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 relation, group theory, and graph theory.
Mathematical Logic
Sets and Relations
Mathematical Induction
Boolean Algebra
Optimization
Ordered Sets & Lattices
Probability Theory
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
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
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