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Introduction to topology and geometry / / Saul Stahl, Catherine Stenson
| Introduction to topology and geometry / / Saul Stahl, Catherine Stenson |
| Autore | Stahl Saul |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2013 |
| Descrizione fisica | 1 online resource (533 p.) |
| Disciplina | 514 |
| Collana | Pure and Applied Mathematics |
| Soggetto topico |
Topology
Geometry |
| ISBN |
0-471-66260-7
1-118-54614-8 1-118-54590-7 1-118-54591-5 |
| Classificazione | MAT038000 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover ; Title Page ; Copyright ; Contents ; Preface ; Acknowledgments ; Chapter 1: Informal Topology ; Chapter 2: Graphs ; 2.1 Nodes and Arcs ; 2.2 Traversability ; 2.3 Colorings ; 2.4 Planarity ; 2.5 Graph Homeomorphisms ; Chapter 3: Surfaces ; 3.1 Polygonal Presentations ; 3.2 Closed Surfaces ; 3.3 Operations on Surfaces ; 3.4 Bordered Surfaces ; 3.5 Riemann Surfaces ; Chapter 4: Graphs and Surfaces ; 4.1 Embeddings and Their Regions ; 4.2 Polygonal Embeddings ; 4.3 Embedding a Fixed Graph ; 4.4 Voltage Graphs and Their Coverings ; Chapter 5: Knots and Links ; 5.1 Preliminaries
5.2 Labelings 5.3 From Graphs to Links and on to Surfaces ; 5.4 The Jones Polynomial ; 5.5 The Jones Polynomial and Alternating Diagrams ; 5.6 Knots and Surfaces ; Chapter 6: The Differential Geometry of Surfaces ; 6.1 Surfaces, Normals, and Tangent Planes ; 6.2 The Gaussian Curvature ; 6.3 The First Fundamental Form ; 6.4 Normal Curvatures ; 6.5 The Geodesic Polar Parametrization ; 6.6 Polyhedral Surfaces I ; 6.7 Gauss''s Total Curvature Theorem ; 6.8 Polyhedral Surfaces II ; Chapter 7: Riemann Geometries ; Chapter 8: Hyperbolic Geometry ; 8.1 Neutral Geometry ; 8.2 The Upper Half-plane 8.3 The Half-plane Theorem of Pythagoras 8.4 Half-plane Isometries ; Chapter 9: The Fundamental Group ; 9.1 Definitions and the Punctured Plane ; 9.2 Surfaces ; 9.3 3-manifolds ; 9.4 The Poincaré Conjecture ; Chapter 10: General Topology ; 10.1 Metric and Topological Spaces ; 10.2 Continuity and Homeomorphisms ; 10.3 Connectedness ; 10.4 Compactness ; Chapter 11: Polytopes ; 11.1 Introduction to Polytopes ; 11.2 Graphs of Polytopes ; 11.3 Regular Polytopes ; 11.4 Enumerating Faces ; Appendix A: Curves ; A.1 Parametrization of Curves and Arclength ; Appendix B: a Brief Survey of Groups B.1 The General Background B.2 Abelian Groups ; B.3 Group Presentations ; Appendix C: Permutations ; Appendix D: Modular Arithmetic ; Appendix E: Solutions and Hints to Selected Exercises ; References and Resources ; Index ; Pure and Applied Mathematics |
| Record Nr. | UNINA-9910133679203321 |
Stahl Saul
|
||
| Hoboken, New Jersey : , : Wiley, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introduction to topology and geometry / / Saul Stahl, Catherine Stenson
| Introduction to topology and geometry / / Saul Stahl, Catherine Stenson |
| Autore | Stahl Saul |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2013 |
| Descrizione fisica | 1 online resource (533 p.) |
| Disciplina | 514 |
| Collana | Pure and Applied Mathematics |
| Soggetto topico |
Topology
Geometry |
| ISBN |
0-471-66260-7
1-118-54614-8 1-118-54590-7 1-118-54591-5 |
| Classificazione | MAT038000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover ; Title Page ; Copyright ; Contents ; Preface ; Acknowledgments ; Chapter 1: Informal Topology ; Chapter 2: Graphs ; 2.1 Nodes and Arcs ; 2.2 Traversability ; 2.3 Colorings ; 2.4 Planarity ; 2.5 Graph Homeomorphisms ; Chapter 3: Surfaces ; 3.1 Polygonal Presentations ; 3.2 Closed Surfaces ; 3.3 Operations on Surfaces ; 3.4 Bordered Surfaces ; 3.5 Riemann Surfaces ; Chapter 4: Graphs and Surfaces ; 4.1 Embeddings and Their Regions ; 4.2 Polygonal Embeddings ; 4.3 Embedding a Fixed Graph ; 4.4 Voltage Graphs and Their Coverings ; Chapter 5: Knots and Links ; 5.1 Preliminaries
