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The Meaning and Application of Discrete Mathematics

Discrete Mathematics is one of the major and most important branches of mathematics. In contrast to calculus, it deals with distinct, countable and arrangeable mathematical structures, and was the first branch of mathematics that humans developed – counting and basic arithmetic are also part of discrete mathematics!

It has applications in a wide variety of fields, from computers to statistics to warfare. Read on to know more; below you will find a quick primer on the definition and application of discrete mathematics.

 WHAT IS DISCRETE  MATHEMATICS?

Discrete Mathematics is the branch of mathematics that deals with distinct and countable values, i.e. integers, graphs and combinations. The objects that discrete mathematics concerns itself with are distinct, countable and separate.

Discrete structures can be counted and arranged, placed into sets and put into ratios with one another. Despite the fact that discrete mathematics is a wide and varied field, there are certain rules that carry over into many topics and are universal throughout the whole of the field of discrete mathematics, and its applications too. 

In fact, there is no formal definition of discrete mathematics. Discrete mathematics is more easily defined by what it excludes - smooth/continuously varying values like in calculus and Euclidean geometry (real numbers) i.e structures that cannot be separated and arranged.

 It encompasses topics like combinatorics (permutations and combinations), set theory, probability, graph theory, statistics and logic (such as in Boolean Algebra)

APPLICATIONS OF DISCRETE MATHEMATICS

Ever since the advent of Isaac Newton and the publishing of his Principia, the main emphasis of applied mathematics has been on continuous mathematics using methods of differential and integral calculus.

However, in the latter half of the 20th Century, with the start of the Computer Age, discrete mathematics came back into the spotlight because digital computers operate in discrete steps and store data in discrete bits.

Thus, concepts and theories from discrete mathematics are extremely useful in studying and describing objects and solving problems in such fields as computer science (such as in computer algorithms, programming languages, cryptography, automated theorem proving as well as software development), geometry, topology, operations research, statistics, logic, algebra, and last but not least, game theory. Even something as basic as counting is an application of discrete mathematics.

Thus we can see that discrete mathematics is one of the most important and relevant fields of mathematics in modern times, with applications in fields like IT, architecture, logistics, accounting, statistics, intelligence, engineering, commerce and even warfare (Operations Research was invented in WW2 to help plan military operations).

In fact, it is hard to imagine the modern world functioning without the help of discrete mathematics! I hope you find this article useful in giving you an overview of discrete mathematics and its applications.

Understanding the concept of discrete mathematics and its applications can be quite tough in the beginning because of it such an all-encompassing subject. If you need further help in understanding this topic, click here. 

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For all streams, like math, chemistry, physics and engineering streams, MathLab has widely used as a computational tool in engineering and science. For applications like –

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We all know that statistics deal with the numeric figures and data which are applied to simplify the complex data and the numerical figures.