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\BOOKMARK [0][-]{chapter*.1}{Acknowledgements}{}% 1
\BOOKMARK [0][-]{chapter*.2}{Preface}{}% 2
\BOOKMARK [0][-]{chapter.1}{Set\040Theory}{}% 3
\BOOKMARK [1][-]{section.1.1}{Set\040Notation\040and\040Relations}{chapter.1}% 4
\BOOKMARK [1][-]{section.1.2}{Basic\040Set\040Operations}{chapter.1}% 5
\BOOKMARK [1][-]{section.1.3}{Cartesian\040Products\040and\040Power\040Sets}{chapter.1}% 6
\BOOKMARK [1][-]{section.1.4}{Binary\040Representation\040of\040Positive\040Integers}{chapter.1}% 7
\BOOKMARK [1][-]{section.1.5}{Summation\040Notation\040and\040Generalizations}{chapter.1}% 8
\BOOKMARK [0][-]{chapter.2}{Combinatorics}{}% 9
\BOOKMARK [1][-]{section.2.1}{Basic\040Counting\040Techniques\040-\040The\040Rule\040of\040Products}{chapter.2}% 10
\BOOKMARK [1][-]{section.2.2}{Permutations}{chapter.2}% 11
\BOOKMARK [1][-]{section.2.3}{Partitions\040of\040Sets\040and\040the\040Law\040of\040Addition}{chapter.2}% 12
\BOOKMARK [1][-]{section.2.4}{Combinations\040and\040the\040Binomial\040Theorem}{chapter.2}% 13
\BOOKMARK [0][-]{chapter.3}{Logic}{}% 14
\BOOKMARK [1][-]{section.3.1}{Propositions\040and\040Logical\040Operators}{chapter.3}% 15
\BOOKMARK [1][-]{section.3.2}{Truth\040Tables\040and\040Propositions\040Generated\040by\040a\040Set}{chapter.3}% 16
\BOOKMARK [1][-]{section.3.3}{Equivalence\040and\040Implication}{chapter.3}% 17
\BOOKMARK [1][-]{section.3.4}{The\040Laws\040of\040Logic}{chapter.3}% 18
\BOOKMARK [1][-]{section.3.5}{Mathematical\040Systems\040and\040Proofs}{chapter.3}% 19
\BOOKMARK [1][-]{section.3.6}{Propositions\040over\040a\040Universe}{chapter.3}% 20
\BOOKMARK [1][-]{section.3.7}{Mathematical\040Induction}{chapter.3}% 21
\BOOKMARK [1][-]{section.3.8}{Quantifiers}{chapter.3}% 22
\BOOKMARK [1][-]{section.3.9}{A\040Review\040of\040Methods\040of\040Proof}{chapter.3}% 23
\BOOKMARK [0][-]{chapter.4}{More\040on\040Sets}{}% 24
\BOOKMARK [1][-]{section.4.1}{Methods\040of\040Proof\040for\040Sets}{chapter.4}% 25
\BOOKMARK [1][-]{section.4.2}{Laws\040of\040Set\040Theory}{chapter.4}% 26
\BOOKMARK [1][-]{section.4.3}{Minsets}{chapter.4}% 27
\BOOKMARK [1][-]{section.4.4}{The\040Duality\040Principle}{chapter.4}% 28
\BOOKMARK [0][-]{chapter.5}{Introduction\040to\040Matrix\040Algebra}{}% 29
\BOOKMARK [1][-]{section.5.1}{Basic\040Definitions\040and\040Operations}{chapter.5}% 30
\BOOKMARK [1][-]{section.5.2}{Special\040Types\040of\040Matrices}{chapter.5}% 31
\BOOKMARK [1][-]{section.5.3}{Laws\040of\040Matrix\040Algebra}{chapter.5}% 32
\BOOKMARK [1][-]{section.5.4}{Matrix\040Oddities}{chapter.5}% 33
\BOOKMARK [0][-]{chapter.6}{Relations}{}% 34
\BOOKMARK [1][-]{section.6.1}{Basic\040Definitions}{chapter.6}% 35
\BOOKMARK [1][-]{section.6.2}{Graphs\040of\040Relations\040on\040a\040Set}{chapter.6}% 36
\BOOKMARK [1][-]{section.6.3}{Properties\040of\040Relations}{chapter.6}% 37
