and teachers and contributing to a deeper mathematical understanding. This book will appeal to both final year undergraduate and post-graduate students wishing to supplement a mathematics course or module in mathematical problem-solving and analysis. It will also be of use as complementary reading for students of engineering or science, and those in self-study Nota de contenido: Part I Concepts: Mappings, composite and inverse functions -- Infinite sequences -- Periodicity -- Part II Tools: Finite Sums -- Inequalities -- Collocation and least squares methods -- Part III Applications: Maximal and minimal values -- Arcs and curves -- Center of mass and moments -- Miscellaneous -- Part IV Appendix En línea: http://dx.doi.org/10.1007/978-0-85729-064-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33117 Discovering Mathematics : A Problem-Solving Approach to Mathematical Analysis with MATHEMATICA® and Maple™ [documento electrónico] / Gregor, Jirí ; SpringerLink (Online service) ; Tišer, Jaroslav . - London : Springer London, 2011 . - VII, 247 p. 16 illus : online resource.
ISBN : 978-0-85729-064-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Clasificación: 51 Matemáticas Resumen: Discovering Mathematics: A Problem-Solving Approach to Analysis with Mathematica and Maple provides a constructive approach to mathematical discovery through innovative use of software technology. Interactive Mathematica and Maple notebooks are integral to this books’ utility as a practical tool for learning. Interrelated concepts, definitions and theorems are connected through hyperlinks, guiding the reader to a variety of structured problems and highlighting multiple avenues of mathematical reasoning. Interactivity is further enhanced through the delivery of online content (available at extras.springer.com), demonstrating the use of software and in turn increasing the scope of learning for both students and teachers and contributing to a deeper mathematical understanding. This book will appeal to both final year undergraduate and post-graduate students wishing to supplement a mathematics course or module in mathematical problem-solving and analysis. It will also be of use as complementary reading for students of engineering or science, and those in self-study Nota de contenido: Part I Concepts: Mappings, composite and inverse functions -- Infinite sequences -- Periodicity -- Part II Tools: Finite Sums -- Inequalities -- Collocation and least squares methods -- Part III Applications: Maximal and minimal values -- Arcs and curves -- Center of mass and moments -- Miscellaneous -- Part IV Appendix En línea: http://dx.doi.org/10.1007/978-0-85729-064-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33117 Ejemplares
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Título : Essays in Constructive Mathematics Tipo de documento: documento electrónico Autores: Edwards, Harold M ; 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] / Edwards, Harold M ; 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 : Excursions in the History of Mathematics Tipo de documento: documento electrónico Autores: Kleiner, Israel ; SpringerLink (Online service) Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2012 Número de páginas: XXI, 347 p. 36 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-8268-2 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) History logic Number theory Study and teaching of Sciences Education Theory Logic Foundations Mathematics, general Clasificación: 51 Matemáticas Resumen: This book comprises five parts. The first three contain ten historical essays on important topics: number theory, calculus/analysis, and proof, respectively. Part four deals with several historically oriented courses, and Part five provides biographies of five mathematicians who played major roles in the historical events described in the first four parts of the work. Each of the first three parts—on number theory, calculus/analysis, and proof—begins with a survey of the respective subject and is followed in more depth by specialized themes. Among the specialized themes are: Fermat as the founder of modern number theory, Fermat’s Last Theorem from Fermat to Wiles, the history of the function concept, paradoxes, the principle of continuity, and an historical perspective on recent debates about proof. The fourth part contains essays describing mathematics courses inspired by history. The essays deal with numbers as a source of ideas in teaching, with famous problems, and with the stories behind various "great" quotations. The last part gives an account of five mathematicians—Dedekind, Euler, Gauss, Hilbert, and Weierstrass—whose lives and work we hope readers will find inspiring. Key features of the work include: * A preface describing in some detail the author's