Discrete Mathematics
What is Discrete Mathematics
Discrete mathematics, also called finite mathematics, is a part of mathematics devoted to the study of discrete objects or values (i.e countable and separate values) and the relationships that bind them. Lets understand discrete mathematics by comparing it with continuous mathematics.
Discrete vs Continuous mathematics
Mathematics is divided into two major branches - discrete mathematics and continuous mathematics.
- Discrete mathematics is a branch of mathematics in which we study discrete(distinct and separate) objects that use arithmetic and algebra, for example - How many integers lie between 1 and 10? we certainly know that eight integers lie between 1 and 10 (those are 2, 3, 4, 5, 6, 7, 8, and 9), so we know that a finite number of integers lie between any two integers, we study these types of objects in discrete mathematics.
- whereas in continuous mathematics, such as calculus, we deal with continuous functions.
for example - How many real numbers lie between 1 and 10? we know that there are infinite real numbers between any two real numbers so we cannot count or do not have a finite number as an answer to this question, we deal with such things in continuous mathematics.
Importance Of Discrete Mathematics
Discrete mathematics has many practical and relevant applications:
- It is an excellent tool for improving reasoning and problem-solving skills.
- Information is stored and manipulated by computing machines in a discrete fashion, this is a key reason for the importance of discrete mathematics.
- Ideas of discrete mathematics are fundamental to the science and technology specific to the computer age.
- Knowledge of discrete mathematics is a prerequisite for understanding many branches of mathematics and computer science such as data structures, operating systems, compiler design, and many more.
Fundamental Concepts
Mathematical Logic
Logic is the science dealing with methods of reasoning. Mathematical logic has become an accepted part of discrete mathematics.
Set Theory
A set is a collection of well-defined objects ("well-defined" means that the definition should not vary from situation to situation and person to person). All mathematical objects can be defined in sets, hence the idea of sets is fundamental in the study of mathematical structures.
Boolean Algebra
Binary logic deals with variables that take only two discrete values (like 1 or 0, true or false)along with operations that assume logical meaning. Boolean algebra is a simple and systematic way of representing and performing the operations of logic circuits in modern digital systems.
Number Theory
Number theory is a part of mathematics that deals with the properties of integers, more specifically the properties of positive integers.
Relation
This concept arises when we consider a pair of objects and compare one with the other. This is a basic concept of computer science as well as in real life.
Combinators
Combinators is the mathematics of counting selecting and arranging objects.
Graph Theory
Graph theory is one of the most important branches of discrete mathematics and the source of many algorithms of practical importance.
NOTE - Other concepts like Functions, Posets-lattices, and many more are also studied under discrete mathematics, in addition to the prominent ones mentioned above.
Conclusion
This was quite a brief survey of a very vast subject called discrete mathematics, the importance of discrete mathematics and its various branches will continue to grow due to its wide range of applications in our modern, data-driven world along with the advancements of fields like computer science and technology.
Thank you for taking the time to go through this Discrete Mathematics blog. I hope this serves as a valuable resource to enhance your understanding of this fundamental branch of mathematics and its practical applications.