\BOOKMARK [1][-]{section.6.4}{Matrices\040of\040Relations}{chapter.6}% 38
\BOOKMARK [1][-]{section.6.5}{Closure\040Operations\040on\040Relations}{chapter.6}% 39
\BOOKMARK [0][-]{chapter.7}{Functions}{}% 40
\BOOKMARK [1][-]{section.7.1}{Definition\040and\040Notation}{chapter.7}% 41
\BOOKMARK [1][-]{section.7.2}{Properties\040of\040Functions}{chapter.7}% 42
\BOOKMARK [1][-]{section.7.3}{Function\040Composition}{chapter.7}% 43
\BOOKMARK [0][-]{chapter.8}{Recursion\040and\040Recurrence\040Relations}{}% 44
\BOOKMARK [1][-]{section.8.1}{The\040Many\040Faces\040of\040Recursion}{chapter.8}% 45
\BOOKMARK [1][-]{section.8.2}{Sequences}{chapter.8}% 46
\BOOKMARK [1][-]{section.8.3}{Recurrence\040Relations}{chapter.8}% 47
\BOOKMARK [1][-]{section.8.4}{Some\040Common\040Recurrence\040Relations}{chapter.8}% 48
\BOOKMARK [1][-]{section.8.5}{Generating\040Functions}{chapter.8}% 49
\BOOKMARK [0][-]{chapter.9}{Graph\040Theory}{}% 50
\BOOKMARK [1][-]{section.9.1}{Graphs\040-\040General\040Introduction}{chapter.9}% 51
\BOOKMARK [1][-]{section.9.2}{Data\040Structures\040for\040Graphs}{chapter.9}% 52
\BOOKMARK [1][-]{section.9.3}{Connectivity}{chapter.9}% 53
\BOOKMARK [1][-]{section.9.4}{Traversals:\040Eulerian\040and\040Hamiltonian\040Graphs}{chapter.9}% 54
\BOOKMARK [1][-]{section.9.5}{Graph\040Optimization}{chapter.9}% 55
\BOOKMARK [1][-]{section.9.6}{Planarity\040and\040Colorings}{chapter.9}% 56
\BOOKMARK [0][-]{chapter.10}{Trees}{}% 57
\BOOKMARK [1][-]{section.10.1}{What\040Is\040a\040Tree?}{chapter.10}% 58
\BOOKMARK [1][-]{section.10.2}{Spanning\040Trees}{chapter.10}% 59
\BOOKMARK [1][-]{section.10.3}{Rooted\040Trees}{chapter.10}% 60
\BOOKMARK [1][-]{section.10.4}{Binary\040Trees}{chapter.10}% 61
\BOOKMARK [0][-]{chapter.11}{Algebraic\040Structures}{}% 62
\BOOKMARK [1][-]{section.11.1}{Operations}{chapter.11}% 63
\BOOKMARK [1][-]{section.11.2}{Algebraic\040Systems}{chapter.11}% 64
\BOOKMARK [1][-]{section.11.3}{Some\040General\040Properties\040of\040Groups}{chapter.11}% 65
\BOOKMARK [1][-]{section.11.4}{Greatest\040Common\040Divisors\040and\040the\040Integers\040Modulo\040n}{chapter.11}% 66
\BOOKMARK [1][-]{section.11.5}{Subsystems}{chapter.11}% 67
\BOOKMARK [1][-]{section.11.6}{Direct\040Products}{chapter.11}% 68
\BOOKMARK [1][-]{section.11.7}{Isomorphisms}{chapter.11}% 69
\BOOKMARK [0][-]{chapter.12}{More\040Matrix\040Algebra}{}% 70
\BOOKMARK [1][-]{section.12.1}{Systems\040of\040Linear\040Equations}{chapter.12}% 71
\BOOKMARK [1][-]{section.12.2}{Matrix\040Inversion}{chapter.12}% 72
\BOOKMARK [1][-]{section.12.3}{An\040Introduction\040to\040Vector\040Spaces}{chapter.12}% 73
\BOOKMARK [1][-]{section.12.4}{The\040Diagonalization\040Process}{chapter.12}% 74
\BOOKMARK [1][-]{section.12.5}{Some\040Applications}{chapter.12}% 75
\BOOKMARK [1][-]{section.12.6}{Linear\040Equations\040over\040the\040Integers\040Mod\0402}{chapter.12}% 76
