Discrete math topics and their concepts are widely used in computer science. Discrete math is all about discrete objects rather than continuous. It focuses on objects that can consider only distinct, separated values. There are no fractions or decimals involved. For example, there can be a set of random integers or graphs that are not continuous and discrete. However, some concepts like calculus or Euclidean geometry are not part of discrete math as they are continuous by nature.^{1}

Discrete means separate, distinct, or distinguishable. Discrete math is applied in our day-to-day life activities as well. Some examples of the study include cryptography, a field of computer science. The field helps users generate passwords for computers and other digital tokens like credit or debit cards. This is because the information usually travels discreetly in bits.

Discrete math is considered the contrast of continuous math. Continuous math includes continuous objects such as calculus, integrations, and some other math concepts.

However, discrete math topics include the theory of computation, graph theory, and the study of algorithms and their implementations. With the increased use of computer science, the use of discrete math in real life has also increased in several ways.

## Popular Discrete Math Concepts

Before we dive into some of the areas that involve the role of discrete math in real life, let’s know some of the popular discrete math concepts. They include:

· **Set Theory**

**· Logic**

**· Number Theory**

**· Graph Theory**

**· Complex and Computable Theory**

**· Algorithms**

**· Probability**

**· Functions**

**· Linear Algebra**

Computer science uses the above concepts, along with some other theories. It mainly uses graph theory, algorithms, and mathematical reasoning. The study of discrete math makes several computer science topics easier.

## Real-life Applications of Discrete Math

Let us now see the real-life applications of discrete math that make our day-to-day life easier.^{2,3,4 }These applications include:

**1. Railway Planning**

The railway department uses the graph theory concepts to identify the right and shortest path between two stations. Along with graph theory, they also use the concepts of linear algebra.

**2. Cell Phone Communication**

Information theory and linear algebra concepts are used for efficiently operating mobile phones and their broadcast spectrum. Graph theory and optimisation techniques help assign the right frequency to the phones without interference.

**3. Password Creation Criteria**

The password is an essential part of several online services. Discrete math algorithms help users create a password and exchange information in an encrypted manner. The use of strong algorithms can serve communication strongly.

**4. Online Delivery Services**

These days many people use online shopping or e-commerce sites. Moreover, people also order food through popular apps. However, the service provider may have to identify the shortest and fastest route for any kind of delivery. TSP or Travelling Salesman Problem-like algorithms help providers define the right and the best path between source and destination.

**5. Use of Discrete Math in Cryptography**

The field of cryptography is all about studying the ways to create passwords and security methods. All these concepts are entirely based on discrete math, as the information is usually sent in bits and discrete forms.^{3}

Number theory, one of the most important concepts of discrete math, allows mathematicians or password creators to generate and break numerical passwords. Mathematicians with strong Number Theory concepts can generate strong passwords and complex encryption methods.

**6. Use of Discrete Math in Financial Organizations Like Banks**

In every business, a relational database plays an important role. It helps in keeping track of employees, resources, and clients. A relational database helps identify the connections between certain pieces of information. For example, if more than one member from the same family is associated with a business, such as a bank, the business can link both clients through relational databases.

**7. Information Routing With Discrete Math**

In the world of the internet, tons of information flows daily from source to destination. There are several topologies in discrete math like computational topology, combinatorics, discrete topological space, finite topological space, and many more. Topology is a mathematical field, but it also plays a major role in computer science real-time applications. These algorithms help optimize the routing path so that information travel can take place in minimum time.

**8. Logistic Management and Discrete Math**

Organizing goods, services and information is known as logistic organizations. Computer programmers use the concepts and theories of discrete math to design and develop the best logistic management algorithms.^{4} Discrete math concepts also help programmers to write algorithms and speed up the algorithm by reducing its steps.

There are plenty of real-world applications of discrete math. Some more applications include Google maps, cell phone communication, digital image processing, healthcare resource management, and many others.

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**References**

1) Ahire, A. (2022, January 21). *Discrete Mathematics in the Real World.* Medium. Retrieved December 1, 2022, from https://anushka93719.medium.com/discrete-mathematics-in-the-real-world-fbfde9d8a4b5

2) *Discrete Mathematics in the Real World*. (n.d.). Discrete Mathematics in the Real World. Retrieved December 1, 2022, from http://www.mathily.org/dm-rw.html#:~:text=Railway%20planning%20uses%20discrete%20math,graph%20theory%20and%20linear%20algebra.

3) C. (2018, October 15). *Application of Discrete Mathematics in the Field of Computer Application*. Application of Discrete Mathematics in the Field of Computer Application – Marwadi University | Techie’s Gazette Blogs. Retrieved December 1, 2022, from http://techiesgazette.marwadiuniversity.ac.in/?p=584

4) H. (2014, June 15). *Application of Discrete Mathematics in Urban Transportation System Analysis*. Hindawi. Retrieved December 1, 2022, from https://www.hindawi.com/journals/mpe/si/593474/