5.2 Labelings 5.3 From Graphs to Links and on to Surfaces ; 5.4 The Jones Polynomial ; 5.5 The Jones Polynomial and Alternating Diagrams ; 5.6 Knots and Surfaces ; Chapter 6: The Differential Geometry of Surfaces ; 6.1 Surfaces, Normals, and Tangent Planes ; 6.2 The Gaussian Curvature ; 6.3 The First Fundamental Form ; 6.4 Normal Curvatures ; 6.5 The Geodesic Polar Parametrization ; 6.6 Polyhedral Surfaces I ; 6.7 Gauss''s Total Curvature Theorem ; 6.8 Polyhedral Surfaces II ; Chapter 7: Riemann Geometries ; Chapter 8: Hyperbolic Geometry ; 8.1 Neutral Geometry ; 8.2 The Upper Half-plane 8.3 The Half-plane Theorem of Pythagoras 8.4 Half-plane Isometries ; Chapter 9: The Fundamental Group ; 9.1 Definitions and the Punctured Plane ; 9.2 Surfaces ; 9.3 3-manifolds ; 9.4 The Poincaré Conjecture ; Chapter 10: General Topology ; 10.1 Metric and Topological Spaces ; 10.2 Continuity and Homeomorphisms ; 10.3 Connectedness ; 10.4 Compactness ; Chapter 11: Polytopes ; 11.1 Introduction to Polytopes ; 11.2 Graphs of Polytopes ; 11.3 Regular Polytopes ; 11.4 Enumerating Faces ; Appendix A: Curves ; A.1 Parametrization of Curves and Arclength ; Appendix B: a Brief Survey of Groups B.1 The General Background B.2 Abelian Groups ; B.3 Group Presentations ; Appendix C: Permutations ; Appendix D: Modular Arithmetic ; Appendix E: Solutions and Hints to Selected Exercises ; References and Resources ; Index ; Pure and Applied Mathematics |
| Record Nr. | UNINA-9910806170003321 |
|
Stahl Saul
|
||
| Hoboken, New Jersey : , : Wiley, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introductory modern algebra : a historical approach / / Saul Stahl
| Introductory modern algebra : a historical approach / / Saul Stahl |
| Autore | Stahl Saul |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2013 |
| Descrizione fisica | 1 online resource (691 p.) |
| Disciplina | 512/.02 |
| Soggetto topico | Algebra, Abstract |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-118-83752-5
1-118-55203-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Half Title page; Title page; Copyright page; Preface; Chapter 1: The Early History; 1.1 The Breakthrough; Chapter 2: Complex Numbers; 2.1 Rational Functions of Complex Numbers; 2.2 Complex Roots; 2.3 Solvability by Radicals I; 2.4 Ruler-and-Compass Constructibility of Regular Polygons; 2.5 Orders of Roots of Unity; 2.6 The Existence of Complex Numbers; Chapter 3: Solutions of Equations; 3.1 The Cubic Formula; 3.2 Solvability by Radicals II; 3.3 Other Types of Solutions; Chapter 4: Modular Arithmetic; 4.1 Modular Addition, Subtraction, and Multiplication
4.2 The Euclidean Algorithm and Modular Inverses4.3 Radicals in Modular Arithmetic; 4.4 The Fundamental Theorem of Arithmetic; Chapter 5: The Binomial Theorem and Modular Powers; 5.1 The Binomial Theorem; 5.2 Fermat's Theorem and Modular Exponents; 5.3 The Multinomial Theorem; 5.4 The Euler φ-Function; Chapter 6: Polynomials Over A Field; 6.1 Fields and Their Polynomials; 6.2 The Factorization of Polynomials; 6.3 The Euclidean Algorithm for Polynomials; 6.4 Elementary Symmetric Polynomials; 6.5 Lagrange's Solution of the Quartic Equation; Chapter 7: Galois Fields 7.1 Galois's Construction of His Fields7.2 The Galois Polynomial; 7.3 The Primitive Element Theorem; 7.4 On the Variety of Galois Fields; Chapter 8: Permutations; 8.1 Permuting the Variables of a Function I; 8.2 Permutations; 8.3 Permuting the Variables of a Function II; 8.4 The Parity of a Permutation; Chapter 9: Groups; 9.1 Permutation Groups; 9.2 Abstract Groups; 9.3 Isomorphisms of Groups and Orders of Elements; 9.4 Subgroups and Their Orders; 9.5 Cyclic Groups and Subgroups; 9.6 Cayley's Theorem; Chapter 10: Quotient Groups and Their Uses; 10.1 Quotient Groups; 10.2 Group Homomorphisms 10.3 The Rigorous Construction of Fields10.4 Galois Groups and the Resolvability of Equations; Chapter 11: Topics in Elementary Group Theory; 11.1 The Direct Product of Groups; 11.2 More Classifications; Chapter 12: Number Theory; 12.1 Pythagorean Triples; 12.2 Sums of Two Squares; 12.3 Quadratic Reciprocity; 12.4 The Gaussian Integers; 12.5 Eulerian Integers and Others; 12.6 What Is the Essence of Primality?; Chapter 