\BOOKMARK [0][-]{chapter.13}{Boolean\040Algebra}{}% 77
\BOOKMARK [1][-]{section.13.1}{Posets\040Revisited}{chapter.13}% 78
\BOOKMARK [1][-]{section.13.2}{Lattices}{chapter.13}% 79
\BOOKMARK [1][-]{section.13.3}{Boolean\040Algebras}{chapter.13}% 80
\BOOKMARK [1][-]{section.13.4}{Atoms\040of\040a\040Boolean\040Algebra}{chapter.13}% 81
\BOOKMARK [1][-]{section.13.5}{Finite\040Boolean\040Algebras\040as\040n-tuples\040of\0400's\040and\0401's}{chapter.13}% 82
\BOOKMARK [1][-]{section.13.6}{Boolean\040Expressions}{chapter.13}% 83
\BOOKMARK [1][-]{section.13.7}{A\040Brief\040Introduction\040to\040Switching\040Theory\040and\040Logic\040Design}{chapter.13}% 84
\BOOKMARK [0][-]{chapter.14}{Monoids\040and\040Automata}{}% 85
\BOOKMARK [1][-]{section.14.1}{Monoids}{chapter.14}% 86
\BOOKMARK [1][-]{section.14.2}{Free\040Monoids\040and\040Languages}{chapter.14}% 87
\BOOKMARK [1][-]{section.14.3}{Automata,\040Finite-State\040Machines}{chapter.14}% 88
\BOOKMARK [1][-]{section.14.4}{The\040Monoid\040of\040a\040Finite-State\040Machine}{chapter.14}% 89
\BOOKMARK [1][-]{section.14.5}{The\040Machine\040of\040a\040Monoid}{chapter.14}% 90
\BOOKMARK [0][-]{chapter.15}{Group\040Theory\040and\040Applications}{}% 91
\BOOKMARK [1][-]{section.15.1}{Cyclic\040Groups}{chapter.15}% 92
\BOOKMARK [1][-]{section.15.2}{Cosets\040and\040Factor\040Groups}{chapter.15}% 93
\BOOKMARK [1][-]{section.15.3}{Permutation\040Groups}{chapter.15}% 94
\BOOKMARK [1][-]{section.15.4}{Normal\040Subgroups\040and\040Group\040Homomorphisms}{chapter.15}% 95
\BOOKMARK [1][-]{section.15.5}{Coding\040Theory,\040Group\040Codes}{chapter.15}% 96
\BOOKMARK [0][-]{chapter.16}{An\040Introduction\040to\040Rings\040and\040Fields}{}% 97
\BOOKMARK [1][-]{section.16.1}{Rings,\040Basic\040Definitions\040and\040Concepts}{chapter.16}% 98
\BOOKMARK [1][-]{section.16.2}{Fields}{chapter.16}% 99
\BOOKMARK [1][-]{section.16.3}{Polynomial\040Rings}{chapter.16}% 100
\BOOKMARK [1][-]{section.16.4}{Field\040Extensions}{chapter.16}% 101
\BOOKMARK [1][-]{section.16.5}{Power\040Series}{chapter.16}% 102
\BOOKMARK [0][-]{appendix.A}{Algorithms}{}% 103
\BOOKMARK [1][-]{section.A.1}{An\040Introduction\040to\040Algorithms}{appendix.A}% 104
\BOOKMARK [1][-]{section.A.2}{The\040Invariant\040Relation\040Theorem}{appendix.A}% 105
\BOOKMARK [0][-]{appendix.B}{Python\040and\040SageMath}{}% 106
\BOOKMARK [1][-]{section.B.1}{Python\040Iterators}{appendix.B}% 107
\BOOKMARK [1][-]{section.B.2}{Dictionaries}{appendix.B}% 108
\BOOKMARK [0][-]{appendix.C}{Determinants}{}% 109
\BOOKMARK [1][-]{section.C.1}{Definition}{appendix.C}% 110
\BOOKMARK [1][-]{section.C.2}{Computation}{appendix.C}% 111
\BOOKMARK [0][-]{appendix.D}{Hints\040and\040Solutions\040to\040Selected\040Exercises}{}% 112
\BOOKMARK [0][-]{appendix.E}{Notation}{}% 113
\BOOKMARK [0][-]{appendix*.1061}{References}{}% 114
\BOOKMARK [0][-]{section*.1062}{Index}{}% 115