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Classical algebra [[electronic resource] ] : its nature, origins, and uses / / Roger Cooke
| Classical algebra [[electronic resource] ] : its nature, origins, and uses / / Roger Cooke |
| Autore | Cooke Roger <1942-> |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley-Interscience, c2008 |
| Descrizione fisica | 1 online resource (220 p.) |
| Disciplina | 512 |
| Soggetto topico |
Algebra
Algebra - History Algebraic logic |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-28501-3
9786611285012 0-470-27798-X 0-470-27797-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Classical Algebra Its Nature, Origins, and Uses; Contents; Preface; Part 1. Numbers and Equations; Lesson 1. What Algebra Is; 1. Numbers in disguise; 1.1.""Classical"" and modern algebra; 2. Arithmetic and algebra; 3. The ""environment"" of algebra: Number systems; 4. Important concepts and principles in this lesson; 5. Problems and questions; 6. Further reading; Lesson 2. Equations and Their Solutions; 1. Polynomial equations, coefficients, and roots; 1.1. Geometric interpretations; 2. The classification of equations; 2.1. Diophantine equations
3. Numerical and formulaic approaches to equations3.1. The numerical approach; 3.2. The formulaic approach; 4. Important concepts and principles in this lesson; 5. Problems and questions; 6. Further reading; Lesson 3. Where Algebra Comes From; 1. An Egyptian problem; 2. A Mesopotamian problem; 3. A Chinese problem; 4. An Arabic problem; 5. A Japanese problem; 6. Problems and questions; 7. Further reading; Lesson 4. Why Algebra Is Important; 1. Example: An ideal pendulum; 2. Problems and questions; 3. Further reading; Lesson 5. Numerical Solution of Equations; 1. A simple but crude method 2. Ancient Chinese methods of calculating2.1. A linear problem in three unknowns; 3. Systems of linear equations; 4. Polynomial equations; 4.1. Noninteger solutions; 5. The cubic equation; 6. Problems and questions; 7. Further reading; Part 2. The Formulaic Approach to Equations; Lesson 6. Combinatoric Solutions I: Quadratic Equations; 1. Why not set up tables of solutions?; 2. The quadratic formula; 3. Problems and questions; 4. Further reading; Lesson 7. Combinatoric Solutions II: Cubic Equations; 1. Reduction from four parameters to one; 2. Graphical solutions of cubic equations 3. Efforts to find a cubic formula3.1. Cube roots of complex numbers; 4. Alternative forms of the cubic formula; 5. The ""irreducible case""; 5.1. Imaginary numbers; 6. Problems and questions; 7. Further reading; Part 3. Resolvents; Lesson 8. From Combinatorics to Resolvents; 1. Solution of the irreducible case using complex numbers; 2. The quartic equation; 3. Viete's solution of the irreducible case of the cubic; 3.1. Comparison of the Viète and Cardano solutions; 4. The Tschirnhaus solution of the cubic equation; 5. Lagrange's reflections on the cubic equation 5.1. The cubic formula in terms of the roots5.2. A test case: The quartic; 6. Problems and questions; 7. Further reading; Lesson 9. The Search for Resolvents; 1. Coefficients and roots; 2. A unified approach to equations of all degrees; 2.1. A resolvent for the cubic equation; 3. A resolvent for the general quartic equation; 4. The state of polynomial algebra in 1770; 4.1. Seeking a resolvent for the quintic; 5. Permutations enter algebra; 6. Permutations of the variables in a function; 6.1.Two-valued functions; 7. Problems and questions; 8. Further reading; Part 4. Abstract Algebra Lesson 10. Existence and Constructibility of Roots |
| Record Nr. | UNINA-9910145585903321 |
Cooke Roger <1942->
