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| -rw-r--r-- | buch/.gitignore | 16 | ||||
| -rw-r--r-- | buch/buch-blx.bib | 11 | ||||
| -rw-r--r-- | buch/buch.aux | 956 | ||||
| -rw-r--r-- | buch/buch.bbl | 20 | ||||
| -rw-r--r-- | buch/buch.blg | 74 | ||||
| -rw-r--r-- | buch/buch.idx | 167 | ||||
| -rw-r--r-- | buch/buch.log | 3498 | ||||
| -rw-r--r-- | buch/buch.out | 234 | ||||
| -rw-r--r-- | buch/buch.pdf | bin | 1412544 -> 2646094 bytes | |||
| -rw-r--r-- | buch/buch.run.xml | 521 | ||||
| -rw-r--r-- | buch/buch.synctex.gz | bin | 2189601 -> 0 bytes | |||
| -rw-r--r-- | buch/buch.toc | 394 | ||||
| -rw-r--r-- | buch/buch1-blx.aux | 15 | ||||
| -rw-r--r-- | buch/buch10-blx.aux | 13 | ||||
| -rw-r--r-- | buch/buch11-blx.aux | 13 | ||||
| -rw-r--r-- | buch/buch2-blx.aux | 13 | ||||
| -rw-r--r-- | buch/buch3-blx.aux | 13 | ||||
| -rw-r--r-- | buch/buch4-blx.aux | 13 | ||||
| -rw-r--r-- | buch/buch5-blx.aux | 13 | ||||
| -rw-r--r-- | buch/buch6-blx.aux | 12 | ||||
| -rw-r--r-- | buch/buch7-blx.aux | 13 | ||||
| -rw-r--r-- | buch/buch8-blx.aux | 13 | ||||
| -rw-r--r-- | buch/buch9-blx.aux | 13 | ||||
| -rw-r--r-- | buch/test1.tex | 93 |
24 files changed, 16 insertions, 6112 deletions
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[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 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[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 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-\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 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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}% 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Rechenoperationen}{19}{section*.29}% -\contentsline {subsubsection}{Algebraische Vollst\IeC {\"a}ndigkeit}{19}{section*.30}% -\contentsline {subsubsection}{Quaternionen und Octonionen}{20}{section*.31}% -\contentsline {chapter}{\numberline {2}Vektoren und Matrizen }{23}{chapter.2}% -\contentsline {section}{\numberline {2.1}Lineare Algebra }{23}{section.2.1}% -\contentsline {subsection}{\numberline {2.1.1}Vektoren }{23}{subsection.2.1.1}% -\contentsline {subsubsection}{Zeilen- und Spaltenvektoren}{23}{section*.32}% -\contentsline {subsubsection}{Standardbasisvektoren}{24}{section*.33}% -\contentsline {subsubsection}{Vektorraum}{24}{section*.34}% -\contentsline {subsubsection}{Gleichungssysteme in Vektorform}{25}{section*.35}% -\contentsline {subsubsection}{Lineare Abh\IeC {\"a}ngigkeit}{26}{section*.36}% -\contentsline {subsubsection}{Basis}{26}{section*.37}% -\contentsline {subsubsection}{Unterr\IeC {\"a}ume}{26}{section*.38}% -\contentsline {subsection}{\numberline {2.1.2}Matrizen 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-\contentsline {subsubsection}{Matrix}{33}{section*.51}% -\contentsline {subsubsection}{Basiswechsel}{33}{section*.52}% -\contentsline {subsubsection}{Umkehrabbbildung}{34}{section*.53}% -\contentsline {subsubsection}{Kern und Bild}{34}{section*.54}% -\contentsline {subsubsection}{Rang und Defekt}{35}{section*.55}% -\contentsline {subsubsection}{Quotient}{35}{section*.56}% -\contentsline {section}{\numberline {2.2}Skalarprodukt }{35}{section.2.2}% -\contentsline {subsection}{\numberline {2.2.1}Bilinearformen und Skalarprodukte }{36}{subsection.2.2.1}% -\contentsline {subsubsection}{Symmetrische bilineare Funktionen}{36}{section*.57}% -\contentsline {subsubsection}{Positiv definite Bilinearformen und Skalarprodukt}{36}{section*.58}% -\contentsline {subsubsection}{Dreiecksungleichung}{37}{section*.59}% -\contentsline {subsubsection}{Polarformel}{38}{section*.60}% -\contentsline {subsubsection}{Komplexe Vektorr\IeC {\"a}ume und Sesquilinearformen}{38}{section*.61}% -\contentsline 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{subsection}{\numberline {6.1.2}Zyklenzerlegung }{126}{subsection.6.1.2}% -\contentsline {subsection}{\numberline {6.1.3}Konjugierte Elemente in $S_n$}{127}{subsection.6.1.3}% -\contentsline {section}{\numberline {6.2}Permutationen und Transpositionen }{127}{section.6.2}% -\contentsline {subsection}{\numberline {6.2.1}Zyklus und Permutationen aus Transpositionen}{128}{subsection.6.2.1}% -\contentsline {subsection}{\numberline {6.2.2}Signum einer Permutation}{128}{subsection.6.2.2}% -\contentsline {section}{\numberline {6.3}Permutationsmatrizen }{129}{section.6.3}% -\contentsline {subsection}{\numberline {6.3.1}Matrizen}{130}{subsection.6.3.1}% -\contentsline {subsection}{\numberline {6.3.2}Transpositionen}{130}{subsection.6.3.2}% -\contentsline {subsection}{\numberline {6.3.3}Determinante und Vorzeichen}{131}{subsection.6.3.3}% -\contentsline {section}{\numberline {6.4}Determinante }{132}{section.6.4}% -\contentsline {chapter}{\numberline {7}Matrizengruppen }{133}{chapter.7}% -\contentsline {section}{\numberline {7.1}Symmetrien }{133}{section.7.1}% -\contentsline {section}{\numberline {7.2}Lie-Gruppen }{133}{section.7.2}% -\contentsline {section}{\numberline {7.3}Lie-Algebren }{133}{section.7.3}% -\contentsline {section}{\numberline {7.4}Homogene R\IeC {\"a}ume }{133}{section.7.4}% -\contentsline {chapter}{\numberline {8}Graphen }{135}{chapter.8}% -\contentsline {section}{\numberline {8.1}Beschreibung von Graphen mit Matrizen }{135}{section.8.1}% -\contentsline {subsection}{\numberline {8.1.1}Definition von Graphen }{136}{subsection.8.1.1}% -\contentsline {subsubsection}{Ungerichtete Graphen}{136}{section*.129}% -\contentsline {subsubsection}{Gerichtete Graphen}{136}{section*.130}% -\contentsline {subsubsection}{Adjazenzmatrix}{137}{section*.131}% -\contentsline {subsubsection}{Adjazenzmatrix und die Anzahl der Pfade}{138}{section*.134}% -\contentsline {subsubsection}{Beschriftete Graphen}{140}{section*.136}% -\contentsline {subsection}{\numberline {8.1.2}Inzidenzmatrix}{140}{subsection.8.1.2}% -\contentsline {subsubsection}{Beschriftete Graphen}{140}{section*.137}% -\contentsline {subsubsection}{Inzidenzmatrix und Adjazenzmatrix}{141}{section*.138}% -\contentsline {subsubsection}{Gradmatrix}{141}{section*.139}% -\contentsline {subsubsection}{Gerichtete Graphen}{141}{section*.140}% -\contentsline {subsubsection}{Anwendung: Netlist}{141}{section*.141}% -\contentsline {subsection}{\numberline {8.1.3}Die Adjazenzmatrix und Laplace-Matrix }{141}{subsection.8.1.3}% -\contentsline {section}{\numberline {8.2}Spektrale Graphentheorie }{142}{section.8.2}% -\contentsline {section}{\numberline {8.3}Wavelets auf Graphen }{142}{section.8.3}% -\contentsline {subsection}{\numberline {8.3.1}Funktionen auf einem Graphen und die Laplace-Matrix}{142}{subsection.8.3.1}% -\contentsline {subsection}{\numberline {8.3.2}Standardbasis und Eigenbasis }{143}{subsection.8.3.2}% -\contentsline {subsection}{\numberline {8.3.3}Wavelet-Basen }{144}{subsection.8.3.3}% -\contentsline {chapter}{\numberline {9}Wahrscheinlichkeitsmatrizen }{145}{chapter.9}% -\contentsline {section}{\numberline {9.1}Google-Matrix }{145}{section.9.1}% -\contentsline {subsection}{\numberline {9.1.1}Ein Modell f\IeC {\"u}r Webseitenbesucher }{146}{subsection.9.1.1}% -\contentsline {subsection}{\numberline {9.1.2}Wahrscheinlichkeitsinterpretation }{146}{subsection.9.1.2}% -\contentsline {subsubsection}{Ereignisse und Wahrscheinlichkeiten}{146}{section*.144}% -\contentsline {subsubsection}{Bedingte Wahrscheinlichkeit}{147}{section*.145}% -\contentsline {subsubsection}{Totale Wahrscheinlichkeit}{147}{section*.146}% -\contentsline {subsection}{\numberline {9.1.3}``Freier Wille'' }{148}{subsection.9.1.3}% -\contentsline {subsubsection}{Erweiterung der Link-Matrix}{148}{section*.147}% -\contentsline {subsubsection}{Die Google-Matrix}{149}{section*.148}% -\contentsline {subsection}{\numberline {9.1.4}Wahrscheinlichkeitsverteilung }{150}{subsection.9.1.4}% -\contentsline {subsubsection}{Station\IeC {\"a}re Verteilung}{150}{section*.149}% -\contentsline {subsubsection}{Potenzverfahren}{151}{section*.150}% -\contentsline {section}{\numberline {9.2}Diskrete Markov-Ketten und Wahrscheinlichkeitsmatrizen }{152}{section.9.2}% -\contentsline {subsection}{\numberline {9.2.1}Markov-Eigenschaft}{152}{subsection.9.2.1}% -\contentsline {subsubsection}{Ged\IeC {\"a}chtnislosigkeit}{152}{section*.151}% -\contentsline {subsubsection}{Die Chapman-Kolmogorov-Gleichung}{153}{section*.152}% -\contentsline {subsection}{\numberline {9.2.2}Diskrete Markov-Kette}{153}{subsection.9.2.2}% -\contentsline {subsubsection}{Zustandswahrscheinlichkeiten}{155}{section*.154}% -\contentsline {subsubsection}{Zeitunabh\IeC {\"a}ngige \IeC {\"U}bergangswahrscheinlichkeiten}{155}{section*.155}% -\contentsline {subsubsection}{Station\IeC {\"a}re Verteilung}{155}{section*.156}% -\contentsline {subsubsection}{Irreduzible Markov-Ketten}{156}{section*.157}% -\contentsline {subsubsection}{Die konvexe Menge der station\IeC {\"a}ren Verteilungen}{158}{section*.159}% -\contentsline {subsubsection}{Grenzverteilung}{158}{section*.161}% -\contentsline {subsubsection}{Erwartungswert und Varianz}{159}{section*.162}% -\contentsline {subsubsection}{Erwartungswert von Werten auf \IeC {\"U}berg\IeC {\"a}ngen}{159}{section*.163}% -\contentsline {subsection}{\numberline {9.2.3}Absorbierende Zust\IeC {\"a}nde}{160}{subsection.9.2.3}% -\contentsline {subsubsection}{Absorbtionszeit}{161}{section*.165}% -\contentsline {subsubsection}{Wartezeit}{162}{section*.166}% -\contentsline {section}{\numberline {9.3}Positive Vektoren und Matrizen }{162}{section.9.3}% -\contentsline {subsection}{\numberline {9.3.1}Elementare Eigenschaften }{163}{subsection.9.3.1}% -\contentsline {subsection}{\numberline {9.3.2}Die verallgemeinerte Dreiecksungleichung }{166}{subsection.9.3.2}% -\contentsline {subsection}{\numberline {9.3.3}Der Satz von Perron-Frobenius }{168}{subsection.9.3.3}% -\contentsline {section}{\numberline {9.4}Das Paradoxon von Parrondo }{172}{section.9.4}% -\contentsline {subsection}{\numberline {9.4.1}Die beiden Teilspiele }{172}{subsection.9.4.1}% -\contentsline {subsubsection}{Das Spiel $A$}{172}{section*.172}% -\contentsline {subsubsection}{Das Spiel $B$}{172}{section*.173}% -\contentsline {subsubsection}{\IeC {\"U}bergangsmatrix im Spiel $B$}{172}{section*.174}% -\contentsline {subsubsection}{Gewinnerwartung in einem Einzelspiel $B$}{173}{section*.176}% -\contentsline {subsubsection}{Das wiederholte Spiel $B$}{174}{section*.177}% -\contentsline {subsubsection}{Das modifizierte Spiel $\mathaccentV {tilde}07E{B}$}{175}{section*.178}% -\contentsline {subsubsection}{Gewinnerwartung im modifizierten Einzelspiel}{176}{section*.180}% -\contentsline {subsubsection}{Iteration des modifizierten Spiels}{177}{section*.181}% -\contentsline {subsection}{\numberline {9.4.2}Kombination der Spiele }{177}{subsection.9.4.2}% -\contentsline {subsubsection}{Das Spiel $C$}{178}{section*.182}% -\contentsline {subsubsection}{Das iterierte Spiel $C$}{178}{section*.183}% -\contentsline {chapter}{\numberline {10}Anwendungen in Kryptographie und Codierungstheorie }{179}{chapter.10}% -\contentsline {section}{\numberline {10.1}Arithmetik f\IeC {\"u}r die Kryptographie }{179}{section.10.1}% -\contentsline {subsection}{\numberline {10.1.1}Potenzieren }{179}{subsection.10.1.1}% -\contentsline {subsection}{\numberline {10.1.2}Rechenoperationen in $\mathbb {F}_p$ }{179}{subsection.10.1.2}% -\contentsline {subsection}{\numberline {10.1.3}Rechenoperationen in $\mathbb {F}_{2^l}$ }{179}{subsection.10.1.3}% -\contentsline {section}{\numberline {10.2}Kryptographie und endliche K\IeC {\"o}rper }{179}{section.10.2}% -\contentsline {subsection}{\numberline {10.2.1}Potenzen in $\mathbb {F}_p$ und diskreter Logarithmus }{179}{subsection.10.2.1}% -\contentsline {subsection}{\numberline {10.2.2}Diffie-Hellman-Schl\IeC {\"u}sseltausch }{181}{subsection.10.2.2}% -\contentsline {subsection}{\numberline {10.2.3}Elliptische Kurven }{181}{subsection.10.2.3}% -\contentsline {subsubsection}{Elliptische Kurven}{182}{section*.185}% -\contentsline {subsubsection}{Geometrische Definition der Gruppenoperation}{183}{section*.187}% -\contentsline {subsubsection}{Gruppenoperation, algebraische Konstruktion}{184}{section*.188}% -\contentsline {subsubsection}{Beispiele}{187}{section*.189}% -\contentsline {subsubsection}{Diffie-Hellman in einer elliptischen Kurve}{187}{section*.190}% -\contentsline {section}{\numberline {10.3}Advanced Encryption Standard -- AES }{187}{section.10.3}% -\contentsline {section}{\numberline {10.4}Fehlerkorrigierende Codes nach Reed-Solomon }{187}{section.10.4}% -\contentsline {subsection}{\numberline {10.4.1}Was ist ein Code? }{188}{subsection.10.4.1}% -\contentsline {subsection}{\numberline {10.4.2}Reed-Solomon-Code }{188}{subsection.10.4.2}% -\contentsline {subsection}{\numberline {10.4.3}Decodierung }{188}{subsection.10.4.3}% -\contentsline {chapter}{\numberline {11}Homologie }{189}{chapter.11}% -\contentsline {section}{\numberline {11.1}Simplexe und simpliziale Komplexe }{189}{section.11.1}% -\contentsline {subsection}{\numberline {11.1.1}Simplexe und Rand }{189}{subsection.11.1.1}% -\contentsline {subsubsection}{Rand eines Dreiecks}{189}{section*.193}% -\contentsline {subsubsection}{Simplizes}{190}{section*.194}% -\contentsline {subsubsection}{Rechnen mit Simplizes}{191}{section*.195}% -\contentsline {subsubsection}{Rand eines Simplex}{191}{section*.196}% -\contentsline {subsection}{\numberline {11.1.2}Triangulation }{192}{subsection.11.1.2}% -\contentsline {section}{\numberline {11.2}Kettenkomplexe }{192}{section.11.2}% -\contentsline {subsection}{\numberline {11.2.1}Randoperator von Simplexen }{192}{subsection.11.2.1}% -\contentsline {subsection}{\numberline {11.2.2}Kettenkomplexe und Morphismen }{192}{subsection.11.2.2}% -\contentsline {section}{\numberline {11.3}Homologie }{192}{section.11.3}% -\contentsline {subsection}{\numberline {11.3.1}Homologie eines Kettenkomplexes }{192}{subsection.11.3.1}% -\contentsline {subsection}{\numberline {11.3.2}Induzierte Abbildung }{192}{subsection.11.3.2}% -\contentsline {subsection}{\numberline {11.3.3}Homologie eines simplizialen Komplexes }{192}{subsection.11.3.3}% -\contentsline {section}{\numberline {11.4}Exaktheit und die Mayer-Vietoris-Folge }{192}{section.11.4}% -\contentsline {subsection}{\numberline {11.4.1}Kurze exakte Folgen von Kettenkomplexen }{192}{subsection.11.4.1}% -\contentsline {subsection}{\numberline {11.4.2}Schlangenlemma und lange exakte Folgen }{192}{subsection.11.4.2}% -\contentsline {subsection}{\numberline {11.4.3}Mayer-Vietoris-Folge }{192}{subsection.11.4.3}% -\contentsline {section}{\numberline {11.5}Fixpunkte }{192}{section.11.5}% -\contentsline {subsection}{\numberline {11.5.1}Lefshetz-Spurformel }{192}{subsection.11.5.1}% -\contentsline {subsection}{\numberline {11.5.2}Brower-Fixpunktsatz }{192}{subsection.11.5.2}% -\contentsline {part}{II\hspace {1em}Anwendungen und weiterf\IeC {\"u}hrende Themen}{193}{part.2}% -\contentsline {chapter}{\numberline {12}Thema}{197}{chapter.12}% -\contentsline {section}{\numberline {12.1}Teil 0}{197}{section.12.1}% -\contentsline {section}{\numberline {12.2}Teil 1 }{197}{section.12.2}% -\contentsline {subsection}{\numberline {12.2.1}De finibus bonorum et malorum }{198}{subsection.12.2.1}% -\contentsline {section}{\numberline {12.3}Teil 2 }{198}{section.12.3}% -\contentsline {subsection}{\numberline {12.3.1}De finibus bonorum et malorum }{198}{subsection.12.3.1}% -\contentsline {section}{\numberline {12.4}Teil 3 }{199}{section.12.4}% -\contentsline {subsection}{\numberline {12.4.1}De finibus bonorum et malorum }{199}{subsection.12.4.1}% -\contentsline {chapter}{\numberline {13}Thema}{201}{chapter.13}% -\contentsline {section}{\numberline {13.1}Teil 0}{201}{section.13.1}% -\contentsline {section}{\numberline {13.2}Teil 1 }{201}{section.13.2}% -\contentsline {subsection}{\numberline {13.2.1}De finibus bonorum et malorum }{202}{subsection.13.2.1}% -\contentsline {section}{\numberline {13.3}Teil 2 }{202}{section.13.3}% -\contentsline {subsection}{\numberline {13.3.1}De finibus bonorum et malorum }{202}{subsection.13.3.1}% -\contentsline {section}{\numberline {13.4}Teil 3 }{203}{section.13.4}% -\contentsline {subsection}{\numberline {13.4.1}De finibus bonorum et malorum }{203}{subsection.13.4.1}% -\contentsline {chapter}{\numberline {14}Thema}{205}{chapter.14}% -\contentsline {section}{\numberline {14.1}Teil 0}{205}{section.14.1}% -\contentsline {section}{\numberline {14.2}Teil 1 }{205}{section.14.2}% -\contentsline {subsection}{\numberline {14.2.1}De finibus bonorum et malorum }{206}{subsection.14.2.1}% -\contentsline {section}{\numberline {14.3}Teil 2 }{206}{section.14.3}% -\contentsline {subsection}{\numberline {14.3.1}De finibus bonorum et malorum }{206}{subsection.14.3.1}% -\contentsline {section}{\numberline {14.4}Teil 3 }{207}{section.14.4}% -\contentsline {subsection}{\numberline {14.4.1}De finibus bonorum et malorum }{207}{subsection.14.4.1}% -\contentsline {chapter}{\numberline {15}Thema}{209}{chapter.15}% -\contentsline {section}{\numberline {15.1}Teil 0}{209}{section.15.1}% -\contentsline {section}{\numberline {15.2}Teil 1 }{209}{section.15.2}% -\contentsline {subsection}{\numberline {15.2.1}De finibus bonorum et malorum }{210}{subsection.15.2.1}% -\contentsline {section}{\numberline {15.3}Teil 2 }{210}{section.15.3}% -\contentsline {subsection}{\numberline {15.3.1}De finibus bonorum et malorum }{210}{subsection.15.3.1}% -\contentsline {section}{\numberline {15.4}Teil 3 }{211}{section.15.4}% -\contentsline {subsection}{\numberline {15.4.1}De finibus bonorum et malorum }{211}{subsection.15.4.1}% -\contentsline {chapter}{\numberline {16}Iterierte Funktionsschemata}{213}{chapter.16}% -\contentsline {section}{\numberline {16.1}Teil 0}{213}{section.16.1}% 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It will be recreated as -% required. -% -\relax -\bibstyle{biblatex} -\bibdata{buch-blx,chapters/references,papers/verkehr/references,papers/multiplikation/references,papers/punktgruppen/references,papers/reedsolomon/references,papers/ifs/references,papers/mceliece/references,papers/clifford/references,papers/spannung/references,papers/erdbeben/references} -\citation{biblatex-control} -\citation{multiplikation:bibtex} diff --git a/buch/buch4-blx.aux b/buch/buch4-blx.aux deleted file mode 100644 index 83be392..0000000 --- a/buch/buch4-blx.aux +++ /dev/null @@ -1,13 +0,0 @@ -% $ biblatex auxiliary file $ -% $ biblatex bbl format version 3.1 $ -% Do not modify this file! -% -% This is an auxiliary file used by the 'biblatex' package. -% This file may safely be deleted. It will be recreated as -% required. -% -\relax -\bibstyle{biblatex} -\bibdata{buch-blx,chapters/references,papers/verkehr/references,papers/multiplikation/references,papers/punktgruppen/references,papers/reedsolomon/references,papers/ifs/references,papers/mceliece/references,papers/clifford/references,papers/spannung/references,papers/erdbeben/references} -\citation{biblatex-control} -\citation{punktgruppen:bibtex} diff --git a/buch/buch5-blx.aux b/buch/buch5-blx.aux deleted file mode 100644 index 437cc2b..0000000 --- a/buch/buch5-blx.aux +++ /dev/null @@ -1,13 +0,0 @@ -% $ biblatex auxiliary file $ -% $ biblatex bbl format version 3.1 $ -% Do not modify this file! -% -% This is an auxiliary file used by the 'biblatex' package. -% This file may safely be deleted. It will be recreated as -% required. -% -\relax -\bibstyle{biblatex} -\bibdata{buch-blx,chapters/references,papers/verkehr/references,papers/multiplikation/references,papers/punktgruppen/references,papers/reedsolomon/references,papers/ifs/references,papers/mceliece/references,papers/clifford/references,papers/spannung/references,papers/erdbeben/references} -\citation{biblatex-control} -\citation{reedsolomon:bibtex} diff --git a/buch/buch6-blx.aux b/buch/buch6-blx.aux deleted file mode 100644 index 2ae8165..0000000 --- a/buch/buch6-blx.aux +++ /dev/null @@ -1,12 +0,0 @@ -% $ biblatex auxiliary file $ -% $ biblatex bbl format version 3.1 $ -% Do not modify this file! -% -% This is an auxiliary file used by the 'biblatex' package. -% This file may safely be deleted. It will be recreated as -% required. -% -\relax -\bibstyle{biblatex} -\bibdata{buch-blx,chapters/references,papers/verkehr/references,papers/multiplikation/references,papers/punktgruppen/references,papers/reedsolomon/references,papers/ifs/references,papers/mceliece/references,papers/clifford/references,papers/spannung/references,papers/erdbeben/references} -\citation{biblatex-control} diff --git a/buch/buch7-blx.aux b/buch/buch7-blx.aux deleted file mode 100644 index 184f205..0000000 --- a/buch/buch7-blx.aux +++ /dev/null @@ -1,13 +0,0 @@ -% $ biblatex auxiliary file $ -% $ biblatex bbl format version 3.1 $ -% Do not modify this file! -% -% This is an auxiliary file used by the 'biblatex' package. -% This file may safely be deleted. It will be recreated as -% required. -% -\relax -\bibstyle{biblatex} -\bibdata{buch-blx,chapters/references,papers/verkehr/references,papers/multiplikation/references,papers/punktgruppen/references,papers/reedsolomon/references,papers/ifs/references,papers/mceliece/references,papers/clifford/references,papers/spannung/references,papers/erdbeben/references} -\citation{biblatex-control} -\citation{mceliece:bibtex} diff --git a/buch/buch8-blx.aux b/buch/buch8-blx.aux deleted file mode 100644 index 5b23357..0000000 --- a/buch/buch8-blx.aux +++ /dev/null @@ -1,13 +0,0 @@ -% $ biblatex auxiliary file $ -% $ biblatex bbl format version 3.1 $ -% Do not modify this file! -% -% This is an auxiliary file used by the 'biblatex' package. -% This file may safely be deleted. It will be recreated as -% required. -% -\relax -\bibstyle{biblatex} -\bibdata{buch-blx,chapters/references,papers/verkehr/references,papers/multiplikation/references,papers/punktgruppen/references,papers/reedsolomon/references,papers/ifs/references,papers/mceliece/references,papers/clifford/references,papers/spannung/references,papers/erdbeben/references} -\citation{biblatex-control} -\citation{clifford:bibtex} diff --git a/buch/buch9-blx.aux b/buch/buch9-blx.aux