Home └Discrete Mathematics

Discrete Mathematics

Syllabus:
Set Theory, Relations, Functions, Graph Theory, Planer Graph and Trees, Direct graphs and Binary Trees, Algebraic Systems, Ordered sets and lattices, Propositional Calculus, Boolean Algebra, Lattices, group theory, cyclic groups, permutation groups, symmetry groups, quotient,
homomorphism, Basic structure theory, Prepositional and Predicate logic, Mathematical reasoning and program techniques. Theories with induction. Counting and countability. Graph and trees. Morphisms, Algebraic structures.

Course Objectives:
The main objectives of the course are to:
1. Introduce concepts of mathematical logic for analyzing propositions and proving theorems.
2. Use sets for solving applied problems, and use the properties of set operations algebraically.
3. Work with relations and investigate their properties.
4. Investigate functions as relations and their properties.
5. Introduce basic concepts of graphs, digraphs and trees.


Learning Outcomes:
1. Analyze logical propositions via truth tables.
2. Prove mathematical theorems using mathematical induction.
3. Understand sets and perform operations and algebra on sets.
4. Determine properties of relations, identify equivalence and partial order relations, sketch relations.
5. Identify functions and determine their properties.
6. Define graphs, digraphs and trees, and identify their main properties.
7. Evaluate combinations and permutations on sets.

Join Course
Responsible Md. Imran Hossain
Last Update 10/25/2022
Completion Time 1 day 6 hours
Members 1
Md. Imran Hossain
  • Part A: Proposition
    • Lecture 1.1: Logic and Proposition
    • Lecture 1.2: Predictions and Quantifiers
    • Lecture 1.3: Set
    • Lecture 1.4: Function
    • Lecture 1.5: Matrix
  • Part B: Mathematical reasoning and counting
    • Lecture 2.1:Mathematical Induction
    • Lecture 2.2: Recursive
    • Lecture 2.:3 Basic of counting
    • Lecture 2.4: pigeonhole principal
    • Lecture 2.5: Permutations and combinations
  • Part C: Advance counting and relations
    • Lecture 3.1: Recurrence Relations
    • Lecture 3.2: Divide and Conquer Algorithm
    • Lecture 3.3: Relation and their properties
    • Lecture 3.4: Representing Relation
    • Lecture 3.5: Equivalence Relation
  • Part D: Graph
    • Lecture 4.1: Introduction of Graph
    • Lecture 4.2: Representing graph
    • Lecture 4.3: Euler and Hamilton Paths
    • Lecture 4.4: Shortest path
    • Lecture 4.5: Planar Graph and Graph coloring
  • Part E: Tree
    • Lecture 5.1: Introduction of Tree
    • Lecture 5.2: Applications of Tree
    • Lecture 5.3: Tree Traversal
    • Lecture 5.4: Spanning Tree
    • Lecture 5.5: Minimum Spanning Tree
  • Part F: Boolean Algebra
    • Lecture 6.1:
    • Lecture 6.2: Representing of Fucntions
    • Lecture 6.3: Logic Gate
    • Lecture 6.4: Minimization of Circuits
    • Lecture 6.5: Quine McCluskey Method