13: The Arithmetic of Ideals; 13.1 Preliminaries; 13.2 Integers of a Quadratic Field; 13.3 Ideals; 13.4 Cancelation of Ideals; 13.5 Norms of Ideals 13.6 Prime Ideals and Unique Factorization13.7 Constructing Prime Ideals; Chapter 14: Abstract Rings; 14.1 Rings; 14.2 Ideals; 14.3 Domains; 14.4 Quotients of Rings; A. Excerpts from Al-Khwarizmi's Solution of the Quadratic Equation1; B. Excerpts from Cardano's Ars Magna1; C. Excerpts from Abel's A Demonstration of the Impossibility of the Algebraic Resolution of General Equations Whose Degree Exceeds Four1; D. Excerpts from Galois's On the Theory of Numbers1; E. Excerpts from Cayley's The Theory of Groups1; F. Mathematical Induction; G. Logic, Predicates, Sets, and Functions G.1 Truth Tables |
| Record Nr. | UNINA-9910462709003321 |
|
Stahl Saul
|
||
| Hoboken, New Jersey : , : Wiley, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introductory modern algebra : a historical approach / / Saul Stahl
| Introductory modern algebra : a historical approach / / Saul Stahl |
| Autore | Stahl Saul |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2013 |
| Descrizione fisica | 1 online resource (462 pages) |
| Disciplina | 512/.02 |
| Soggetto topico | Algebra, Abstract |
| ISBN |
9781118552032
1118552032 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910795971003321 |
|
Stahl Saul
|
||
| Hoboken, New Jersey : , : Wiley, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Introductory modern algebra : a historical approach / / Saul Stahl
| Introductory modern algebra : a historical approach / / Saul Stahl |
| Autore | Stahl Saul |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2013 |
| Descrizione fisica | 1 online resource (462 pages) |
| Disciplina | 512/.02 |
| Soggetto topico | Algebra, Abstract |
| ISBN |
9781118552032
1118552032 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910820110303321 |
|
Stahl Saul
|
||
| Hoboken, New Jersey : , : Wiley, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Real analysis [[electronic resource] ] : a historical approach / / Saul Stahl
| Real analysis [[electronic resource] ] : a historical approach / / Saul Stahl |
| Autore | Stahl Saul |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, 2011 |
| Descrizione fisica | 1 online resource (316 p.) |
| Disciplina |
515.8
515/.8 |
| Collana | Pure and applied mathematics |
| Soggetto topico |
Mathematical analysis
Functions of real variables |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-283-28114-7
9786613281142 1-118-09685-1 1-118-09686-X 1-118-09684-3 |
| Classificazione | MAT005000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Real Analysis: A Historical Approach; Contents; Preface to the Second Edition; Acknowledgments; 1 Archimedes and the Parabola; 1.1 The Area of the Parabolic Segment; 1.2 The Geometry of the Parabola; 2 Fermat, Differentiation, and Integration; 2.1 Fermat's Calculus; 3 Newton's Calculus (Part 1); 3.1 The Fractional Binomial Theorem; 3.2 Areas and Infinite Series; 3.3 Newton's Proofs; 4 Newton's Calculus (Part 2); 4.1 The Solution of Differential Equations; 4.2 The Solution of Algebraic Equations; Chapter Appendix: Mathematica Implementations of Newton's Algorithm; 5 Euler
5.1 Trigonometric Series6 The Real Numbers; 6.1 An Informal Introduction; 6.2 Ordered Fields; 6.3 Completeness and Irrational Numbers; 6.4 The Euclidean Process; 6.5 Functions; 7 Sequences and Their Limits; 7.1 The Definitions; 7.2 Limit Theorems; 8 The Cauchy Property; 8.1 Limits of Monotone Sequences; 8.2 The Cauchy Property; 9 The Convergence of Infinite Series; 9.1 Stock Series; 9.2 Series of Positive Terms; 9.3 Series of Arbitrary Terms; 9.4 The Most Celebrated Problem; 10 Series of Functions; 10.1 Power Series; 10.2 Trigonometric Series; 11 Continuity; 11.1 An Informal Introduction 11.2 The Limit of a Function11.3 Continuity; 11.4 Properties of Continuous Functions; 12 Differentiability; 12.1 An Informal Introduction to Differentiation; 12.2 The Derivative; 12.3 The Consequences of Differentiability; 