|
||
| Hoboken, N.J., : Wiley-Interscience, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Classical algebra [[electronic resource] ] : its nature, origins, and uses / / Roger Cooke
| Classical algebra [[electronic resource] ] : its nature, origins, and uses / / Roger Cooke |
| Autore | Cooke Roger <1942-> |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley-Interscience, c2008 |
| Descrizione fisica | 1 online resource (220 p.) |
| Disciplina | 512 |
| Soggetto topico |
Algebra
Algebra - History Algebraic logic |
| ISBN |
1-281-28501-3
9786611285012 0-470-27798-X 0-470-27797-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Classical Algebra Its Nature, Origins, and Uses; Contents; Preface; Part 1. Numbers and Equations; Lesson 1. What Algebra Is; 1. Numbers in disguise; 1.1.""Classical"" and modern algebra; 2. Arithmetic and algebra; 3. The ""environment"" of algebra: Number systems; 4. Important concepts and principles in this lesson; 5. Problems and questions; 6. Further reading; Lesson 2. Equations and Their Solutions; 1. Polynomial equations, coefficients, and roots; 1.1. Geometric interpretations; 2. The classification of equations; 2.1. Diophantine equations
3. Numerical and formulaic approaches to equations3.1. The numerical approach; 3.2. The formulaic approach; 4. Important concepts and principles in this lesson; 5. Problems and questions; 6. Further reading; Lesson 3. Where Algebra Comes From; 1. An Egyptian problem; 2. A Mesopotamian problem; 3. A Chinese problem; 4. An Arabic problem; 5. A Japanese problem; 6. Problems and questions; 7. Further reading; Lesson 4. Why Algebra Is Important; 1. Example: An ideal pendulum; 2. Problems and questions; 3. Further reading; Lesson 5. Numerical Solution of Equations; 1. A simple but crude method 2. Ancient Chinese methods of calculating2.1. A linear problem in three unknowns; 3. Systems of linear equations; 4. Polynomial equations; 4.1. Noninteger solutions; 5. The cubic equation; 6. Problems and questions; 7. Further reading; Part 2. The Formulaic Approach to Equations; Lesson 6. Combinatoric Solutions I: Quadratic Equations; 1. Why not set up tables of solutions?; 2. The quadratic formula; 3. Problems and questions; 4. Further reading; Lesson 7. Combinatoric Solutions II: Cubic Equations; 1. Reduction from four parameters to one; 2. Graphical solutions of cubic equations 3. Efforts to find a cubic formula3.1. Cube roots of complex numbers; 4. Alternative forms of the cubic formula; 5. The ""irreducible case""; 5.1. Imaginary numbers; 6. Problems and questions; 7. Further reading; Part 3. Resolvents; Lesson 8. From Combinatorics to Resolvents; 1. Solution of the irreducible case using complex numbers; 2. The quartic equation; 3. Viete's solution of the irreducible case of the cubic; 3.1. Comparison of the Viète and Cardano solutions; 4. The Tschirnhaus solution of the cubic equation; 5. Lagrange's reflections on the cubic equation 5.1. The cubic formula in terms of the roots5.2. A test case: The quartic; 6. Problems and questions; 7. Further reading; Lesson 9. The Search for Resolvents; 1. Coefficients and roots; 2. A unified approach to equations of all degrees; 2.1. A resolvent for the cubic equation; 3. A resolvent for the general quartic equation; 4. The state of polynomial algebra in 1770; 4.1. Seeking a resolvent for the quintic; 5. Permutations enter algebra; 6. Permutations of the variables in a function; 6.1.Two-valued functions; 7. Problems and questions; 8. Further reading; Part 4. Abstract Algebra Lesson 10. Existence and Constructibility of Roots |
| Record Nr. | UNINA-9910830823203321 |
|
