Preface ixThe companion web site xixTo the student xxiPRAT 1The foundations : logic , sets , and function1.Logic2.Propositional equivalences3.Predicates and quantifiers4.Sets 5.Set operations6.Functions7.Sequences and summations8.The growth of functionsPART 2The fundamentals : algorithms , the integers , and matrices1.Algorithms2.Complexity of algorithms3.The integers and division4.Integers and algorithms5.Applications of number theory6.MatricesPART 3Mathematical reasoning1.Methods of proof2.Mathematical induction3.Recursive definitions4.Recursive algorithms5.Program correctnessPART 4Counting1.The basics of counting2.The pigeonhole principle3.Permutations and combinations4.Discrete probability5.Probability theory6.Generalized permutations and combinations7.Generating permutations and combinationsPART 5Advanced counting techniques1.Recurrence relations2.Solving recurrence relations3.Divide-and-conquer relations4.Generating functions5.Inclusion-Exclusion6.Applications of inclusion-exclusionPART 6Relations1.Relations and their properties2.n-ary relations and their applications3.Representing relations4.Closures of relations5.Equivalence relations6.Partial orderingsPART 7Graphs1.Introduction to graphs2.Graph terminology3.Representing graphs and graph isomorphism4.Connectivity5.Euler and Hamilton paths6.Shortest path problems7.Planar graphs8.Graph coloringPART 8Trees1.Introduction to trees2.Applications of trees3.Tree traversal4.Trees and sorting5.Spanning trees6.Minimum spanning treesPART 9Boolean algebra1.Boolean functions2.Representing Boolean functions3.Logic gates4.Minimization of circuitsPART 10Modeling computation1.Languages and grammars2.Finite-state machines with output3.Finite-state machines with no output4.Language recognition5.Turing machinesApp
以下为对购买帮助不大的评价