Discrete Mathematics
( 25 Modules )

Module #1
Introduction to Discrete Mathematics
Overview of discrete mathematics, its significance, and applications

Module #2
Sets and Operations
Basic set operations, types of sets, and set identities

Module #3
Set Relations and Functions
Introduction to relations, functions, and their properties

Module #4
Combinatorics:Counting Principles
Basic counting principles, permutations, and combinations

Module #5
Combinatorics:Recurrence Relations
Introduction to recurrence relations and their applications

Module #6
Number Theory:Divisibility and Primes
Properties of integers, divisibility, and prime numbers

Module #7
Number Theory:Congruences
Introduction to congruences, modular arithmetic, and cryptographic applications

Module #8
Algebraic Structures:Groups
Definition and properties of groups, subgroups, and homomorphisms

Module #9
Algebraic Structures:Rings and Fields
Definition and properties of rings, fields, and their applications

Module #10
Graph Theory:Basics
Introduction to graph theory, basic definitions, and graph representations

Module #11
Graph Theory:Traversability
Graph traversability, Eulerian and Hamiltonian paths, and circuits

Module #12
Graph Theory:Connectivity
Graph connectivity, connected components, and minimax theorems

Module #13
Discrete Probability
Introduction to discrete probability, events, and probability spaces

Module #14
Discrete Random Variables
Discrete random variables, probability distributions, and expected values

Module #15
Trees and Forests
Introduction to trees, forests, and their applications in computer science

Module #16
Lattices and Boolean Algebras
Introduction to lattices, Boolean algebras, and their applications

Module #17
Recursion and Induction
Recursion, mathematical induction, and structural induction

Module #18
Discrete Optimization
Introduction to discrete optimization, linear programming, and integer programming

Module #19
Modeling with Discrete Mathematics
Applications of discrete mathematics in computer science, networking, and coding theory

Module #20
Computational Complexity
Introduction to computational complexity, time and space complexity, and reducibility

Module #21
Logic and Propositional Calculus
Introduction to propositional logic, propositional calculus, and logical operators

Module #22
Predicate Logic
Introduction to predicate logic, predicates, and quantifiers

Module #23
Model Theory
Introduction to model theory, structures, and interpretations

Module #24
Applications of Discrete Mathematics
Real-world applications of discrete mathematics in computer science, cryptography, and data analysis

Module #25
Course Wrap-Up & Conclusion
Planning next steps in Discrete Mathematics career

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