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diff --git a/buch/buch.out b/buch/buch.out deleted file mode 100644 index 3a9971a..0000000 --- a/buch/buch.out +++ /dev/null @@ -1,234 +0,0 @@ -\BOOKMARK [-1][-]{part.1}{I Grundlagen}{}% 1 -\BOOKMARK [0][-]{chapter*.3}{Einleitung}{part.1}% 2 -\BOOKMARK [0][-]{chapter.1}{Zahlen }{part.1}% 3 -\BOOKMARK [1][-]{section.1.1}{Nat\374rliche Zahlen }{chapter.1}% 4 -\BOOKMARK [1][-]{section.1.2}{Ganze Zahlen }{chapter.1}% 5 -\BOOKMARK [1][-]{section.1.3}{Rationale Zahlen }{chapter.1}% 6 -\BOOKMARK [1][-]{section.1.4}{Reelle Zahlen }{chapter.1}% 7 -\BOOKMARK [1][-]{section.1.5}{Komplexe Zahlen }{chapter.1}% 8 -\BOOKMARK [0][-]{chapter.2}{Vektoren und Matrizen }{part.1}% 9 -\BOOKMARK [1][-]{section.2.1}{Lineare Algebra }{chapter.2}% 10 -\BOOKMARK [2][-]{subsection.2.1.1}{Vektoren }{section.2.1}% 11 -\BOOKMARK [2][-]{subsection.2.1.2}{Matrizen }{section.2.1}% 12 -\BOOKMARK [2][-]{subsection.2.1.3}{Gleichungssysteme }{section.2.1}% 13 -\BOOKMARK [2][-]{subsection.2.1.4}{Lineare Abbildungen }{section.2.1}% 14 -\BOOKMARK [1][-]{section.2.2}{Skalarprodukt }{chapter.2}% 15 -\BOOKMARK [2][-]{subsection.2.2.1}{Bilinearformen und Skalarprodukte }{section.2.2}% 16 -\BOOKMARK [2][-]{subsection.2.2.2}{Orthognormalbasis }{section.2.2}% 17 -\BOOKMARK [2][-]{subsection.2.2.3}{Symmetrische und selbstadjungierte Abbilungen }{section.2.2}% 18 -\BOOKMARK [2][-]{subsection.2.2.4}{Orthogonale und unit\344re Matrizen }{section.2.2}% 19 -\BOOKMARK [2][-]{subsection.2.2.5}{Orthogonale Unterr\344ume }{section.2.2}% 20 -\BOOKMARK [2][-]{subsection.2.2.6}{Andere Normen auf Vektorr\344umen }{section.2.2}% 21 -\BOOKMARK [1][-]{section.2.3}{Algebraische Strukturen }{chapter.2}% 22 -\BOOKMARK [2][-]{subsection.2.3.1}{Gruppen }{section.2.3}% 23 -\BOOKMARK [2][-]{subsection.2.3.2}{Ringe und Moduln }{section.2.3}% 24 -\BOOKMARK [2][-]{subsection.2.3.3}{Algebren }{section.2.3}% 25 -\BOOKMARK [2][-]{subsection.2.3.4}{K\366rper }{section.2.3}% 26 -\BOOKMARK [1][-]{section.2.4}{Hadamard-Algebra }{chapter.2}% 27 -\BOOKMARK [2][-]{subsection.2.4.1}{Hadamard-Produkt }{section.2.4}% 28 -\BOOKMARK [2][-]{subsection.2.4.2}{Hadamard-Produkt und Matrizenalgebra }{section.2.4}% 29 -\BOOKMARK [2][-]{subsection.2.4.3}{Weitere Verkn\374pfungen }{section.2.4}% 30 -\BOOKMARK [0][-]{chapter.3}{Polynome }{part.1}% 31 -\BOOKMARK [1][-]{section.3.1}{Definitionen }{chapter.3}% 32 -\BOOKMARK [2][-]{subsection.3.1.1}{Skalare }{section.3.1}% 33 -\BOOKMARK [2][-]{subsection.3.1.2}{Der Polynomring }{section.3.1}% 34 -\BOOKMARK [2][-]{subsection.3.1.3}{Grad }{section.3.1}% 35 -\BOOKMARK [2][-]{subsection.3.1.4}{Teilbarkeit }{section.3.1}% 36 -\BOOKMARK [2][-]{subsection.3.1.5}{Formale Potenzreihen }{section.3.1}% 37 -\BOOKMARK [1][-]{section.3.2}{Polynome als Vektoren }{chapter.3}% 38 -\BOOKMARK [2][-]{subsection.3.2.1}{Polynome beliebigen Grades }{section.3.2}% 39 -\BOOKMARK [2][-]{subsection.3.2.2}{Multiplikative Struktur }{section.3.2}% 40 -\BOOKMARK [1][-]{section.3.3}{Polynommultiplikation mit Matrizen }{chapter.3}% 41 -\BOOKMARK [1][-]{section.3.4}{Minimalpolynom }{chapter.3}% 42 -\BOOKMARK [0][-]{chapter.4}{Endliche K\366rper }{part.1}% 43 -\BOOKMARK [1][-]{section.4.1}{Der euklidische Algorithmus }{chapter.4}% 44 -\BOOKMARK [2][-]{subsection.4.1.1}{Ganze Zahlen}{section.4.1}% 45 -\BOOKMARK [2][-]{subsection.4.1.2}{Matrixschreibweise }{section.4.1}% 46 -\BOOKMARK [2][-]{subsection.4.1.3}{Vereinfachte Durchf\374hrung }{section.4.1}% 47 -\BOOKMARK [2][-]{subsection.4.1.4}{Polynome}{section.4.1}% 48 -\BOOKMARK [1][-]{section.4.2}{Galois-K\366rper }{chapter.4}% 49 -\BOOKMARK [2][-]{subsection.4.2.1}{Arithmetik modulo p }{section.4.2}% 50 -\BOOKMARK [2][-]{subsection.4.2.2}{Charakteristik }{section.4.2}% 51 -\BOOKMARK [1][-]{section.4.3}{Wurzeln }{chapter.4}% 52 -\BOOKMARK [2][-]{subsection.4.3.1}{Irreduzible Polynome }{section.4.3}% 53 -\BOOKMARK [2][-]{subsection.4.3.2}{K\366rpererweiterungen }{section.4.3}% 54 -\BOOKMARK [2][-]{subsection.4.3.3}{Zerf\344llungsk\366rper }{section.4.3}% 55 -\BOOKMARK [0][-]{chapter.5}{Eigenwerte und Eigenvektoren }{part.1}% 56 -\BOOKMARK [1][-]{section.5.1}{Grundlagen }{chapter.5}% 57 -\BOOKMARK [2][-]{subsection.5.1.1}{Kern und Bild von Matrixpotenzen }{section.5.1}% 58 -\BOOKMARK [2][-]{subsection.5.1.2}{Invariante Unterr\344ume }{section.5.1}% 59 -\BOOKMARK [2][-]{subsection.5.1.3}{Nilpotente Matrizen }{section.5.1}% 60 -\BOOKMARK [2][-]{subsection.5.1.4}{Eigenwerte und Eigenvektoren }{section.5.1}% 61 -\BOOKMARK [2][-]{subsection.5.1.5}{Verallgemeinerte Eigenr\344ume }{section.5.1}% 62 -\BOOKMARK [2][-]{subsection.5.1.6}{Zerlegung in invariante Unterr\344ume }{section.5.1}% 63 -\BOOKMARK [2][-]{subsection.5.1.7}{Das charakteristische Polynom }{section.5.1}% 64 -\BOOKMARK [1][-]{section.5.2}{Normalformen }{chapter.5}% 65 -\BOOKMARK [2][-]{subsection.5.2.1}{Diagonalform}{section.5.2}% 66 -\BOOKMARK [2][-]{subsection.5.2.2}{Jordan-Normalform }{section.5.2}% 67 -\BOOKMARK [2][-]{subsection.5.2.3}{Reelle Normalform }{section.5.2}% 68 -\BOOKMARK [2][-]{subsection.5.2.4}{Obere Hessenberg-Form }{section.5.2}% 69 -\BOOKMARK [1][-]{section.5.3}{Funktionen einer Matrix }{chapter.5}% 70 -\BOOKMARK [2][-]{subsection.5.3.1}{Polynom-Funktionen }{section.5.3}% 71 -\BOOKMARK [2][-]{subsection.5.3.2}{Approximation von f\(A\) }{section.5.3}% 72 -\BOOKMARK [2][-]{subsection.5.3.3}{Potenzreihen }{section.5.3}% 73 -\BOOKMARK [2][-]{subsection.5.3.4}{Gelfand-Radius und Eigenwerte }{section.5.3}% 74 -\BOOKMARK [1][-]{section.5.4}{Numerische Verfahren zur Eigenwertbestimmung }{chapter.5}% 75 -\BOOKMARK [1][-]{section.5.5}{Spektraltheorie }{chapter.5}% 76 -\BOOKMARK [0][-]{chapter.6}{Permutationen }{part.1}% 77 -\BOOKMARK [1][-]{section.6.1}{Permutationen einer endlichen Menge }{chapter.6}% 78 -\BOOKMARK [2][-]{subsection.6.1.1}{Permutationen als 2n-Matrizen}{section.6.1}% 79 -\BOOKMARK [2][-]{subsection.6.1.2}{Zyklenzerlegung }{section.6.1}% 80 -\BOOKMARK [2][-]{subsection.6.1.3}{Konjugierte Elemente in Sn}{section.6.1}% 81 -\BOOKMARK [1][-]{section.6.2}{Permutationen und Transpositionen }{chapter.6}% 82 -\BOOKMARK [2][-]{subsection.6.2.1}{Zyklus und Permutationen aus Transpositionen}{section.6.2}% 83 -\BOOKMARK [2][-]{subsection.6.2.2}{Signum einer Permutation}{section.6.2}% 84 -\BOOKMARK [1][-]{section.6.3}{Permutationsmatrizen }{chapter.6}% 85 -\BOOKMARK [2][-]{subsection.6.3.1}{Matrizen}{section.6.3}% 86 -\BOOKMARK [2][-]{subsection.6.3.2}{Transpositionen}{section.6.3}% 87 -\BOOKMARK [2][-]{subsection.6.3.3}{Determinante und Vorzeichen}{section.6.3}% 88 -\BOOKMARK [1][-]{section.6.4}{Determinante }{chapter.6}% 89 -\BOOKMARK [0][-]{chapter.7}{Matrizengruppen }{part.1}% 90 -\BOOKMARK [1][-]{section.7.1}{Symmetrien }{chapter.7}% 91 -\BOOKMARK [1][-]{section.7.2}{Lie-Gruppen }{chapter.7}% 92 -\BOOKMARK [1][-]{section.7.3}{Lie-Algebren }{chapter.7}% 93 -\BOOKMARK [1][-]{section.7.4}{Homogene R\344ume }{chapter.7}% 94 -\BOOKMARK [0][-]{chapter.8}{Graphen }{part.1}% 95 -\BOOKMARK [1][-]{section.8.1}{Beschreibung von Graphen mit Matrizen }{chapter.8}% 96 -\BOOKMARK [2][-]{subsection.8.1.1}{Definition von Graphen }{section.8.1}% 97 -\BOOKMARK [2][-]{subsection.8.1.2}{Inzidenzmatrix}{section.8.1}% 98 -\BOOKMARK [2][-]{subsection.8.1.3}{Die Adjazenzmatrix und Laplace-Matrix }{section.8.1}% 99 -\BOOKMARK [1][-]{section.8.2}{Spektrale Graphentheorie }{chapter.8}% 100 -\BOOKMARK [1][-]{section.8.3}{Wavelets auf Graphen }{chapter.8}% 101 -\BOOKMARK [2][-]{subsection.8.3.1}{Funktionen auf einem Graphen und die Laplace-Matrix}{section.8.3}% 102 -\BOOKMARK [2][-]{subsection.8.3.2}{Standardbasis und Eigenbasis }{section.8.3}% 103 -\BOOKMARK [2][-]{subsection.8.3.3}{Wavelet-Basen }{section.8.3}% 104 -\BOOKMARK [0][-]{chapter.9}{Wahrscheinlichkeitsmatrizen }{part.1}% 105 -\BOOKMARK [1][-]{section.9.1}{Google-Matrix }{chapter.9}% 106 -\BOOKMARK [2][-]{subsection.9.1.1}{Ein Modell f\374r Webseitenbesucher }{section.9.1}% 107 -\BOOKMARK [2][-]{subsection.9.1.2}{Wahrscheinlichkeitsinterpretation }{section.9.1}% 108 -\BOOKMARK [2][-]{subsection.9.1.3}{``Freier Wille'' }{section.9.1}% 109 -\BOOKMARK [2][-]{subsection.9.1.4}{Wahrscheinlichkeitsverteilung }{section.9.1}% 110 -\BOOKMARK [1][-]{section.9.2}{Diskrete Markov-Ketten und Wahrscheinlichkeitsmatrizen }{chapter.9}% 111 -\BOOKMARK [2][-]{subsection.9.2.1}{Markov-Eigenschaft}{section.9.2}% 112 -\BOOKMARK [2][-]{subsection.9.2.2}{Diskrete Markov-Kette}{section.9.2}% 113 -\BOOKMARK [2][-]{subsection.9.2.3}{Absorbierende Zust\344nde}{section.9.2}% 114 -\BOOKMARK [1][-]{section.9.3}{Positive Vektoren und Matrizen }{chapter.9}% 115 -\BOOKMARK [2][-]{subsection.9.3.1}{Elementare Eigenschaften }{section.9.3}% 116 -\BOOKMARK [2][-]{subsection.9.3.2}{Die verallgemeinerte Dreiecksungleichung }{section.9.3}% 117 -\BOOKMARK [2][-]{subsection.9.3.3}{Der Satz von Perron-Frobenius }{section.9.3}% 118 -\BOOKMARK [1][-]{section.9.4}{Das Paradoxon von Parrondo }{chapter.9}% 119 -\BOOKMARK [2][-]{subsection.9.4.1}{Die beiden Teilspiele }{section.9.4}% 120 -\BOOKMARK [2][-]{subsection.9.4.2}{Kombination der Spiele }{section.9.4}% 121 -\BOOKMARK [0][-]{chapter.10}{Anwendungen in Kryptographie und Codierungstheorie }{part.1}% 122 -\BOOKMARK [1][-]{section.10.1}{Arithmetik f\374r die Kryptographie }{chapter.10}% 123 -\BOOKMARK [2][-]{subsection.10.1.1}{Potenzieren }{section.10.1}% 124 -\BOOKMARK [2][-]{subsection.10.1.2}{Rechenoperationen in Fp }{section.10.1}% 125 -\BOOKMARK [2][-]{subsection.10.1.3}{Rechenoperationen in F2l }{section.10.1}% 126 -\BOOKMARK [1][-]{section.10.2}{Kryptographie und endliche K\366rper }{chapter.10}% 127 -\BOOKMARK [2][-]{subsection.10.2.1}{Potenzen in Fp und diskreter Logarithmus }{section.10.2}% 128 -\BOOKMARK [2][-]{subsection.10.2.2}{Diffie-Hellman-Schl\374sseltausch }{section.10.2}% 129 -\BOOKMARK [2][-]{subsection.10.2.3}{Elliptische Kurven }{section.10.2}% 