A Abel, Nils Henrik, 56, 188, 217 Angle, 23 Archimedean Property of Real Numbers, 38, 103 Archimedes, 16 Ars Magna, 50 Artin, Emil, 2 B Binomial Theorem, 123 Bracket product, 100 C C,7 Cancellation Property, 53 Cardano's Formula, 51 Cardinality, 9 Cartan, Elle, 100 Cartan-Dieudonne' Theorem, 31 Cartesian product, 7 casus irreducibilis, 54 Cauchy, Augustin Louis, 78 Cauchy Counting Formula, 86 Cauchy cycle notation, 80 Cauchy's Theorem, 140 Cayley, Arthur, 139-140 Characteristic polynomial, 29 Chinese Remainder Theorem, 134-135 Classification of Semisimple Lie Algebras over C, 100 Closed, See operation Complex number, 60 conjugate of, 60 norm of, 60 polar form of, 61 trace of, 60 INDE X Congruence of geometric figures, 15, 17 of numbers, 124 Constructible angle, 173 number, 170 polygon, 173 Constructions, See Straight-Edge and Compass Constructions Coset (left, right), 137 D Dn,33 Da Coi, Zuanne, 57 Da Vinci, Leonardo, 41 Dedekind, Richard, 163 Del Ferro, Scipione, 50 De Moivre, Abraham, 61 De Moivre's Formula, 61, 63 Descartes, Rene', 7, 123 Descartes' Factor Theorem, 52-53 Descartes' Formula, 41^-2 Diophantus' Chord and Tangent Method, 56 Disquisitiones Arithmeticae, 170 Division Algorithm for numbers, 102 for polynomials, 117 Divisor, 104 common, 107 greatest common, 107 Domain, 7, 114 of numbers, 110 unique factorization (UFD), 163 Dual space, 214 dual basis, 214 E Eigenvalue, 29 Eigenvector, 29 223
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