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Cajori F. — An introduction to the modern theory of equations
Cajori F. — An introduction to the modern theory of equations

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Название: An introduction to the modern theory of equations

Автор: 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: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1919

Количество страниц: 239

Добавлена в каталог: 07.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
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 $f(x)$      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 $f(x)=0$      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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