130 -\BOOKMARK [1][-]{section.10.3}{Advanced Encryption Standard \205 AES }{chapter.10}% 131 -\BOOKMARK [1][-]{section.10.4}{Fehlerkorrigierende Codes nach Reed-Solomon }{chapter.10}% 132 -\BOOKMARK [2][-]{subsection.10.4.1}{Was ist ein Code? }{section.10.4}% 133 -\BOOKMARK [2][-]{subsection.10.4.2}{Reed-Solomon-Code }{section.10.4}% 134 -\BOOKMARK [2][-]{subsection.10.4.3}{Decodierung }{section.10.4}% 135 -\BOOKMARK [0][-]{chapter.11}{Homologie }{part.1}% 136 -\BOOKMARK [1][-]{section.11.1}{Simplexe und simpliziale Komplexe }{chapter.11}% 137 -\BOOKMARK [2][-]{subsection.11.1.1}{Simplexe und Rand }{section.11.1}% 138 -\BOOKMARK [2][-]{subsection.11.1.2}{Triangulation }{section.11.1}% 139 -\BOOKMARK [1][-]{section.11.2}{Kettenkomplexe }{chapter.11}% 140 -\BOOKMARK [2][-]{subsection.11.2.1}{Randoperator von Simplexen }{section.11.2}% 141 -\BOOKMARK [2][-]{subsection.11.2.2}{Kettenkomplexe und Morphismen }{section.11.2}% 142 -\BOOKMARK [1][-]{section.11.3}{Homologie }{chapter.11}% 143 -\BOOKMARK [2][-]{subsection.11.3.1}{Homologie eines Kettenkomplexes }{section.11.3}% 144 -\BOOKMARK [2][-]{subsection.11.3.2}{Induzierte Abbildung }{section.11.3}% 145 -\BOOKMARK [2][-]{subsection.11.3.3}{Homologie eines simplizialen Komplexes }{section.11.3}% 146 -\BOOKMARK [1][-]{section.11.4}{Exaktheit und die Mayer-Vietoris-Folge }{chapter.11}% 147 -\BOOKMARK [2][-]{subsection.11.4.1}{Kurze exakte Folgen von Kettenkomplexen }{section.11.4}% 148 -\BOOKMARK [2][-]{subsection.11.4.2}{Schlangenlemma und lange exakte Folgen }{section.11.4}% 149 -\BOOKMARK [2][-]{subsection.11.4.3}{Mayer-Vietoris-Folge }{section.11.4}% 150 -\BOOKMARK [1][-]{section.11.5}{Fixpunkte }{chapter.11}% 151 -\BOOKMARK [2][-]{subsection.11.5.1}{Lefshetz-Spurformel }{section.11.5}% 152 -\BOOKMARK [2][-]{subsection.11.5.2}{Brower-Fixpunktsatz }{section.11.5}% 153 -\BOOKMARK [-1][-]{part.2}{II Anwendungen und weiterf\374hrende Themen}{}% 154 -\BOOKMARK [0][-]{chapter.12}{Thema}{part.2}% 155 -\BOOKMARK [1][-]{section.12.1}{Teil 0}{chapter.12}% 156 -\BOOKMARK [1][-]{section.12.2}{Teil 1 }{chapter.12}% 157 -\BOOKMARK [2][-]{subsection.12.2.1}{De finibus bonorum et malorum }{section.12.2}% 158 -\BOOKMARK [1][-]{section.12.3}{Teil 2 }{chapter.12}% 159 -\BOOKMARK [2][-]{subsection.12.3.1}{De finibus bonorum et malorum }{section.12.3}% 160 -\BOOKMARK [1][-]{section.12.4}{Teil 3 }{chapter.12}% 161 -\BOOKMARK [2][-]{subsection.12.4.1}{De finibus bonorum et malorum }{section.12.4}% 162 -\BOOKMARK [0][-]{chapter.13}{Thema}{part.2}% 163 -\BOOKMARK [1][-]{section.13.1}{Teil 0}{chapter.13}% 164 -\BOOKMARK [1][-]{section.13.2}{Teil 1 }{chapter.13}% 165 -\BOOKMARK [2][-]{subsection.13.2.1}{De finibus bonorum et malorum }{section.13.2}% 166 -\BOOKMARK [1][-]{section.13.3}{Teil 2 }{chapter.13}% 167 -\BOOKMARK [2][-]{subsection.13.3.1}{De finibus bonorum et malorum }{section.13.3}% 168 -\BOOKMARK [1][-]{section.13.4}{Teil 3 }{chapter.13}% 169 -\BOOKMARK [2][-]{subsection.13.4.1}{De finibus bonorum et malorum }{section.13.4}% 170 -\BOOKMARK [0][-]{chapter.14}{Thema}{part.2}% 171 -\BOOKMARK [1][-]{section.14.1}{Teil 0}{chapter.14}% 172 -\BOOKMARK [1][-]{section.14.2}{Teil 1 }{chapter.14}% 173 -\BOOKMARK [2][-]{subsection.14.2.1}{De finibus bonorum et malorum }{section.14.2}% 174 -\BOOKMARK [1][-]{section.14.3}{Teil 2 }{chapter.14}% 175 -\BOOKMARK [2][-]{subsection.14.3.1}{De finibus bonorum et malorum }{section.14.3}% 176 -\BOOKMARK [1][-]{section.14.4}{Teil 3 }{chapter.14}% 177 -\BOOKMARK [2][-]{subsection.14.4.1}{De finibus bonorum et malorum }{section.14.4}% 178 -\BOOKMARK [0][-]{chapter.15}{Thema}{part.2}% 179 -\BOOKMARK [1][-]{section.15.1}{Teil 0}{chapter.15}% 180 -\BOOKMARK [1][-]{section.15.2}{Teil 1 }{chapter.15}% 181 -\BOOKMARK [2][-]{subsection.15.2.1}{De finibus bonorum et malorum }{section.15.2}% 182 -\BOOKMARK [1][-]{section.15.3}{Teil 2 }{chapter.15}% 183 -\BOOKMARK [2][-]{subsection.15.3.1}{De finibus bonorum et malorum }{section.15.3}% 184 -\BOOKMARK [1][-]{section.15.4}{Teil 3 }{chapter.15}% 185 -\BOOKMARK [2][-]{subsection.15.4.1}{De finibus bonorum et malorum }{section.15.4}% 186 -\BOOKMARK [0][-]{chapter.16}{Iterierte Funktionsschemata}{part.2}% 187 -\BOOKMARK [1][-]{section.16.1}{Teil 0}{chapter.16}% 188 -\BOOKMARK [1][-]{section.16.2}{Teil 1 }{chapter.16}% 189 -\BOOKMARK [2][-]{subsection.16.2.1}{De finibus bonorum et malorum }{section.16.2}% 190 -\BOOKMARK [1][-]{section.16.3}{Teil 2 }{chapter.16}% 191 -\BOOKMARK [2][-]{subsection.16.3.1}{De finibus bonorum et malorum }{section.16.3}% 192 -\BOOKMARK [1][-]{section.16.4}{Teil 3 }{chapter.16}% 193 -\BOOKMARK [2][-]{subsection.16.4.1}{De finibus bonorum et malorum }{section.16.4}% 194 -\BOOKMARK [0][-]{chapter.17}{McEliece-Kryptosystem}{part.2}% 195 -\BOOKMARK [1][-]{section.17.1}{Teil 0}{chapter.17}% 196 -\BOOKMARK [1][-]{section.17.2}{Teil 1 }{chapter.17}% 197 -\BOOKMARK [2][-]{subsection.17.2.1}{De finibus bonorum et malorum }{section.17.2}% 198 -\BOOKMARK [1][-]{section.17.3}{Teil 2 }{chapter.17}% 199 -\BOOKMARK [2][-]{subsection.17.3.1}{De finibus bonorum et malorum }{section.17.3}% 200 -\BOOKMARK [1][-]{section.17.4}{Teil 3 }{chapter.17}% 201 -\BOOKMARK [2][-]{subsection.17.4.1}{De finibus bonorum et malorum }{section.17.4}% 202 -\BOOKMARK [0][-]{chapter.18}{Thema}{part.2}% 203 -\BOOKMARK [1][-]{section.18.1}{Teil 0}{chapter.18}% 204 -\BOOKMARK [1][-]{section.18.2}{Teil 1 }{chapter.18}% 205 -\BOOKMARK [2][-]{subsection.18.2.1}{De finibus bonorum et malorum }{section.18.2}% 206 -\BOOKMARK [1][-]{section.18.3}{Teil 2 }{chapter.18}% 207 -\BOOKMARK [2][-]{subsection.18.3.1}{De finibus bonorum et malorum }{section.18.3}% 208 -\BOOKMARK [1][-]{section.18.4}{Teil 3 }{chapter.18}% 209 -\BOOKMARK [2][-]{subsection.18.4.1}{De finibus bonorum et malorum }{section.18.4}% 210 -\BOOKMARK [0][-]{chapter.19}{Thema}{part.2}% 211 -\BOOKMARK [1][-]{section.19.1}{Teil 0}{chapter.19}% 212 -\BOOKMARK [1][-]{section.19.2}{Teil 1 }{chapter.19}% 213 -\BOOKMARK [2][-]{subsection.19.2.1}{De finibus bonorum et malorum }{section.19.2}% 214 -\BOOKMARK [1][-]{section.19.3}{Teil 2 }{chapter.19}% 215 -\BOOKMARK [2][-]{subsection.19.3.1}{De finibus bonorum et malorum }{section.19.3}% 216 -\BOOKMARK [1][-]{section.19.4}{Teil 3 }{chapter.19}% 217 -\BOOKMARK [2][-]{subsection.19.4.1}{De finibus bonorum et malorum }{section.19.4}% 218 -\BOOKMARK [0][-]{chapter.20}{Thema}{part.2}% 219 -\BOOKMARK [1][-]{section.20.1}{Teil 0}{chapter.20}% 220 -\BOOKMARK [1][-]{section.20.2}{Teil 1 }{chapter.20}% 221 -\BOOKMARK [2][-]{subsection.20.2.1}{De finibus bonorum et malorum }{section.20.2}% 222 -\BOOKMARK [1][-]{section.20.3}{Teil 2 }{chapter.20}% 223 -\BOOKMARK [2][-]{subsection.20.3.1}{De finibus bonorum et malorum }{section.20.3}% 224 -\BOOKMARK [1][-]{section.20.4}{Teil 3 }{chapter.20}% 225 -\BOOKMARK [2][-]{subsection.20.4.1}{De finibus bonorum et malorum }{section.20.4}% 226 -\BOOKMARK [0][-]{chapter.21}{Thema}{part.2}% 227 -\BOOKMARK [1][-]{section.21.1}{Teil 0}{chapter.21}% 228 -\BOOKMARK [1][-]{section.21.2}{Teil 1 }{chapter.21}% 229 -\BOOKMARK [2][-]{subsection.21.2.1}{De finibus bonorum et malorum }{section.21.2}% 230 -\BOOKMARK [1][-]{section.21.3}{Teil 2 }{chapter.21}% 231 -\BOOKMARK [2][-]{subsection.21.3.1}{De finibus bonorum et malorum }{section.21.3}% 232 -\BOOKMARK [1][-]{section.21.4}{Teil 3 }{chapter.21}% 233 -\BOOKMARK [2][-]{subsection.21.4.1}{De finibus bonorum et malorum }{section.21.4}% 234 |