Discrete Mathematics

Explore Discrete Mathematics, a key field in computer science, cryptography, and algorithm design. Covering set theory, logic, combinatorics, and graph theory, it provides essential tools for solving complex problems. Mastering these concepts equips you for success in technology-driven industries and enhances analytical skills.

• Properties Of Groups
• Properties Of Rings
• Introduction To Algebra
• Rings
• Lagrange’s Theorem
• Subrings
• Groups
• Normal Subgroups
• Homomorphisms And Quotient Rings
• Symmetric Groups
• Homomorphisms And Normal Subgroups
• Subgroups
• Mathematical Induction
• Set Theory
• Theory Of Inference For The Predicate Calculas
• Conditional Statements
• Decimal Number System
• The Computer Representation Of Sets
• Binary Number System
• Predicates And Quantifiers
• Recurrence Relation
• Sets And Membership
• Octal Number System
• Binary Arithmetic
• Relations
• Logical Equivalance
• Maximal, Minimal Elements And Lattices
• Hexadecimal Number System
• Method For Solving Linear Homogeneous Recurrence Relations With Constant Coefficients:
• The Algebra Of Sets
• Method Of Solving Recurrence Relation
• Formulation Of Recurrence Relation
• Introduction To Partial Order Relations
• Subsets
• Digramatic Representation Of Sets
• Representation Of Relations
• Digramatic Representation Of Partial Order Relations And Posets
• Partial Order Relations On A Lattice
• Properties Of Lattices
• Lattice Isomorphism
• Resolution And Fallacies
• The Transitive Closure Of A Relation
• Least Upper Bounds And Latest Lower Bounds In A Lattice
• Bounded, Complemented And Distributive Lattices
• Sublattices
• Representing Boolean Functions
• Cartesian Product Of Lattices
• The Abstract Definition Of A Boolean Algebra
• Duality
• Karnaugh Maps
• Minimization Of Circuits
• Boolean Algebra
• The Quine–mccluskey Method
• Identities Of Boolean Algebra
• Logic Gates
• Quantifiers
• Introduction To Lattices
• Don’t Care Conditions
• Lattices As Algebraic System
• Using Rules Of Inference To Build Arguments
• Translating From Nested Quantifiers Into English
• Introductio To Planer Graphs
• Propositional Logic
• Rules Of Inference For Quantified Statements
• Nested Quantifiers
• Precedence Of Logical Operators And Logic And Bit Operations
• Introduction To Logical Operations
• Logical Implications
• Normal Forms And Truth Table
• Rules Of Inference For Propositional Logic
• Normal Form Of A Well Formed Formula
• Principle Disjunctive Normal Form
• Inference
• Truth Tables Of Compound Propositions
• Applications Of Propositional Logic
• Principal Conjunctive Normal Form
• Logical Operations And Logical Connectivity
• Propositional Satisfiability
• Isomorphism Of Graphs
• Trees As Models
• Original And Sub Graphs
• Paths And Isomorphism
• Paths In The Graphs
• Connectivity Of Graphs
• Representing Graphs
• Connectedness In Undirected Graphs
• Applications Of Graph Colorings
• Properties Of Trees
• Incidence Matrices
• Introduction To Graphs
• Applications Of Trees
• Graph Models
• Tree Traversal
• Bipartite Graphs
• Graph Terminology
• Directed Graph
• Some Special Simple Graphs
• Hamilton Paths And Circuits
• Applications Of Graphs
• Huffman Coding
• Rooted Trees
• Adjacency Matrices
• Euler Paths And Circuits
• Decision Trees
• A Shortest-path Algorithm (Dijkstra’s Algorithm.)
• Introduction To Trees
• The Traveling Salesperson Problem
• Game Trees
• Bipartite Graphs And Matchings
• Shortest-path Problems
• Graph Coloring
• Prefix Codes