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Cajori F. — An introduction to the modern theory of equations
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Название: An introduction to the modern theory of equationsАвтор: Cajori F. Аннотация: The main difference between this text and others on the same subject, published in the English language, consists in the selection of the material. In proceeding from the elementary to the more advanced properties of equations, the subject of invariants and со variants is here omitted, to make room for a discussion of the elements of substitutions and substitution-groups, of domains of rationality, and of their application to equations. Thereby the reader acquires some familiarity with the fundamental results on the theory of equations, reached by Gauss, Abel, Galois, and Kronecker.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1919Количество страниц: 239Добавлена в каталог: 07.12.2009Операции: Положить на полку |
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Abel 233 Abelian equations 210 Abelian groups 210 Adjunction 135 151 219 Algebraic numbers 136 Algebraic solutions 60 219 Algebraic solutions, of cubic and quartic 68 Angle, trisection of 207 208 Bachmann 206 Ball 233 Beman, W. W. 206 Binomial equations 74 219 Biquadratic see Quartic Bjerknes, C. A. 233 Budan 50 Burkhardt 233 Burnside and Panton 79 233 Cantor 233 Cardan’s formula 69 Carvallo, M. E. 67 Cole, E. N. 189 Complex roots 6 42 58 67 232 Composite sub-groups 123 Conjugate sub-groups 122 Constructions by ruler and compasses 202 Continuity of 25 Cross-ratio 100 127 Cube, duplication of 207 Cubic, algebraic solution 68 Cubic, cyclic 196 Cubic, equation of squared differences of 38 Cubic, irreducible case 69 208 Cubic, nature of roots 41 Cubic, reducing cubic 72 Cubic, removal of second term 36 Cyclic equations 187 196 198 220 Cyclic function 115 127 128 133 Cyclic group 115 128 132 133 Cyclotomic equations 142 198 De Moivre’s Theorem 24 Delian problem 207 Descartes 50 Descartes’ Rule of Signs 7 50 Dialytic method of elimination 95 Discriminant 110 Discriminant, of 97 Discriminant, of cubic 40 Discriminant, of quadratic 97 Discriminant, of quartic 59 Division of the circle 75 203—206 Domain, conjugate 143 Domain, defined 134 Domain, degree of 142 Domain, Galois 153 Domain, normal 142 150 Domain, primitive 144 Domain, substitutions of 160 Duplication of the cube 207 Easton, B. S. 233 Eink 233 Eisenstein’s theorem 141 Eliminants 92 Equal roots 21 53 142 Equations, Abelian 210 Equations, algebraic 2 Equations, algebraic solution of 219 Equations, binomial 74 219 Equations, cubic 36 38 41 68 69 72 196 208 Equations, cyclic 187 220 Equations, cyclotomic 142 Equations, irreducible 137 Equations, melacyclic 223 Equations, quadratic 184 Equations, quartic 185 Equations, quintic 186 227 229 232 233 Equations, reciprocal 33 Euler’s cubic 71 Euler’s method of elimination 94 Euler’s solution of quartic 71 Fine, H. B. 233 FOURIER 50 Function, alternating 115 Function, cyclic 115 127 128 Function, def 1 Function, derived 18 Function, resolvents of Lagrange 129 Function, Sturm’s 50 Function, symmetric 13 84 114 Function, “belongs to 115 124 125 Galois 143 176 233 Galois’ theory of numbers 134 Galois’ theory of numbers, determination of 169 Galois’ theory of numbers, domain 153 Galois’ theory of numbers, groups 164 Galois’ theory of numbers, reduction of 174 178 Galois’ theory of numbers, resolvent 155 156 Gauss 26 206 Graphic representation 15 23 75 groups 112 Groups, Abelian 210 Groups, alternating 115 Groups, composite 123 Groups, cyclic 115 128 132 133 Groups, degree and order of 113 Groups, Galois 164 Groups, index of 122 Groups, list of 118 119 Groups, normal sub-groups 122 124 Groups, primitive and imprimitive 110 Groups, simple 122 Groups, sub-groups 120 Groups, symmetric 114 Groups, transitive and intransitive 116 hermite 137 Historical references 233 Homographic transformation 99 Horner’s method 63 Imaginary roots 6 42 58 67 232 Imprimitive group 116 127 Invariant sub-groups 122 Irreducible case in cubic 69 208 Klein, F. 206 233 kronecker 187 233 Lagrange 233 Lagrange, resolvents of 129 Lagrange, theorem of 176 Lemma 138 Lindemann 137 Marie 233 Matthiessen, L. 186 McClintock, E. 67 230 Metacyclic equations 223 227 Miller, G. A. 233 Moritz 26 Multiple roots 21 53 142 Netto 189 218 228 229 Newton 50 Newton’s formula for sums of pow¬ers 84 Newton’s method of approximation 66 Normal domain 142 145 150 Normal equations 149 151 Normal sub-groups 122 Normal sub-groups, of prime index 124 Numbers, algebraic 136 Numbers, conjugate 144 Numbers, primitive 144 147 Numbers, transcendental 137 Panton see Burnside and Panton Picard 233 Pierpont, J. 233 Primitive congruence roots 199 Primitive domains 144 147 Quadratic equation 184 Quartic, cyclic 198 Quartic, Euler’s solution 71 Quartic, groups of 172 173 Quartic, in the Galois theory 185 Quartic, nature of roots 56 Quartic, removal of second term 37 Quartic, symmetric functions of roots 91 Quartic, when solvable by square roots 72 Quintic 186 227 229 232 233 Radicals, solution by 60 Reciprocal equations 33 Reciprocal equations, depression of 81 Reducibility 134 135 139 Reducing cubic 72 Regular polygons, inscription of 20 Resolvents of Lagrange 129 Resultants 92 Rolle’s Theorem 49 Roots 2 Roots, complex 6 42 58 67 232 Roots, fractional 61 Roots, fundamental theorem 26 Roots, incommensurable 61 Roots, integral 62 Roots, multiple or equal roots 21 53 142 Roots, of unity 76 198 Roots, primitive 78 Roots, primitive congruence roots 199 Roots, reciprocal 33 Ruffini, P. 233 Runge, C. 229 Self-con juga/te sub-groups 122 Simple groups 122 Smith, D. E. 206 Solvable equations 223 Sturm 50 Sturm’s Theorem 50 51 Sturm’s theorem, applied to quartic 56 Sub-groups 120 Sub-groups, index of 122 Sub-groups, of prime index 124 substitution groups see Groups Substitutions 104 Substitutions, cyclic 107 Substitutions, even and odd 111 Substitutions, identical 106 Substitutions, inverse 106 Substitutions, laws of 105 Substitutions, product of 105 Sylvester 50 Sylvester’s method of elimination 95 Symmetric functions 13 84 114 Symmetric functions, elimination by 93 Symmetric functions, fundamental theorem 87 Symmetric group 114 Synthetic division 3 Taylor’s Theorem 19 Transcendental numbers 137 transpositions 109 Trigonometric solution of binomial equations 74 82 83 Trigonometric solution of irreducible case 70 Trisecting an angle 207 208 Tschirnhausen’s transformation 99 102 Unity, primitive roots of 78 Unity, roots of 76 198 Waring 50 Weber, H. 29 134 228 231 Zeuthen 233
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