ideas on teaching mathematics courses, in particular, the role of history in such courses; * Explicit comments and suggestions for teachers on how history can affect the teaching of mathematics; * A description of a course in the history of mathematics taught in an In-Service Master's Program for high school teachers; * Inclusion of issues in the philosophy of mathematics; * An extensive list of relevant references at the end of each chapter. Excursions in the History of Mathematics was written with several goals in mind: to arouse mathematics teachers’ interest in the history of their subject; to encourage mathematics teachers with at least some knowledge of the history of mathematics to offer courses with a strong historical component; and to provide an historical perspective on a number of basic topics taught in mathematics courses Nota de contenido: A. Number Theory -- 1. Highlights in the History of Number Theory: 1700 BC - 2008 -- 2. Fermat: The Founder of Modern Number Theory -- 3. Fermat's Last Theorem: From Fermat to Wiles -- B. Calculus/Analysis -- 4. A History of the Infinitely Small and the Infinitely Large in Calculus, with Remarks for the Teacher -- 5. A Brief History of the Function Concept -- 6. More on the History of Functions, Including Remarks on Teaching -- C. Proof -- 7. Highlights in the Practice of Proof: 1600 BC - 2009 -- 8. Paradoxes: What are they Good for? -- 9. Principle of Continuity: 16th - 19th centuries -- 10. Proof: A Many-Splendored Thing -- D. Courses Inspired by History -- 11. Numbers as a Source of Mathematical Ideas -- 12. History of Complex Numbers, with a Moral for Teachers -- 13. A History-of-Mathematics Course for Teachers, Based on Great Quotations -- 14. Famous Problems in Mathematics -- E. Brief Biographies of Selected Mathematicians -- 15. The Biographies -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-8268-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32679 Excursions in the History of Mathematics [documento electrónico] / Kleiner, Israel ; SpringerLink (Online service) . - Boston : Birkhäuser Boston, 2012 . - XXI, 347 p. 36 illus : online resource.
ISBN : 978-0-8176-8268-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) History logic Number theory Study and teaching of Sciences Education Theory Logic Foundations Mathematics, general Clasificación: 51 Matemáticas Resumen: This book comprises five parts. The first three contain ten historical essays on important topics: number theory, calculus/analysis, and proof, respectively. Part four deals with several historically oriented courses, and Part five provides biographies of five mathematicians who played major roles in the historical events described in the first four parts of the work. Each of the first three parts—on number theory, calculus/analysis, and proof—begins with a survey of the respective subject and is followed in more depth by specialized themes. Among the specialized themes are: Fermat as the founder of modern number theory, Fermat’s Last Theorem from Fermat to Wiles, the history of the function concept, paradoxes, the principle of continuity, and an historical perspective on recent debates about proof. The fourth part contains essays describing mathematics courses inspired by history. The essays deal with numbers as a source of ideas in teaching, with famous problems, and with the stories behind various "great" quotations. The last part gives an account of five mathematicians—Dedekind, Euler, Gauss, Hilbert, and Weierstrass—whose lives and work we hope readers will find inspiring. Key features of the work include: * A preface describing in some detail the author's ideas on teaching mathematics courses, in particular, the role of history in such courses; * Explicit comments and suggestions for teachers on how history can affect the teaching of mathematics; * A description of a course in the history of mathematics taught in an In-Service Master's Program for high school teachers; * Inclusion of issues in the philosophy of mathematics; * An extensive list of relevant references at the end of each chapter. Excursions in the History of Mathematics was written with several goals in mind: to arouse mathematics teachers’ interest in the history of their subject; to encourage mathematics teachers with at least some knowledge of the history of mathematics to offer courses with a strong historical component; and to provide an historical perspective on a number of basic topics taught in mathematics courses Nota de contenido: A. Number Theory -- 1. Highlights in the History of Number Theory: 1700 BC - 2008 -- 2. Fermat: The Founder of Modern Number Theory -- 3. Fermat's Last Theorem: From Fermat to Wiles -- B. Calculus/Analysis -- 4. A History of the Infinitely Small and the Infinitely Large in Calculus, with Remarks