My Library

University LibraryCatalogue

     
Limit search to items available for borrowing or consultation
Result Page: Previous Next
 
Look for full text

Search Discovery

Search Trove

Add record to RefWorks

PRINTED BOOKS
Author Tignol, Jean-Pierre.

Title Galois' theory of algebraic equations / Jean-Pierre Tignol.

Published Singapore ; River Edge, NJ : World Scientific, [2001]
©2001

Copies

Location Call No. Status
 UniM Bund  512.32 TIGN {Bund89 20200519}    AVAILABLE
Uniform title Leçons sur la théorie des équations. English
Physical description xiii, 333 pages : illustrations ; 22 cm
Bibliography Includes bibliographical references (pages 325-329) and index.
Contents Chapter 1 Quadratic Equations 1 -- 1.2 Babylonian algebra 2 -- 1.3 Greek algebra 5 -- 1.4 Arabic algebra 9 -- Chapter 2 Cubic Equations 13 -- 2.1 Priority disputes on the solution of cubic equations 13 -- 2.2 Cardano's formula 15 -- 2.3 Developments arising from Cardano's formula 16 -- Chapter 3 Quartic Equations 21 -- 3.1 Unnaturalness of quartic equations 21 -- 3.2 Ferrari's method 22 -- Chapter 4 Creation of Polynomials 25 -- 4.1 Rise of symbolic algebra 25 -- 4.2 Relations between roots and coefficients 30 -- Chapter 5 A Modern Approach to Polynomials 41 -- 5.2 Euclidean division 43 -- 5.3 Irreducible polynomials 48 -- 5.4 Roots 50 -- 5.5 Multiple roots and derivatives 53 -- 5.6 Common roots of two polynomials 56 -- Appendix Decomposition of rational fractions in sums of partial fractions 58 -- Chapter 6 Alternative Methods for Cubic and Quartic Equations 61 -- 6.1 Viete on cubic equations 61 -- 6.2 Descartes on quartic equations 64 -- 6.3 Rational solutions for equations with rational coefficients 65 -- 6.4 Tschirnhaus' method 67 -- Chapter 7 Roots of Unity 73 -- 7.2 Origin of de Moivre's formula 74 -- 7.3 Roots of unity 81 -- 7.4 Primitive roots and cyclotomic polynomials 86 -- Appendix Leibniz and Newton on the summation of series 92 -- Chapter 8 Symmetric Functions 97 -- 8.2 Waring's method 100 -- 8.3 Discriminant 106 -- Appendix Euler's summation of the series of reciprocals of perfect squares 110 -- Chapter 9 Fundamental Theorem of Algebra 115 -- 9.2 Girard's theorem 116 -- 9.3 Proof of the fundamental theorem 119 -- Chapter 10 Lagrange 123 -- 10.1 Theory of equations comes of age 123 -- 10.2 Lagrange's observations on previously known methods 127 -- 10.3 First results of group theory and Galois theory 138 -- Chapter 11 Vandermonde 153 -- 11.2 Solution of general equations 154 -- 11.3 Cyclotomic equations 158 -- Chapter 12 Gauss on Cyclotomic Equations 167 -- 12.2 Number-theoretic preliminaries 168 -- 12.3 Irreducibility of the cyclotomic polynomials of prime index 175 -- 12.4 Periods of cyclotomic equations 182 -- 12.5 Solvability by radicals 192 -- 12.6 Irreducibility of the cyclotomic polynomials 196 -- Appendix Ruler and compass construction of regular polygons 200 -- Chapter 13 Ruffini and Abel on General Equations 209 -- 13.2 Radical extensions 212 -- 13.3 Abel's theorem on natural irrationalities 218 -- 13.4 Proof of the unsolvability of general equations of degree higher than 4 225 -- Chapter 14 Galois 231 -- 14.2 Galois group of an equation 235 -- 14.3 Galois group under field extension 254 -- 14.4 Solvability by radicals 264 -- 14.5 Applications 281 -- Appendix Galois' description of groups of permutations 295 -- Appendix Fundamental theorem of Galois theory 307.
Subject Equations, Theory of.
Galois theory.
ISBN 9810245416 (paperback)