Discrete Mathematics is a branch of mathematics that is concerned with “discrete” mathematical structures instead of “continuous”. Discrete mathematical structures include objects with distinct values like graphs, integers, logic-based statements, etc. In this tutorial, we have covered all the topics of Discrete Mathematics for computer science like set theory, recurrence relation, group theory, and graph theory.
Recent Articles on Discrete Mathematics!
Mathematical Logic
- Introduction to Propositional Logic
- Applications of Propositional Logic
- Propositional and Predicate Logic
- Propositional Equivalences
- Normal and Principle Forms
- Predicates and Quantifiers
- Nested Quantifiers Theorem
- Rules of Inference
- Introduction to Proofs
Sets and Relations
- Set Theory
- Types of Sets
- Set Operations
- Rough Set Theory
- Functions
- Sequence and Summations
- Representations of Matrices and Graphs in Relations
- Types of Relation
- Closure of Relation and Equivalence Relations
Mathematical Induction
- Mathematical Induction
- Basics of Counting
- Pascal’s Identity
- Pigeonhole Principle
- Permutations and Combinations
- Generalized Permutations and Combinations
- Generating Functions
- Inclusion-Exclusion Principle
- Discrete Probability Theory
Boolean Algebra
- Boolean Functions
- Boolean Algebraic Theorem
- Properties of Boolean Algebra
- Number of Boolean Functions
- Minimization of Boolean Functions
Optimization
Ordered Sets & Lattices
Probability Theory
- Basic Concepts of Probability
- Probability Axioms
- Properties of Probability
- Conditional Probability
- Bayes’ Theorem
- Uniform Distribution
- Exponential Distribution
- Normal Distribution
- Poisson Distribution
Graph Theory
- Introduction to Graph
- Basic terminology of a Graph
- Types of a Graph
- Walks, Trails, Paths, and Circuits
- Graph Distance components
- Cut-Vertices and Cut-Edges
- Bridge in Graph
- Independent sets
- Shortest Path Algorithms [Dijkstra’s Algorithm]
- Application of Graph Theory
- Graph Traversals[DFS]
- Graph Traversals[BFS]
- Characterizations of Trees
- Prim’s Minimum Spanning Tree
- Kruskal’s Minimum Spanning Tree
- Huffman Codes
- Tree Traversals
- Traveling Salesman Problem
Special Graph
- Bipartite Graphs
- Independent Sets and Covering
- Eulerian graphs
- Eulerian graphs- Fleury’s algorithm
- Eulerian graphs- Chinese-Postman-Problem Hamilton
Matching
Vertex Colorings
- Chromatic Numbers, Greedy Coloring Algorithm
- Edge Coloring
- Vizing Theorem
- Planar Graph- Basics, Planarity Testing
- Directed Graphs- Degree Centrality
- Directed Graphs- Weak Connectivity
- Directed Graphs- Strong Components
- Directed Graphs- Eulerian, Hamilton Directed Graphs
- Directed Graphs- Tarjans’ Algorithm To Find Strongly Connected Component
- Handshaking in Graph Theorem
Group Theory
- Groups, Subgroups, Semi Groups
- Isomorphism, Homomorphism
- Automorphism
- Rings, Integral domains, Fields