deleted file mode 100644 index 20f2950..0000000 --- a/buch/buch9-blx.aux +++ /dev/null @@ -1,13 +0,0 @@ -% $ biblatex auxiliary file $ -% $ biblatex bbl format version 3.1 $ -% Do not modify this file! -% -% This is an auxiliary file used by the 'biblatex' package. -% This file may safely be deleted. It will be recreated as -% required. -% -\relax -\bibstyle{biblatex} -\bibdata{buch-blx,chapters/references,papers/verkehr/references,papers/multiplikation/references,papers/punktgruppen/references,papers/reedsolomon/references,papers/ifs/references,papers/mceliece/references,papers/clifford/references,papers/spannung/references,papers/erdbeben/references} -\citation{biblatex-control} -\citation{spannung:bibtex} diff --git a/buch/test1.tex b/buch/test1.tex deleted file mode 100644 index 8345230..0000000 --- a/buch/test1.tex +++ /dev/null @@ -1,93 +0,0 @@ -% -% test1.tex -- Test 1 -% -% (c) 2012 Prof. Dr. Andreas Mueller, HSR -% -%\documentclass[a4paper,12pt]{book} -\documentclass[a4paper,12pt]{article} -\usepackage{geometry} -\geometry{papersize={210mm,297mm},total={165mm,260mm}} -\usepackage{ngerman} -\usepackage[utf8]{inputenc} -\usepackage[T1]{fontenc} -\usepackage{times} -\usepackage{amsmath} -\usepackage{amssymb} -\usepackage{amsfonts} -\usepackage{amsthm} -\usepackage{graphicx} -\usepackage{fancyhdr} -\usepackage{textcomp} -\usepackage[all]{xy} -\usepackage{txfonts} -\usepackage{alltt} -\usepackage{verbatim} -\usepackage{paralist} -\usepackage{makeidx} -\usepackage{array} -\usepackage{hyperref} -\usepackage{caption} -\usepackage{subcaption} -\usepackage{standalone} -\usepackage{environ} -\usepackage{tikz} -\input{../common/linsys.tex} -\newcounter{beispiel} -\newenvironment{beispiele}{ -\bgroup\smallskip\parindent0pt\bf Beispiele\egroup - -\begin{list}{\arabic{beispiel}.} - {\usecounter{beispiel} - \setlength{\labelsep}{5mm} - \setlength{\rightmargin}{0pt} -}}{\end{list}} -\newcounter{uebungsaufgabe} -% environment fuer uebungsaufgaben -\newenvironment{uebungsaufgaben}{ -\begin{list}{\arabic{uebungsaufgabe}.} - {\usecounter{uebungsaufgabe} - \setlength{\labelwidth}{2cm} - \setlength{\leftmargin}{0pt} - \setlength{\labelsep}{5mm} - \setlength{\rightmargin}{0pt} - \setlength{\itemindent}{0pt} -}}{\end{list}\vfill\pagebreak} -\newenvironment{teilaufgaben}{ -\begin{enumerate} -\renewcommand{\labelenumi}{\alph{enumi})} -}{\end{enumerate}} -% Loesung -\NewEnviron{loesung}{% -\begin{proof}[L"osung]% -\renewcommand{\qedsymbol}{$\bigcirc$} -\BODY -\end{proof}} -\NewEnviron{bewertung}{\relax} -\NewEnviron{diskussion}{ -\BODY -} -\RenewEnviron{loesung}{\relax} -\RenewEnviron{diskussion}{\relax} -\newenvironment{hinweis}{% -\renewcommand{\qedsymbol}{} -\begin{proof}[Hinweis]}{\end{proof}} - -\begin{document} -{\parindent0pt\hbox to\hsize{% -Name: \hbox to7cm{\dotfill} Vorname: \dotfill}} -\vspace{0.5cm} - -\section*{Kurztest 1} - -\begin{uebungsaufgaben} - -\item -\input chapters/30-endlichekoerper/uebungsaufgaben/3003.tex -\item -\input chapters/30-endlichekoerper/uebungsaufgaben/3004.tex -\item -\input chapters/30-endlichekoerper/uebungsaufgaben/3005.tex - -\end{uebungsaufgaben} - -\end{document} |