Discrete Mathematics Tutorial

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 relations, 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

• Linear Programming 
• Graphical Solution For Linear Programming
• Simplex Algorithm
• PERT 

Ordered Sets & Lattices

• Partially Ordered Sets
• Elements of POSET
• Hasse Diagrams
• 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

• Matching- Basics, Perfect, Bipartite
• Approximation Algorithms

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

Quick Links

• Last-Minute Notes (LMNs)
• Quizzes on Discrete Mathematics

Discrete Mathematics Tutorial – FAQs

What is Discrete Mathematics?

Discrete Mathematics deals with mathematical structures involving distinct values, such as graphs, integers, and logic-based statements. It’s essential for computer science and problem-solving1.

Why is Discrete Mathematics important?

• It improves reasoning and problem-solving capabilities.
• It finds practical applications in fields like computer science and cryptography.

What topics does Discrete Mathematics cover?

• Set Theory: Study of collections of objects, their properties, and operations.
• Graph Theory: Analyzing relationships between nodes (vertices) and edges.
• Combinatorics: Counting and arranging objects.
• Logic: Propositional and predicate logic.
• Recurrence Relations: Describing sequences using recursive formulas.

How does Discrete Mathematics differ from continuous mathematics?

• Continuous math deals with real numbers and continuous functions.
• Discrete math focuses on separate, countable elements.

What are some practical applications of Discrete Mathematics?

• Cryptography: Secure communication and data protection.
• Algorithms: Design and analysis of efficient algorithms.
• Network Optimization: Routing, flow, and connectivity problems.

Conclusion

This Discrete Mathematics Tutorial and taken a giant leap towards mastering the fundamental concepts that will propel you to greatness in the world of software engineering and beyond. By applying the concepts learned in this tutorial to practice problems and real-world examples.

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Article Tags :

• Computer Subject
• Engineering Mathematics
• Discrete Mathematics