for the Teacher -- 5. A Brief History of the Function Concept -- 6. More on the History of Functions, Including Remarks on Teaching -- C. Proof -- 7. Highlights in the Practice of Proof: 1600 BC - 2009 -- 8. Paradoxes: What are they Good for? -- 9. Principle of Continuity: 16th - 19th centuries -- 10. Proof: A Many-Splendored Thing -- D. Courses Inspired by History -- 11. Numbers as a Source of Mathematical Ideas -- 12. History of Complex Numbers, with a Moral for Teachers -- 13. A History-of-Mathematics Course for Teachers, Based on Great Quotations -- 14. Famous Problems in Mathematics -- E. Brief Biographies of Selected Mathematicians -- 15. The Biographies -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-8268-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32679 Ejemplares
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Título : Mathematics and Its History Tipo de documento: documento electrónico Autores: Stillwell, John ; 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: XXII, 662 p Il.: online resource ISBN/ISSN/DL: 978-1-4419-6053-5 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Geometry History Number theory of Sciences Theory Clasificación: 51 Matemáticas Resumen: From the reviews of the second edition: "This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here." (David Parrott, Australian Mathematical Society) "The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community." (European Mathematical Society) "Since Stillwell treats many topics, most mathematicians will learn a lot from this book as well as they will find pleasant and rather clear expositions of custom materials. The book is accessible to students that have already experienced calculus, algebra and geometry and will give them a good account of how the different branches of mathematics interact." (Denis Bonheure, Bulletin of the Belgian Society) This third edition includes new chapters on simple groups and combinatorics, and new sections on several topics, including the Poincare conjecture. The book has also been enriched by added exercises Nota de contenido: The Theorem of Pythagoras -- Greek Geometry -- Greek Number Theory -- Infinity in Greek Mathematics -- Number Theory in Asia -- Polynomial Equations -- Analytic Geometry -- Projective Geometry -- Calculus -- Infinite Series -- The Number Theory Revival -- Elliptic Functions -- Mechanics -- Complex Numbers in Algebra -- Complex Numbers and Curves -- Complex Numbers and Functions -- Differential Geometry -- Non-Euclidean Geometry -- Group Theory -- Hypercomplex Numbers -- Algebraic Number Theory -- Topology -- Simple Groups -- Sets, Logic, and Computation -- Combinatorics En línea: http://dx.doi.org/10.1007/978-1-4419-6053-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33625 Mathematics and Its History [documento electrónico] / Stillwell, John ; SpringerLink (Online service) . - New York, NY : Springer New York, 2010 . - XXII, 662 p : online resource. - (Undergraduate Texts in Mathematics, ISSN 0172-6056) .
ISBN : 978-1-4419-6053-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Geometry History Number theory of Sciences Theory Clasificación: 51 Matemáticas Resumen: From the reviews of the second edition: "This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here." (David Parrott, Australian Mathematical Society) "The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community." (European Mathematical Society) "Since Stillwell treats many topics, most mathematicians will learn a lot from this book as well as they will find pleasant and rather clear expositions of custom materials. The book is accessible to students that have already experienced calculus, algebra and geometry and will give them a good account of how the different branches of mathematics interact." (Denis Bonheure, Bulletin of the Belgian Society) This third edition includes new chapters on simple groups and combinatorics, and new sections on several topics, including the Poincare conjecture. The book has also been enriched by added exercises Nota de contenido: The Theorem of Pythagoras -- Greek Geometry -- Greek Number Theory -- Infinity in Greek Mathematics -- Number Theory in Asia -- Polynomial Equations -- Analytic Geometry -- Projective Geometry -- Calculus -- Infinite Series -- The Number Theory Revival -- Elliptic Functions -- Mechanics -- Complex Numbers in Algebra -- Complex Numbers and Curves -- Complex Numbers and Functions -- Differential Geometry -- Non-Euclidean Geometry -- Group Theory -- Hypercomplex Numbers -- Algebraic Number Theory -- Topology -- Simple Groups -- Sets, Logic, and Computation -- Combinatorics En línea: http://dx.doi.org/10.1007/978-1-4419-6053-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33625 Ejemplares
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