The importance of discrete mathematics and its applications in today’s world

Discrete mathematics is a feature of mathematics devoted to the study of separate or distinct objects.

This is in variation to connected objects of mathematics such as Calculus.

Some example of discrete objects includes:

• Integers
• Steps that are taken in a computer program
• Distinct paths to travel from point A to Point B on a map along with a road network
• Ways to pick up a winning set of numbers in a lottery

Discrete mathematics and its applications are useful in the implementation of

Algorithms

Performance analysis

Information management.

Discrete mathematics provides mathematical ideas for computer science.

The technological age requires a collective effort to understand the diverse discrete system.

Some of the various aspects of discrete mathematics include

i. Theory and techniques can be combined well with applications and implementation. Such as coding theory that works well data compression, protocols, and communication security. Similarly with Graph theory that works well algorithmic design and analysis etc.

ii. A particular solution can be used in various discrete problems. Like, pattern matching in computational biology as well as information retrieval.

iii. Discrete mathematics links mathematics to communications and computing, such as spectral methods, when used in graph algorithms to collect massive data sets.

Information technology has opened doors to discrete mathematics with its access to a vast information pool.

Discrete mathematics is playing a new role in creating technology for the future.

Here is a list of problems that can be solved using Discrete Mathematics:

1. How many ways is a password chosen following a specific rule?
2. How many different valid internet addresses are there?
3. What is the probability of winning a lottery?
4. Is there a link between computers in a network?
5. How can I identify spam messages?
6. How can I encrypt a message to avoid unintended readers?
7. How can I build a circuit that adds two integers?

Although continuous mathematics forms a part of information technology, discrete mathematics forms a dominant counterpart.

Let’s looks at some notable applications of discrete mathematics in Information technology

Graph embeddings and Massive graphs

Embedding one graph into another is the primary complication. It is also a matter of preserving distances and minimizing the cost at the same time.

If the graph is incomplete or the size is too large, new complications give rise to the direction the research wants to take.

For instance, the presentation of large data sets into a small chart may come off as protruding. Similarly, the inverse of constructing a graph from projects has applications in

• Memory management
• Computational biology
• Internet tomography and many others.

Random and Random-like graphs

A lot of efforts have been implanted in the understanding of random graphs. However, there is a fascination in understanding structure graphs as well.

This requires a proper understanding of the graph, and discrete mathematics happens to be an appropriate medium.

Massive graphs in communication or computation share similarities to sparse random graphs.

Combinatorics

Economics is the core of combinatorial optimization. This includes planning and management of operation along with efficient use of resources.

Production schedule, capital budget, transport system planning, and design of fault resistive networks, etc. are some technical problems that are categorized optimization problems.

Combinatorial optimization has an enormous impact on problems in e-commerce, planning of next-generation networks, etc.

Cryptology

The coding theory provides reliable transmission of data. Cryptography deals with the integrity and security of the transmitted data.

The information age has expanded the applications of cryptography into

• Authentication protocols
• Timestamp
• Availability of service
• Protection of intellectual property.

Computation geometry

Discrete and computation geometry finds the relations between line, shapes in a lane, and multidimensional spaces.

This kind of relations has applications in a wide array of fields, especially in graphics and data management.

Bioinformatics

Discrete mathematics serves as an essential tool for patterning, matching, and sequencing and analyzing genetic codes.

Combinatorial algorithms and graph theory forms the essential tools for the purpose.

Additionally, a discrete probabilistic approach and Markov chains are used to identify discrete structures.

The applications also process massive data in problems arising from computational biology.

I have been teaching in a renowned university since ten years. Currently, I have also launched my own websites. I love reading books and also participate in many educational events.