LEADER 05225nam 2200637 a 450 001 9910145585903321 005 20170815114847.0 010 $a1-281-28501-3 010 $a9786611285012 010 $a0-470-27798-X 010 $a0-470-27797-1 035 $a(CKB)1000000000407996 035 $a(EBL)335766 035 $a(OCoLC)228509122 035 $a(SSID)ssj0000123013 035 $a(PQKBManifestationID)11157703 035 $a(PQKBTitleCode)TC0000123013 035 $a(PQKBWorkID)10174110 035 $a(PQKB)11190487 035 $a(MiAaPQ)EBC335766 035 $a(EXLCZ)991000000000407996 100 $a20071004d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aClassical algebra$b[electronic resource] $eits nature, origins, and uses /$fRoger Cooke 210 $aHoboken, N.J. $cWiley-Interscience$dc2008 215 $a1 online resource (220 p.) 300 $aDescription based upon print version of record. 311 $a0-470-25952-3 320 $aIncludes bibliographical references and indexes. 327 $aClassical 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 327 $a3. 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 327 $a2. 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 327 $a3. 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 Vie?te and Cardano solutions; 4. The Tschirnhaus solution of the cubic equation; 5. Lagrange's reflections on the cubic equation 327 $a5.1. 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 327 $aLesson 10. Existence and Constructibility of Roots 330 $aThis insightful book combines the history, pedagogy, and popularization of algebra to present a unified discussion of the subject. Classical Algebra provides a complete and contemporary perspective on classical polynomial algebra through the exploration of how it was developed and how it exists today. With a focus on prominent areas such as the numerical solutions of equations, the systematic study of equations, and Galois theory, this book facilitates a thorough understanding of algebra and illustrates how the concepts of modern algebra originally developed from classical algebraic precurso 606 $aAlgebra 606 $aAlgebra$xHistory 606 $aAlgebraic logic 608 $aElectronic books. 615 0$aAlgebra. 615 0$aAlgebra$xHistory. 615 0$aAlgebraic logic. 676 $a512 700 $aCooke$b Roger$f1942-$0731611 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910145585903321 996 $aClassical algebra$92198560 997 $aUNINA