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Tignol J.-P. — Galois' Theory of Algebraic Equations
Tignol J.-P. — Galois' Theory of Algebraic Equations

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Название: Galois' Theory of Algebraic Equations

Автор: Tignol J.-P.

Аннотация:

As an example of general methodology, the evolution of the theory of equations from the Babylonian solution of a quadratic equation to its completion by Galois in 1830 is the focus of these lectures given to undergraduate math majors by Tignol (U. Catholique de Louvain, Belgium) from 1978-89. Includes technical appendices, exercises with selected solutions, and multilingual references from the 16th to 20th centuries. Earlier editions were published in 1988 by Longman and in 1980 in French.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 333

Добавлена в каталог: 02.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel, Niels-Henrik      210-212
Abelian group      242
Abel’s condition      231-232 242-243 293-294
Abel’s theorem on natural irrationalities      219-225
al-Khowarizmi, Mohammed ibn Musa      9-11 22
Alembeit, Jean Le Rond d’      115
Alternating group      228 276
Ap$\acute{e}$ry, Roger      112
Arabic algebra      9-12 22
Artin, Emil      305-306 309
Babylonian algebra      2-5 7 22
Bachet de M$\acute{e}$ziriac, Claude      87
Bernoulli, Jacques      110
Bernoulli, Nicholas      75
Bezout’s elimination theory      69
Bezout’s method      123-126 134-137
Bezout’s Theorem      87
Bolzano, Bernhard      121
Bombelli, Rafaele      20 26
Bourbaki, Nicolas      306
Cardano, Girolamo      13-15 21-22 25-26 40
Cardano’s Formula      15-20 78 128-132 277
Casus irreducibilis      19 109
Cauchy, Augustin-Louis      117 210-212 228
Common root of two polynomials      56
Complete solvability (by radicals)      264
Congruence (modulo an integer)      168
Constructible point      201
Coset      141 255
Cotes — de Moivre formula      73 76-81 83 94-95
Cotes, Roger      75-77
Cubic equation      13-20 61-63 70-71 109 125-126 128-134 156 277
Cyclic group      89
Cyclotomic equation      98 209 241 276 292;see
Cyclotomic polynomial (or equation)      90-92 231
Cyclotomy      83
De Moivre’s Formula      42;see Cotes-de Moivre formula monic polynomial
Dedekind, Richard      196 305 309
Degree (of a field extension)      307
Delambre, Jean-Baptiste      209
Derivative (of a polynomial)      53
Descartes, Ren$\acute{e}$      22 28-30 37
Descartes’ method for quartic equations      64-65
Diophantus of Alexandria      8 29
Discriminant      106 112-114 276-278 292
Eisenstein, Ferdinand Gotthold Max      176
Elementary symmetric polynomial      99
Elimination theory      56 68 88 124
Equation of squared differences      113
Euclid      5-8 11 22
Euclidean division property      43 87
Euclid’s algorithm      27 44
Euler, Leonhard      56 73 80 96 110 115 171 205 206
Euler’s method of a root of unity      86;see Bezout’s method exponent
Euler’s method of an element in a group      174;see Bezout’s method exponent
Euler’s method of an integer modulo a prime      172;see Bezout’s method exponent
Expression (solution) by radicals      213 264
Fermat prime      205
Fermat’s theorem      171 174 206
Ferraii’s method      22-24 134-135 262 277-278
Ferrari, Ludovico      21
Ferro, Scipione del      13
Fior, Antonio Maria      13
Foncenex, Daviet Francois de      116
Fourier, Jean-Baptiste Joseph      232
Fundamental theorem of algebra      36 74 80 104 115-122
Fundamental Theorem of Galois Theory      142 307-316
Fundamental theorem of symmetric fractions or polynomials      99-106
Galois extension (of fields)      307
Galois group      241-242
Galois group of a field extension      307
Galois group of a polynomial      237
Galois resolvent      236 245
Galois, $\acute{E}$variste      232-234 236 240 264 298
Gandz, Solomon      5
Gauss on cyclotomic equations      175-196 231
Gauss on number theory      168-175
Gauss on regular polygons      206
Gauss on the fundamental theorem of algebra      104 105 116 121 210
Gauss, Carl Friedrich      167
Girard, Albert      28 35-38 65
Girard’s theorem      35 116
greatest common divisor (GCD)      44
Greek algebra      5-9 21
Group early results      138-142 157 228
Group of arrangement      296
Group of substitutions      296
Height (of a radical extension)      213
Hero      8
Hippasus of Metapontum      6
Hudde, Johann      53
Ideal (in a commutative ring)      117
Index (of a subgroup)      142 266
Irreducibility      175-178 188 196-200
Irreducible polynomial      48
Isotropy group      139 282
Jacobson, Nathan      306
Khayyam, Omar      11
Kieman, Melvin      305
Knon, Wilbur Richard      6
Kronecker, Leopold      48 117 196 219 305
Lacroix, Sylvestre-Franfois      209
Lagrange resolvent      138 146-150 156 193 196 271
Lagrange, Joseph-Louis      100 116 126-146 153 209 285
Landau, Edmund      175
Leading coefficient      42
Lebesgue, Henri      153 164
Legendre, Adrien-Marie      209
Leibniz, Gottfried Wilhelm      67 74-75 92-93 110
Liouville, Joseph      233
Mertens, Franz      175
Minimum polynomial      181 236
Moivre, Abraham de      77-81 83 84 115 123 158
Multiple root      51 108
Newton, Isaac      38 74 75 93-94
Newton’s Formulas      38-39 110
Normal subgroup      255
Novy, Lubos      305
Nunes, Pedro      26 37
Orbit      279 281
Order of a group      139
Order of an element in a group      174
Pacioli, Luca      12
Period (of a cyclotomic equation)      184
Primitive root of a prime number      169
Primitive root of unity      86
Pythagoras      6
Quadratic equation      1-11
Quartic equation      21-24 64-65 126 134-135 156-157 262-264 277-278
Quotient ring (by an ideal)      117
Radical field extension      213
Rational equation      65-66
Rational root      65
Recorde, Robert      26
Regular polygon      83 167 200-206
Resolvent cubic equation      24 262-264 277
Resultant      56 69 96 113
Root of a complex number      80 81
Root of a polynomial      51
Root of unity      82
Ruffini, Paolo      209-212 219 225
Ruler and compass constructions      167 200-206 232
Schur, Issai      175
Solvability by radicals      83 158-164 192-196
Solvable group      265 294
Stevin, Simon      1 26-28 40
Symmetric group S$_{n}$      138
Symmetric polynomial (or rational fraction)      99
Tartaglia      13-15 Fontana Niccolo
Transitive (group of permutations)      279
Tschimhaus, Ehrenfried Walter      67-68
Tschimhaus’ method      68-71 132-134
van der Waerden, Bartel Leendert      305
van Roomen, Adriaan      30-34;see Romanus Adrianus
Vandermonde, Alexandre-Th$\acute{e}$ophile      100 153-164 182
Vi$\grave{e}$te, Fran$\k{c}$ois      1 29 32-35 40 61-63
Wantzel, Pierre Laurent      204 212 225
Waring, Edward      100-103 126
Weil, Andre      5 304
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