دانلود کتاب Discrete Mathematics with Applications, Metric Version

فهرست مطالب :

Cover Contents Preface Chapter 1: Speaking Mathematically 1.1 Variables 1.2 The Language of Sets 1.3 The Language of Relations and Functions 1.4 The Language of Graphs Chapter 2: The Logic of Compound Statements 2.1 Logical Form and Logical Equivalence 2.2 Conditional Statements 2.3 Valid and Invalid Arguments 2.4 Application: Digital Logic Circuits 2.5 Application: Number Systems and Circuits for Addition Chapter 3: The Logic of Quantified Statements 3.1 Predicates and Quantified Statements I 3.2 Predicates and Quantified Statements II 3.3 Statements with Multiple Quantifiers 3.4 Arguments with Quantified Statements Chapter 4: Elementary Number Theory and Methods of Proof 4.1 Direct Proof and Counterexample I: Introduction 4.2 Direct Proof and Counterexample II: Writing Advice 4.3 Direct Proof and Counterexample III: Rational Numbers 4.4 Direct Proof and Counterexample IV: Divisibility 4.5 Direct Proof and Counterexample V: Division into Cases and the Quotient-Remainder Theorem 4.6 Direct Proof and Counterexample VI: Floor and Ceiling 4.7 Indirect Argument: Contradiction and Contraposition 4.8 Indirect Argument: Two Famous Theorems 4.9 Application: The Handshake Theorem 4.10 Application: Algorithms Chapter 5: Sequences, Mathematical Induction, and Recursion 5.1 Sequences 5.2 Mathematical Induction I: Proving Formulas 5.3 Mathematical Induction II: Applications 5.4 Strong Mathematical Induction and the Well-Ordering Principle for the Integers 5.5 Application: Correctness of Algorithms 5.6 Defining Sequences Recursively 5.7 Solving Recurrence Relations by Iteration 5.8 Second-Order Linear Homogeneous Recurrence Relations with Constant Coefficients 5.9 General Recursive Definitions and Structural Induction Chapter 6: Set Theory 6.1 Set Theory: Definitions and the Element Method of Proof 6.2 Properties of Sets 6.3 Disproofs and Algebraic Proofs 6.4 Boolean Algebras, Russell's Paradox, and the Halting Problem Chapter 7: Properties of Functions 7.1 Functions Defined on General Sets 7.2 One-to-One, Onto, and Inverse Functions 7.3 Composition of Functions 7.4 Cardinality with Applications to Computability Chapter 8: Properties of Relations 8.1 Relations on Sets 8.2 Reflexivity, Symmetry, and Transitivity 8.3 Equivalence Relations 8.4 Modular Arithmetic with Applications to Cryptography 8.5 Partial Order Relations Chapter 9: Counting and Probability 9.1 Introduction to Probability 9.2 Possibility Trees and the Multiplication Rule 9.3 Counting Elements of Disjoint Sets: The Addition Rule 9.4 The Pigeonhole Principle 9.5 Counting Subsets of a Set: Combinations 9.6 r-Combinations with Repetition Allowed 9.7 Pascal's Formula and the Binomial Theorem 9.8 Probability Axioms and Expected Value 9.9 Conditional Probability, Bayes' Formula, and Independent Events Chapter 10: Theory of Graphs and Trees 10.1 Trails, Paths, and Circuits 10.2 Matrix Representations of Graphs 10.3 Isomorphisms of Graphs 10.4 Trees: Examples and Basic Properties 10.5 Rooted Trees 10.6 Spanning Trees and a Shortest Path Algorithm Chapter 11: Analysis of Algorithm Efficiency 11.1 Real-Valued Functions of a Real Variable and Their Graphs 11.2 Big-O, Big-Omega, and Big-Theta Notations 11.3 Application: Analysis of Algorithm Efficiency I 11.4 Exponential and Logarithmic Functions: Graphs and Orders 11.5 Application: Analysis of Algorithm Efficiency II Chapter 12: Regular Expressions and Finite-State Automata 12.1 Formal Languages and Regular Expressions 12.2 Finite-State Automata 12.3 Simplifying Finite-State Automata Appendix A: Properties of the Real Numbers Appendix B: Solutions and Hints to Selected Exercises Index