What Exactly is Discrete Math?

As this article from the Ivy League Education Center explains it, discrete math deals with mathematical objects that can only take on distinct, separated values. It focuses on the study of entities/things that can be quantified or represented in a finite way. Discrete means separate, distinct, distinguishable, which implies discontinuous or non-continuous, so integers are discrete despite being countable in the sense that you can count them. Thus, the term Discrete Math is used in opposition to Continuous Math, an area of math dealing with smoothly varying objects, for example, calculus. Continuous objects need real numbers, whereas discrete objects can frequently be described by integers. Discrete math covers a broad spectrum of subjects that can be used to respond to a lot of real-world questions.1

MathILy, a project of the Mathematical Staircase, Inc., explains the ways in which discrete math is applied in our daily lives, some of which are as follows:2

• Computers are used to store and run programs. Large strings of 1s and 0s are used to store both the software and the files. Discrete math includes binary math.
• Networks are fundamentally discrete structures. Long cables connect the routers that control the internet. Social media allows people to communicate, share multimedia, and stay connected with one another.
• Web Searches in multiple languages simultaneously, and producing a summary requires discrete math.
• Analog Clocks contain gears, and the sizes/teeth required for accurate timekeeping are determined using discrete math.
• Cryptography is a branch of discrete math, which includes encryption and decryption.
• Google Maps employs discrete math to calculate the quickest driving routes and times.
• Railway Planning makes use of discrete math. From determining how to expand train rail lines, scheduling train timetables and crews to equipment for train trips, all make use of graph theory and linear algebra.
• The Development of Vaccines makes use of discrete math.
• Computer Graphics, such as in video games, objects are transformed using discrete math. That holds true for operating systems as well as applications like game development.
• Communications on Cell Phones use discrete math. Information theory and linear algebra are used to effectively utilize the broadcast spectrum for mobile phones. Discrete optimization or graph theory is widely used to assign frequencies without interfering with nearby phones.
• The Digital Image Processing process combines or filters images using discrete math.
• Health Care Resource Management—medical procedures necessitate the use of space, as well as health care workers and equipment. A type of discrete math known as integer programming is used in optimizing hospital resources in order to avoid wasting space, properly schedule staff, ensure equipment is both used and maintained, and allocate resources equitably.

In our increasingly technological society, discrete math can be a powerful way to build citizens who are better able to function, possess better problem-solving skills, enhanced critical thinking, and know what math means to us as a society. And, apart from this, it also prepares students for future careers that will require sophisticated analytical and technical skills.

Visit BYJU’S FutureSchool Blog to learn more about a variety of other math disciplines, their applications in real-world situations, and a host of other fascinating topics.

References:

1. The Importance of Discrete Mathematics | Ivy League Education Center. (n.d.). Retrieved July 29, 2022, from https://ivyleaguecenter.org/2015/03/17/why-discrete-math-is-very-important/
2. Discrete Mathematics in the Real World. (n.d.). Retrieved July 29, 2022, from http://www.mathily.org/dm-rw.html