Applied discrete structures for computer science / Alan Doerr and Kenneth Levvasseur.

CHAPTER-1- SET THEORY-- Description-- Basic Operations--Venn Diagrams--Pascal Note

CHAPTER -2 COMBINATIONS--Rule's of Products--Permutations--Combinations--Power

CHAPTER-3 LOGIC--Proportions and Logical Operators--Propositions--Logical Operators--Trump Tables and Propositions Generoltd by a Set--Equivalence and Implication--Tautologies --Implication--Pascal Note--The Laws of Logic--Pascal Note--Mathematical Systems Proofs--Proofs in Propositional Calculus Direct Proofs--Conditional Conclusions--Indirect Proofs--"Proof Style-- Propositions Over a Universe--Truth Set--Pascal Note--Mathematical Introduction--The Principle of Mathematical Induction--Variations--Historical Note--Quantifiers--The Existential Quantifier--The Universal Quantifier--The Negation of Quantified Propositions--Multiple Quantifiers--

CHAPTER- 4 ON STATISTICS--Methods of Proof for Sets--Examples and Counterexamples--Proof Using Venn Diagrams--Proof Using Set-Membership Tables--Proof Using Definitions--Lows of Set Theory--Proofs Using Previously Proven Theorems--Proof Using the Indirect Method--Partitions of Sets--Minutes--The Duality Principle

CHAPTER -5 INTRODUCTION TO MATRIX" ALGEBRA--Basic Definitions-- Addition and Scalar Multiplication--Multiplication of Matrices--Special Types of Matrices--Lows of Matrix Algebra--Matrix Oddities

CHAPTER- 6 RELATION--Basic Definitions--Relation Notation--Propitious of Relations--Properties of Relations--Matrices Of Relations--Closure Operations on Relations--
'Marshall's Algorithm

CHAPTER-7 FUNCTIONS--Definition of o Function and Notation--Functions of Two Variables--Pascal Note--Composition, Identity and Inverse--Composition--Identity Function--Inverse Function

CHAPTER-8 RECURSION AND RECURRENCE RELATIONS--The Many Faces of Recursion--Polynomials and Their Evaluation--Pascal Note--Recursion Iteration--
Induction and Recursion--Sequences, or Discrete Functions--A Fundamental Problem--Recurrence Relations--Solving a Recurrence Relation--Recurrence Relations Obtained from "Solutions"--Solution of Non homogeneous Finite Order--X.Nieves Relations--Base of Right-Hand Side Equal to Characteristic Root--Some Common Recurrence Relations--Review of Logarithms--Meriting Functions--Solution of a Recurrence Relation Using--Generating Functions--Closed Form Expressions for Generating Functions--Extra for Experts

CHAPTER-9 GRAPH THEORY--Grants—A General Introduction--A Summary of Path Notation and Terminology--Isomorphic Graphs--Data Structures for Gratis--Connectivity--Traversals--The Kornberg Bridge Problem and Valerian Graphs--Hamiltonian Graphs--Graph Optimization--The Traveling Salesman Problem--The Traveling Salesman Problem--Unit Square--Version--Networks and the Maximum Flow Problem--Maximal Flows--Other Graph Optimization Problems--Planetary and Coloring's--Graph Coloring--

CHAPTER-10 TREES--What Is a Tree?--Spanning Trees--The Minimal Spanning Tree Problem--The Minimum Diameter Spanning Tree Problem--Rooted Trees--Kruskal's Algorithm--Binary Trees--Traversals of Binary Trees--Expression Trees--Counting Binary Trees--

CHAPTER-11 ALGEBRAIC SYSTEMS--Operations--Common Properties of Operations--Operation Tables-- Algebraic Systems--Levels of Abstraction--Groups--Some General Properties of Groups--In The Integers Modulo--Properties of Modular Arithmetic on Z.--Pascal Note --Subsystems--Direct Products--Isomorphic--Procedure for Showing Groups are Isomorphic--Procedure for Showing Groups are not Isomorphic--Object-Orin ted Programming

CHAPTER-12 ALGEBRA--Systems of Linear Equations-- Matrix inversion--An introduction to Vector Spaces and the Denationalization Process--The Denationalization Process.-- Some Applications--

CHAPTER-13 BOOLEAN ALGEBRA--Lattices-- Boolean Algebras--Atoms of a Boolean Algebra--Finite Boolean Algebras--Boolean Expressions--A Brief introduction to the Application of Boolean Algebra to Switching Theory

CHAPTER 14 CONCEPT OF MONGOLOIDS LANGUAGES, GRAMMARS, AND AUTOMATA--MORE ON MONOIDS AND AUTOMATA-- Mongoloids--General Concepts and Properties of Monoids--Monoid Isomorphic--Free Mongoloids and Languages--Free Monoids Over an Alphabet--Languages--Two Fundamental Problems: Recognition and Generation Phase Structure Grammars and Languages-- Automata, Finite-State Moelilnet--Recognition in Regular Languages--The Machine of a Monoids--FINITE AUTOMATA--GROUP THEORY AND APPLICATION--Cyclic Groups--Application: Fast Adders--Co-sets and Factor Group--Permutation Groups--Normal Subgroups and Group
Homomorphisms--Normal Subgroups--Homomorphisms--Coding Theory—Group Codes--Binary Symmetric Channel--The Coding Process


CHAPTER-16 AN INTRODUCTION TO RINGS AND FIELDS--Rings—Basic Definitions and Concepts--Direct Products of Rings--Fields--Polynomial Rings--Field Extensions--
Power Series-