- Discrete Mathematics Tutorial
- Discrete Mathematics - Home
- Discrete Mathematics - Introduction
- Sets, Relations, & Functions
- Discrete Mathematics - Sets
- Discrete Mathematics - Relations
- Discrete Mathematics - Functions
- Mathematical Logic
- Propositional Logic
- Predicate Logic
- Rules of Inference
- Group Theory
- Operators & Postulates
- Group Theory
- Counting & Probability
- Counting Theory
- Probability
- Mathematical & Recurrence
- Mathematical Induction
- Recurrence Relation
- Discrete Structures
- Graph & Graph Models
- More on Graphs
- Introduction to Trees
- Spanning Trees
- Boolean Algebra
- Boolean Expressions & Functions
- Simplification of Boolean Functions
- Discrete Mathematics Resources
- Discrete Mathematics - Quick Guide
- Discrete Mathematics - Resources
- Discrete Mathematics - Discussion
Discrete Mathematics - Introduction
Mathematics can be broadly classified into two categories −
Continuous Mathematics − It is based upon continuous number line or the real numbers. It is characterized by the fact that between any two numbers, there are almost always an infinite set of numbers. For example, a function in continuous mathematics can be plotted in a smooth curve without breaks.
Discrete Mathematics − It involves distinct values; i.e. between any two points, there are a countable number of points. For example, if we have a finite set of objects, the function can be defined as a list of ordered pairs having these objects, and can be presented as a complete list of those pairs.
Topics in Discrete Mathematics
Though there cannot be a definite number of branches of Discrete Mathematics, the following topics are almost always covered in any study regarding this matter −
- Sets, Relations and Functions
- Mathematical Logic
- Group theory
- Counting Theory
- Probability
- Mathematical Induction and Recurrence Relations
- Graph Theory
- Trees
- Boolean Algebra
We will discuss each of these concepts in the subsequent chapters of this tutorial.