Cooke Roger <1942->
|
||
| Hoboken, N.J., : Wiley-Interscience, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Classical algebra : its nature, origins, and uses / / Roger Cooke
| Classical algebra : its nature, origins, and uses / / Roger Cooke |
| Autore | Cooke Roger <1942-> |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley-Interscience, c2008 |
| Descrizione fisica | 1 online resource (220 p.) |
| Disciplina | 512 |
| Soggetto topico |
Algebra
Algebra - History Algebraic logic |
| ISBN |
1-281-28501-3
9786611285012 0-470-27798-X 0-470-27797-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Classical Algebra Its Nature, Origins, and Uses; Contents; Preface; Part 1. Numbers and Equations; Lesson 1. What Algebra Is; 1. Numbers in disguise; 1.1.""Classical"" and modern algebra; 2. Arithmetic and algebra; 3. The ""environment"" of algebra: Number systems; 4. Important concepts and principles in this lesson; 5. Problems and questions; 6. Further reading; Lesson 2. Equations and Their Solutions; 1. Polynomial equations, coefficients, and roots; 1.1. Geometric interpretations; 2. The classification of equations; 2.1. Diophantine equations
3. Numerical and formulaic approaches to equations3.1. The numerical approach; 3.2. The formulaic approach; 4. Important concepts and principles in this lesson; 5. Problems and questions; 6. Further reading; Lesson 3. Where Algebra Comes From; 1. An Egyptian problem; 2. A Mesopotamian problem; 3. A Chinese problem; 4. An Arabic problem; 5. A Japanese problem; 6. Problems and questions; 7. Further reading; Lesson 4. Why Algebra Is Important; 1. Example: An ideal pendulum; 2. Problems and questions; 3. Further reading; Lesson 5. Numerical Solution of Equations; 1. A simple but crude method 2. Ancient Chinese methods of calculating2.1. A linear problem in three unknowns; 3. Systems of linear equations; 4. Polynomial equations; 4.1. Noninteger solutions; 5. The cubic equation; 6. Problems and questions; 7. Further reading; Part 2. The Formulaic Approach to Equations; Lesson 6. Combinatoric Solutions I: Quadratic Equations; 1. Why not set up tables of solutions?; 2. The quadratic formula; 3. Problems and questions; 4. Further reading; Lesson 7. Combinatoric Solutions II: Cubic Equations; 1. Reduction from four parameters to one; 2. Graphical solutions of cubic equations 3. Efforts to find a cubic formula3.1. Cube roots of complex numbers; 4. Alternative forms of the cubic formula; 5. The ""irreducible case""; 5.1. Imaginary numbers; 6. Problems and questions; 7. Further reading; Part 3. Resolvents; Lesson 8. From Combinatorics to Resolvents; 1. Solution of the irreducible case using complex numbers; 2. The quartic equation; 3. Viete's solution of the irreducible case of the cubic; 3.1. Comparison of the Viète and Cardano solutions; 4. The Tschirnhaus solution of the cubic equation; 5. Lagrange's reflections on the cubic equation 5.1. The cubic formula in terms of the roots5.2. A test case: The quartic; 6. Problems and questions; 7. Further reading; Lesson 9. The Search for Resolvents; 1. Coefficients and roots; 2. A unified approach to equations of all degrees; 2.1. A resolvent for the cubic equation; 3. A resolvent for the general quartic equation; 4. The state of polynomial algebra in 1770; 4.1. Seeking a resolvent for the quintic; 5. Permutations enter algebra; 6. Permutations of the variables in a function; 6.1.Two-valued functions; 7. Problems and questions; 8. Further reading; Part 4. Abstract Algebra Lesson 10. Existence and Constructibility of Roots |
| Record Nr. | UNINA-9910877703503321 |
|
Cooke Roger <1942->
|
||
