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## Chapter content of Discrete mathematics schaum series pdf-

CHAPTER 1 : Set Theory

1.1 Introduction | 1.2 Sets and Elements, Subsets | 1.3 Venn Diagrams | 1.4 Set Operations | 1.5 Algebra of Sets, Duality  1.6 Finite Sets, Counting Principle | 1.7 Classes of Sets, Power Sets, Partitions |1.8 Mathematical Induction | Solved Problems | Supplementary Problems |

CHAPTER 2 : Relations

2.1 Introduction | 2.2 Product Sets | 2.3 Relations | 2.4 Pictorial Representatives of Relations | 2.5 Composition of Relations | 2.6 Types of Relations | 2.7 Closure Properties | 2.8 Equivalence Relations | 2.9 Partial Ordering Relations | Solved Problems | Supplementary Problems |

CHAPTER 3 : Functions and Algorithms

3.1 Introduction | 3.2 Functions | 3.3 One-to-One, Onto, and Invertible Functions  3.4 Mathematical Functions, Exponential and Logarithmic Functions | 3.5 Sequences, Indexed Classes of Sets | 3.6 Recursively Defined Functions | 3.7 Cardinality | 3.8 Algorithms and Functions | 3.9 Complexity of Algorithms | Solved Problems | Supplementary Problems |

CHAPTER 4 : Logic and Propositional Calculus

4.1 Introduction | 4.2 Propositions and Compound Statements | 4.3 Basic Logical Operations | 4.4 Propositions and Truth Tables | 4.5 Tautologies and Contradictions | 4.6 Logical Equivalence | 4.7 Algebra of Propositions | 4.8 Conditional and Biconditional Statements | 4.9 Arguments | 4.10 Propositional Functions, Quantifiers | 4.11 Negation of Quantified Statements | Solved Problems | Supplementary Problems |

CHAPTER 5 : Techniques of Counting

5.1 Introduction | 5.2 Basic Counting Principles | 5.3 Mathematical Functions | 5.4 Permutations | 5.5 Combinations | 5.6 The Pigeonhole Principle | 5.7 The Inclusion–Exclusion Principle | 5.8 Tree Diagrams | Solved Problems | Supplementary Problems |

CHAPTER 6 : Advanced Counting Techniques, Recursion

6.1 Introduction | 6.2 Combinations with Repetitions | 6.3 Ordered and Unordered Partitions | 6.4 Inclusion–Exclusion Principle Revisited | 6.5 Pigeonhole Principle Revisited | 6.6 Recurrence Relations | 6.7 Linear Recurrence Relations with Constant Coefficients  | 6.8 Solving Second-Order Homogeneous Linear Recurrence Relations | 6.9 Solving General Homogeneous Linear Recurrence Relations | Solved Problems | Supplementary Problems |

CHAPTER 7 : Probability

7.1 Introduction | 7.2 Sample Space and Events | 7.3 Finite Probability Spaces | 7.4 Conditional Probability | 7.5 Independent Events | 7.6 Independent Repeated Trials, Binomial Distribution | 7.7 Random Variables | 7.8 Chebyshev’s Inequality, Law of Large Numbers | Solved Problems | Supplementary Problems |

CHAPTER 8 : Graph Theory

8.1 Introduction, Data Structures | 8.2 Graphs and Multigraphs | 8.3 Subgraphs, Isomorphic and Homeomorphic Graphs | 8.4 Paths, Connectivity | 8.5 Traversable and Eulerian Graphs, Bridges of Königsberg | 8.6 Labeled and Weighted Graphs | 8.7 Complete, Regular, and Bipartite Graphs | 8.8 Tree Graphs | 8.9 Planar Graphs |  8.10 Graph Colorings | 8.11 Representing Graphs in Computer Memory | 8.12 Graph Algorithms | 8.13 Traveling-Salesman Problem | Solved Problems | Supplementary Problems |

