Fundamental Principles of Counting
The Rules of Sum and Product
Permutations
Combinations
Permutations and Combinations with Repetition

Fundamentals of Logic
Basic Connectives and Truth Tables
Logical Equivalence: The Laws of Logic
Logical Implication: Rules of Inference
The use of Quantifiers

Set Theory
Sets and Subsets
Set Operations and The Laws of Set Theory
Counting and Venn Diagrams

Properties of Integers: Mathematical Induction
The Well Ordering Principle: Mathematical Induction
Recursive Definitions

Relations and Functions
Cartesian Products and Relations
Properties of Relations
Partial Orders
Equivalence Relations and Partitions
Functions: Plain and One to One
Onto Functions

An Introduction To Graph Theory
Definitions and Examples
Subgraphs, Complements and Graph Isomorphisms
Vertex Degree: Euler Trails and Circuits
Hamilton Paths and Cycles

Trees
Definitions, Properties and Examples
Rooted Trees
Weighted Trees and Prefix Codes

Q1 : What is discrete mathematics?
A1 : Discrete mathematics is a branch of mathematics that deals with distinct and countable objects, rather than continuous quantities. It involves topics such as sets theory, fundamental of logic, relations and functions, graphs, combinatorics, and others.

Q2 : Why is discrete mathematics important?
A2 : Discrete mathematics provides the foundation for solving real-world problems in fields of computer science, cryptography, network analysis, and decision-making. It offers tools to model and solve discrete situations.

Q3 : How does discrete mathematics relate to computer science?
A3 : Discrete mathematics is fundamental to computer science. It's used to design algorithms, analyze data structures, optimize processes, and solve computational problems efficiently.

Q4 : How is discrete mathematics used in everyday life?
A4 : Discrete mathematics is applied in various real-life scenarios, such as making decisions, solving puzzles, arranging schedules, designing networks, and even predicting outcomes in games of chance.