| Hoboken, N.J., : Wiley-Interscience, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The history of mathematics : a brief course / / Roger L. Cooke
| The history of mathematics : a brief course / / Roger L. Cooke |
| Autore | Cooke Roger <1942-> |
| Edizione | [Third edition.] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : Wiley, , 2013 |
| Descrizione fisica | 1 online resource (1042 p.) |
| Disciplina | 510/.9 |
| Soggetto topico | Mathematics - History |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-118-46497-4
1-118-46029-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Title Page; Copyright; Preface; Changes from the Second Edition; Elementary Texts on the History of Mathematics; Part I: What is Mathematics?; Contents of Part I; Chapter 1: Mathematics and its History; 1.1 Two Ways to Look at the History of Mathematics; 1.2 The Origin of Mathematics; 1.3 The Philosophy of Mathematics; 1.4 Our Approach to the History of Mathematics; Questions for Reflection; Chapter 2: Proto-mathematics; 2.1 Number; 2.2 Shape; 2.3 Symbols; 2.4 Mathematical Reasoning; Problems and Questions; Part II: The Middle East, 2000-1500 BCE; Contents of Part II
Chapter 3: Overview of Mesopotamian Mathematics3.1 A Sketch of Two Millennia of Mesopotamian History; 3.2 Mathematical Cuneiform Tablets; 3.3 Systems of Measuring and Counting; 3.4 The Mesopotamian Numbering System; Problems and Questions; Chapter 4: Computations in Ancient Mesopotamia; 4.1 Arithmetic; 4.2 Algebra; Problems and Questions; Chapter 5: Geometry in Mesopotamia; 5.1 The Pythagorean Theorem; 5.2 Plane Figures; 5.3 Volumes; 5.4 Plimpton 322; Problems and Questions; Chapter 6: Egyptian Numerals and Arithmetic; 6.1 Sources; 6.2 The Rhind Papyrus; 6.3 Egyptian Arithmetic 6.4 ComputationProblems and Questions; Chapter 7: Algebra and Geometry in Ancient Egypt; 7.1 Algebra Problems in the Rhind Papyrus; 7.2 Geometry; 7.3 Areas; Problems and Questions; Part III: Greek Mathematics From 500 BCE to 500 CE; Contents of Part III; Chapter 8: An Overview of Ancient Greek Mathematics; 8.1 Sources; 8.2 General Features of Greek Mathematics; 8.3 Works and Authors; Questions; Chapter 9: Greek Number Theory; 9.1 The Euclidean Algorithm; 9.2 The Arithmetica of Nicomachus; 9.3 Euclid's Number Theory; 9.4 The Arithmetica of Diophantus; Problems and Questions Chapter 10: Fifth-Century Greek Geometry10.1 "Pythagorean" Geometry; 10.2 Challenge No. 1: Unsolved Problems; 10.3 Challenge No. 2: The Paradoxes of Zeno of Elea; 10.4 Challenge No. 3: Irrational Numbers and Incommensurable Lines; Problems and Questions; Chapter 11: Athenian Mathematics I: The Classical Problems; 11.1 Squaring the Circle; 11.2 Doubling the Cube; 11.3 Trisecting the Angle; Problems and Questions; Chapter 12: Athenian Mathematics II: Plato and Aristotle; 12.1 The Influence of Plato; 12.2 Eudoxan Geometry; 12.3 Aristotle; Problems and Questions; Chapter 13: Euclid of Alexandria 13.1 The Elements13.2 The Data; Problems and Questions; Chapter 14: Archimedes of Syracuse; 14.1 The Works of Archimedes; 14.2 The Surface of a Sphere; 14.3 The Archimedes Palimpsest; 14.4 Quadrature of the Parabola; Problems and Questions; Chapter 15: Apollonius of Perga; 15.1 History of the Conics; 15.2 Contents of the Conics; 15.3 Foci and the Three-and Four-line Locus; Problems and Questions; Chapter 16: Hellenistic and Roman Geometry; 16.1 Zenodorus; 16.2 The Parallel Postulate; 16.3 Heron; 16.4 Roman Civil Engineering; Problems and Questions Chapter 17: Ptolemy's Geography and Astronomy |
| Record Nr. | UNINA-9910462934303321 |
|
Cooke Roger <1942->
|
||