CHAPTER 9 : Directed Graphs

9.1 Introduction | 9.2 Directed Graphs | 9.3 Basic Definitions | 9.4 Rooted Trees | 9.5 Sequential Representation of Directed Graphs | 9.6 Warshall’s Algorithm, Shortest Paths | 9.7 Linked Representation of Directed Graphs | 9.8 Graph Algorithms: Depth-First and Breadth-First Searches | 9.9 Directed Cycle-Free Graphs, Topological Sort | 9.10 Pruning Algorithm for Shortest Path | Solved Problems | Supplementary Problems |

CHAPTER 10 : Binary Trees

10.1 Introduction | 10.2 Binary Trees | 10.3 Complete and Extended Binary Trees | 10.4 Representing Binary Trees in Memory | 10.5 Traversing Binary Trees | 10.6 Binary Search Trees | 10.7 Priority Queues, Heaps | 10.8 Path Lengths, Huffman’s Algorithm | 10.9 General (Ordered Rooted) Trees Revisited | Solved Problems | Supplementary Problems |

CHAPTER 11 : Properties of the Integers

11.1 Introduction | 11.2 Order and Inequalities, Absolute Value | 11.3 Mathematical Induction | 11.4 Division Algorithm |11.5 Divisibility, Primes | 11.6 Greatest Common Divisor, Euclidean Algorithm | 11.7 Fundamental Theorem of Arithmetic | 11.8 Congruence Relation | 11.9 Congruence Equations | Solved Problems | Supplementary Problems |

CHAPTER 12 : Languages, Automata, Grammars

12.1 Introduction | 12.2 Alphabet, Words, Free Semigroup | 12.3 Languages | 12.4 Regular Expressions, Regular Languages | 12.5 Finite State Automata | 12.6 Grammars | Solved Problems | Supplementary Problems |

CHAPTER 13 : Finite State Machines and Turing Machines

13.1 Introduction | 13.2 Finite State Machines | 13.3 Godel Numbers | 13.4 Turing Machines | 13.5 Computable Functions | Solved Problems | Supplementary Problems |

CHAPTER 14 : Ordered Sets and Lattices

14.1 Introduction | 14.2 Ordered Sets | 14.3 Hasse Diagrams of Partially Ordered Sets | 14.4 Consistent Enumeration | 14.5 Supremum and Infimum | 14.6 Isomorphic (Similar) Ordered Sets | 14.7 Well-Ordered Sets | 14.8 Lattices | 14.9 Bounded Lattices | 14.10 Distributive Lattices | 14.11 Complements, Complemented Lattices | Solved Problems | Supplementary Problems |

CHAPTER 15 : Boolean Algebra

15.1 Introduction | 15.2 Basic Definitions | 15.3 Duality | 15.4 Basic Theorems | 15.5 Boolean Algebras as Lattices | 15.6 Representation Theorem | 15.7 Sum-of-Products Form for Sets | 15.8 Sum-of-Products Form for Boolean Algebras | 15.9 Minimal Boolean Expressions, Prime Implicants | 15.10 Logic Gates and Circuits | 15.11 Truth Tables, Boolean Functions | 15.12 Karnaugh Maps | Solved Problems | Supplementary Problems |

APPENDIX A Vectors and Matrices

A.1 Introduction | A.2 Vectors | A.3 Matrices | A.4 Matrix Addition and Scalar Multiplication | A.5 Matrix Multiplication | A.6 Transpose | A.7 Square Matrices | A.8 Invertible (Nonsingular) Matrices, Inverses | A.9 Determinants | A.10 Elementary Row Operations, Gaussian Elimination (Optional) | A.11 Boolean (Zero-One) Matrices | Solved Problems | Supplementary Problems |

APPENDIX B  : Algebraic Systems

B.1 Introduction | B.2 Operations | B.3 Semigroups | B.4 Groups | B.5 Subgroups, Normal Subgroups, and Homomorphisms | B.6 Rings, Internal Domains, and Fields | B.7 Polynomials Over a Field  | Solved Problems | Supplementary Problems

INDEX