Discrete Mathematics and Graph Theory Course Content Primary Atomic Statement or Propositions Connectives and Compound Statement Truth Tables Constructing Truth Tables Examples Conditional or Implies With an Example Biconditional or Double Implies with Truth Table Conditional Biconditional Practice Examples Tautology Contradiction and Contingency Equivalence of Propositions List of Equivalence Formulas Equivalence without Truth Table Examples Show Tautology without Truth Table Converse Inverse Contrapositive and Dual Law Functionally Complete Set of Connectives Conversion to Functionally Complete Set Connectives Examples Connectives Nand Nor Xor Elementary Product Sum and Normal Forms Conversion to Disjunctive Normal Form Conversion to Conjunctive Normal Form Min Max Terms and Canonical Forms Conversion to Principal Conjunctive Normal Form PCNF Tautological Implication Understanding Inference Rules List of Inference Rules Showing Valid Inference Examples 1 Showing Valid Inference Examples 2 Conditional Proof or Deduction Theorem Examples Indirect Method of Proof Examples Consistency of Premises Examples Predicate Logic Basics Multiple Variable Predicate Examples Universal and Existential Quantifiers Free and Bound Variables Universal Existential Specification or Instantiation Understanding Universal Generalization with Example Showing Valid Predicate Inference Examples 1 Equivalence of Predicate Formulas Showing Valid Predicate Inference Examples 2 Validity of Predicate Statements Examples Set Theory Introduction Null Universal Proper and Subset Power Set with Examples Venn Diagrams for Representing Sets Union Intersection Difference Set Operations Disjoint Complement Symmetric Difference of Sets Properties of Set Union Operations with Proofs Properties of Set Intersection Operation Properties of Set Complement operation with Proof Properties of Set Difference with Proofs Properties of Set Symmetric Difference Showing Equivalence using Set Properties 1 Showing Equivalence using Set Properties 2 Principle of Inclusion and Exclusion Formulae Examples on Principle of inclusion and Exclusion Applications of Inclusion and Exclusion Principle Introduction to Relations Operations on Relations Properties Reflexive Relation Symmetric AntiSymmetric Asymmetric Relations Transitive Irreflexive Relations Representing Relations Table and Graph Equivalence Relation With an Example Partially and Totally Ordered Set POSET Construct Hasse or Poset Diagram Construct Hasse Diagrams Examples Minimal Maximal Least and Greatest Members Least Upper Bound and Greatest Lower Bound Semi Lattice and Lattice with Examples Properties of Lattice with Proofs Distributive Lattice with Examples Bounded Unbounded Complemented Lattice Sub Lattice with an Example Introduction to Function One to One Onto and Bijective Functions Showing Bijective Functions Examples Understanding Composition of Functions Composition of Functions Examples 1 Composition of Functions Examples 2 Inverse of a Function with Examples Theorems on Inverse of a Function Permutation Functions with Examples Inverse and Cyclic Permutations with Examples Algebraic Structure and Semi Group with Examples Monoid and Group with Examples Abelian Group and Group Examples Properties of a Group with Proofs Sub Group with Examples Cyclic Group with Examples Homomorphism of Groups with Examples Isomorphism of Groups with Example Understanding Permutations with an Example Permutations Formulae without Repetitions Permutation Examples on Numbers Permutations Examples on Numbers1 Permutations Examples on Alphabets Permutations Examples on Alphabets1 Permutations Examples on Travel Understanding Combinations Formulae with Example Combinations Examples on Bit Strings Combinations Examples on Men and Women Combinations Examples on Fruits Combinations Examples on Couples Understanding Permutations with Repetitions Formulae Permutations with Repetitions Examples on Alphabets1 Permutations with Repetitions Examples on Alphabets2 Permutations with Repetitions Examples on Numbers1 Permutations with Repetitions Examples on Numbers2 Combinations with Repetitions Formulae Combinations with Repetitions Examples1 Permutation Examples Rank of the Word Permutation Examples Rank of the Word1 Understanding Circular Permutations Formulae Circular Permutations Examples Selections with Repetitions Examples1 Selections with Repetitions Examples 2 Permutations Examples on Order1 Permutations Examples on Order2 Find GCD Using Euclidean Algorithm Understanding Division Algorithm Basics for GCD Using Euclidean Algorithm Finding GCD Using Euclidean Algorithm Proof Prime Factorization Examples Understanding Fundamental Theorem of Arithmetic Properties of GCD Examples on GCD Properties
