Discrete Mathematics.

Cover -- Preface to the Fourth Edition -- Contents -- Chapter 1. Mathematical Logic -- 1.1 Logical Statement or Proposition -- 1.2 Type of Propositions -- 1.3 The Propositional Calculus -- 1.4 The Negation of a Proposition -- 1.5 Disjunction -- 1.6 Conjunction -- Problem -- 1.7 Tautologies and Contradictions -- 1.8 Logical Equivalence -- Problem 1.3 -- 1.9 The Algebra of Propositions -- Problem 1.4 -- 1.10 Conditional Propositions -- 1.11 Converse, Inverse and Contrapositive Propositions -- 1.12 The Negation of a Conditional Proposition -- 1.13 Biconditional Propositions -- Problem 1.5 -- 1.14 Arguments -- Problem 1.6 -- Chapter 2. Set Theory -- 2.1 Sets -- 2.2 Set Designation -- 2.3 Null Sets and Unit Sets -- 2.4 Special Sets of Numbers -- 2.5 Universal Set -- Problem 2.1 -- 2.6 Subsets: Proper Subsets and Equal Sets -- Problem 2.2 -- 2.7 Set Operations -- 2.8 Union Operation -- 2.9 Properties of Union Operations -- 2.10 Intersection -- 2.11 Properties of Intersection Operation -- 2.12 Distributive Properties -- 2.13 Complementation -- 2.14 Relative Complement (or Difference of Sets) -- 2.15 Properties of Complement -- 2.16 Properties of Difference -- 2.17 Symmetric Difference -- Problem 2.3 -- 2.18 Power Set -- Problem 2.4 -- 2.19 Cartesian Prodcuts -- Problem 2.5 -- 2.20 Generalized Set Theory -- Problem 2.6 -- Chapter 3. Relation and Functions -- 3.1 Relation -- Problem 3.1 -- 3.2 Equivalence Relation -- 3.3 Partition -- 3.4 Partial Order Relation -- Problem 3.2 -- 3.5 Functions (Mappings) -- Problem 3.3 -- 3.6 Inverse Mapping -- 3.7 Composition of Mappings -- Problem 3.4 -- 3.8 Binary Operations -- Problem 3.5 -- 3.9 Countable and Uncountable Sets -- Problem 3.6 -- Chapter 4. Ordered Sets and Lattices -- 4.1 Poset -- 4.2 Product Set and Order -- 4.3 Hasse Diagrams of Partially Ordered Sets -- 4.4 Minimal and Maximal, and First and Last Point.

Problem 4.1 -- 4.5 Lattices -- 4.6 Lattices and Partially Ordered Sets -- 4.7 Principle of Quality -- Problem 4.2 -- 4.8 Lattices as Algebraic Systems -- 4.9 Lattice and Order -- 4.10 Sublattices -- 4.11 Direct Product of Two Lattices -- 4.12 Isomorphic Lattices -- Problem 4.3 -- 4.13 Complete Lattice -- 4.14 Complemented Lattices -- 4.15 Distributive Lattice -- 4.16 Modular Lattices -- Problem 4.4 -- Chapter 5. Boolean Algebra and Switching Circuits -- 5.1 Introdcution -- Problem 5.1 -- 5.2 Boolean Functions -- 5.3 Normal Form -- 5.4 Fundamental Forms of Boolean/Functions -- Problem 5.2 -- 5.5 Application to Switching Networks -- Problem 5.3 -- Chapter 6. Matrices -- 6.1 Revision -- 6.2 Diagonal, Scalar, Unit and Triangular Matrix -- 6.3 Equal Matrices -- 6.4 The Transpose of Matrix: Symmetric and Skew Symmetric Matrix -- 6.5 Algebra of Matrices -- 6.6 Properties of Addition of Matrices -- 6.7 Scalar Multiples of Matrices -- 6.8 Multiplication of Matrices -- Problem 6.1 -- 6.9 Inverse of a Matrix -- Problem 6.2 -- 6.10 Geometric Transformation -- 6.11 Geometric Properties of Plane Linear Transformation -- 6.12 Rotation -- 6.13 Reflection -- 6.14 Expansions and Compressions -- 6.15 Shears -- 6.16 Translation -- 6.17 Successive Transformations -- 6.18 Inverse Transformation -- Problem 6.3 -- 6.19 Complex Numbers in the Form of a Matrix -- Chapter 7. Rank and Equivalence -- 7.1 The Concept of a Rank -- Problem 7.1 -- 7.2 Elementary Transformations -- 7.3 Equivalent Matrices -- 7.4 Elementary Matrices -- Problem 7.2 -- 7.5 Normal Form -- Problem 7.3 -- 7.6 Elementary Transformation by Matrix Multiplication -- Problem 7.4 -- Problem 7.5 -- 7.7 Computation of the Inverse of Matrix by Elementary Transformation -- Problem 7.6 -- Problem 7.7 -- Chapter 8. Linear Equations -- 8.1 System of Linear Equations and Consistency.

8.2 Solution of n Linear Equations in n Unknowns -- 8.3 Solutions of m Linear Equation in n Unknown with m&lt -- n and m&gt -- n -- Problem 8.1 -- 8.4 Homogeneous Linear Equations -- Problem 8.2 -- 8.5 Cramer's Rule -- Problem 8.3 -- Chapter 9. Characteristics Roots and Vectors of a Matrix -- 9.1 Definition and Examples -- 9.2 Properties of the Characteristic Polynomial -- 9.3 Application of the Cayley-Hamilton Theorem in Finding Out the Inverse of a Non-Singular Matrix -- Problem 9.1 -- 9.4 Characteristic Roots and Vectors of a Square Matrix -- 9.5 Similar Matrices -- Problem 9.2 -- Problem 9.3 -- Chapter 10. Combinatorics -- 10.1 Introduction -- 10.2 Sum Rule Principle -- 10.3 Product Rule Principle -- 10.4 Factorial Notation -- 10.5 Permutations -- Problem 10.1 -- 10.6 Permutation of Things not all Different -- Problem 10.2 -- 10.7 Circular Permutations -- 10.8 To Find the Number of Circular Permutation of n different things Taken All at a Time -- Problem 10.3 -- 10.9 Combinations -- 10.10 To Find the Number of Combinations of n Dissimilar things Taken r at a Time that is, Mathematically to Find the Value of nCr -- 10.4 Problem 10.4 -- Problem 10.4 -- 10.11 Division into Groups (Partitions) -- 10.12 To Find the Number of Ways in Which (m+n+q) Different Things be Divided into Three Groups of m,n and p Things Respectively -- 10.13 To Find the Total Number of Ways in Which it is Possible to Make Selection by Taking Some or All of n Things at a Time -- 10.14 To Find the Total Number of Ways in Which a Selection Can be Made Out of p+q+r Things, of Which p are Alike of One Kind, q Alike of Second Kind and r Alike of Third Kind -- 10.15 To Find the Value of r for Which nCr Which nCr is Greatest -- 10.16 The Pigeonhole Principle -- 10.17 The Inclusion-Exclusion Principle -- Problem 10.5 -- Answers to Problems -- Index.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.