12.4 Integrability; 13 Uniform Convergence; 13.1 Uniform and Nonuniform, Convergence; 13.2 Consequences of Uniform Convergence; 14 The Vindication; 14.1 Trigonometric Series; 14.2 Power Series; 15 The Riemann Integral; 15.1 Continuity Revisited; 15.2 Lower and Upper Sums; 15.3 Integrability; Appendix A: Excerpts from ""Quadrature of the Parabola"" by Archimedes Appendix B: On a Method for the Evaluation of Maxima and Minima by Pierre de FermatAppendix C: From a Letter to Henry Oldenburg on the Binomial Series (June 13, 1676) by Isaac Newton; Appendix D: From a Letter to Henry Oldenburg on the Binomial Series (October 24, 1676) by Isaac Newton; Appendix E: Excerpts from ""Of Analysis by Equations of an Infinite Number of Terms"" by Isaac Newton; Appendix F: Excerpts from ""Subsiduum Calculi Sinuum"" by Leonhard Euler; Solutions to Selected Exercises; Bibliography; Index |
| Record Nr. | UNINA-9910139574403321 |
|
Stahl Saul
|
||
| Hoboken, N.J., : Wiley, 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Real analysis [[electronic resource] ] : a historical approach / / Saul Stahl
| Real analysis [[electronic resource] ] : a historical approach / / Saul Stahl |
| Autore | Stahl Saul |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, 2011 |
| Descrizione fisica | 1 online resource (316 p.) |
| Disciplina |
515.8
515/.8 |
| Collana | Pure and applied mathematics |
| Soggetto topico |
Mathematical analysis
Functions of real variables |
| ISBN |
1-283-28114-7
9786613281142 1-118-09685-1 1-118-09686-X 1-118-09684-3 |
| Classificazione | MAT005000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Real Analysis: A Historical Approach; Contents; Preface to the Second Edition; Acknowledgments; 1 Archimedes and the Parabola; 1.1 The Area of the Parabolic Segment; 1.2 The Geometry of the Parabola; 2 Fermat, Differentiation, and Integration; 2.1 Fermat's Calculus; 3 Newton's Calculus (Part 1); 3.1 The Fractional Binomial Theorem; 3.2 Areas and Infinite Series; 3.3 Newton's Proofs; 4 Newton's Calculus (Part 2); 4.1 The Solution of Differential Equations; 4.2 The Solution of Algebraic Equations; Chapter Appendix: Mathematica Implementations of Newton's Algorithm; 5 Euler
5.1 Trigonometric Series6 The Real Numbers; 6.1 An Informal Introduction; 6.2 Ordered Fields; 6.3 Completeness and Irrational Numbers; 6.4 The Euclidean Process; 6.5 Functions; 7 Sequences and Their Limits; 7.1 The Definitions; 7.2 Limit Theorems; 8 The Cauchy Property; 8.1 Limits of Monotone Sequences; 8.2 The Cauchy Property; 9 The Convergence of Infinite Series; 9.1 Stock Series; 9.2 Series of Positive Terms; 9.3 Series of Arbitrary Terms; 9.4 The Most Celebrated Problem; 10 Series of Functions; 10.1 Power Series; 10.2 Trigonometric Series; 11 Continuity; 11.1 An Informal Introduction 11.2 The Limit of a Function11.3 Continuity; 11.4 Properties of Continuous Functions; 12 Differentiability; 12.1 An Informal Introduction to Differentiation; 12.2 The Derivative; 12.3 The Consequences of Differentiability; 12.4 Integrability; 13 Uniform Convergence; 13.1 Uniform and Nonuniform, Convergence; 13.2 Consequences of Uniform Convergence; 14 The Vindication; 14.1 Trigonometric Series; 14.2 Power Series; 15 The Riemann Integral; 15.1 Continuity Revisited; 15.2 Lower and Upper Sums; 15.3 Integrability; Appendix A: Excerpts from ""Quadrature of the Parabola"" by Archimedes Appendix B: On a Method for the Evaluation of Maxima and Minima by Pierre de FermatAppendix C: From a Letter to Henry Oldenburg on the Binomial Series (June 13, 1676) by Isaac Newton; Appendix D: From a Letter to Henry Oldenburg on the Binomial Series (October 24, 1676) by Isaac Newton; Appendix E: Excerpts from ""Of Analysis by Equations of an Infinite Number of Terms"" by Isaac Newton; Appendix F: Excerpts from ""Subsiduum Calculi Sinuum"" by Leonhard Euler; Solutions to Selected Exercises; Bibliography; Index |
| Record Nr. | UNINA-9910676502103321 |
|
Stahl Saul
|
||
| Hoboken, N.J., : Wiley, 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||