| Hoboken, New Jersey : , : Wiley, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The history of mathematics : a brief course / / Roger Cooke
| The history of mathematics : a brief course / / Roger Cooke |
| Autore | Cooke Roger <1942-> |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley-Interscience, c2005 |
| Descrizione fisica | 1 online resource (630 p.) |
| Disciplina | 510/.9 |
| Soggetto topico |
Mathematics - History
Mathematics |
| ISBN |
1-282-25340-9
9786613814050 1-118-03309-4 1-118-03024-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
The History of Mathematics: A Brief Course; Contents; Preface; Part 1. The World of Mathematics and the Mathematics of the World; Chapter 1. The Origin and Prehistory of Mathematics; 1. Numbers; 1.1. Animals' use of numbers; 1.2. Young children's use of numbers; 1.3. Archaeological evidence of counting; 2. Continuous magnitudes; 2.1. Perception of shape by animals; 2.2. Children's concepts of space; 2.3. Geometry in arts and crafts; 3. Symbols; 4. Mathematical inference; 4.1. Visual reasoning; 4.2. Chance and probability; Questions and problems; Chapter 2. Mathematical Cultures I
1. The motives for creating mathematics1.1. Pure versus applied mathematics; 2. India; 2.1. The Sulva Sutras; 2.2. Buddhist and Jaina mathematics; 2.3. The Bakshali Manuscript; 2.4. The siddhantas; 2.5. Aryabhata I; 2.6. Brahmagupta; 2.7. Bhaskara II; 2.8. Muslim India; 2.9. Indian mathematics in the colonial period and after; 3. China; 3.1. Works and authors; 3.2. China's encounter with Western mathematics; 4. Ancient Egypt; 5. Mesopotamia; 6. The Maya; 6.1. The Dresden Codex; Questions and problems; Chapter 3. Mathematical Cultures II; 1. Greek and Roman mathematics; 1.1. Sources 1.2. General features of Greek mathematics1.3. Works and authors; 2. Japan; 2.1. Chinese influence and calculating devices; 2.2. Japanese mathematicians and their works; 3. The Muslims; 3.1. Islamic science in general; 3.2. Some Muslim mathematicians and their works; 4. Europe; 4.1. Monasteries, schools, and universities; 4.2. The high Middle Ages; 4.3. Authors and works; 5. North America; 5.1. The United States and Canada before 1867; 5.2. The Canadian Federation and post Civil War United States; 5.3. Mexico; 6. Australia and New Zealand; 6.1. Colonial mathematics; 7. The modern era 7.1. Educational institutions7.2. Mathematical societies; 7.3. Journals; Questions and problems; Chapter 4. Women Mathematicians; 1. Individual achievements and obstacles to achievement; 1.1. Obstacles to mathematical careers for women; 2. Ancient women mathematicians; 3. Modern European women; 3.1. Continental mathematicians; 3.2. Nineteenth-century British women; 3.3. Four modern pioneers; 4. American women; 5. The situation today; Questions and problems; Part 2. Numbers; Chapter 5. Counting; 1. Number words; 2. Bases for counting; 2.1. Decimal systems; 2.2. Nondecimal systems 3. Counting around the world3.1. Egypt; 3.2. Mesopotamia; 3.3. India; 3.4. China; 3.5. Greece and Rome; 3.6. The Maya; 4. What was counted?; 4.1. Calendars; 4.2. Weeks; Questions and problems; Chapter 6. Calculation; 1. Egypt; 1.1. Multiplication and division; 1.2. ""Parts""; 1.3. Practical problems; 2. China; 2.1. Fractions and roots; 2.2. The Jiu Zhang Suanshu; 3. India; 4. Mesopotamia; 5. The ancient Greeks; 6. The Islamic world; 7. Europe; 8. The value of calculation; 9. Mechanical methods of computation; 9.1. Software: prosthaphaeresis and logarithms 9.2. Hardware: slide rules and calculating machines |
| Record Nr. | UNINA-9910139339003321 |
|
Cooke Roger <1942->
|
||
| Hoboken, N.J., : Wiley-Interscience, c2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||