It is the branch of mathematics that deals with the object that can consider only distinct, separated values. It consists of foundational concepts of set, mathematical logic, Boolean algebra, graph theory, trees, group theory, probability, recurrence relations, counting theory, relation, and theory.  Discrete Mathematics is also known as the language of computer science. It is widely used in machine learning, software engineering, and data science fields. In this course, the student will get to know about the basis for mathematical reasoning in computational and applied sciences. Discrete Mathematics plays a fundamental role in; network, analysis of algorithms, cryptography, and computer programming.

This particular term discrete mathematics is used in contradiction with continuous mathematics. This branch of mathematics concerns objects that can vary easily or smoothly (it includes calculus). Although discrete objects can often be identified by integers and real numbers. It is the study of how discrete objects blend with one another and the chances of various results are familiar as combinatorics. There are other zones of it that are called to be the part of this subject including the theory of computation and graph theory Congruences and recurrence relations can be called as part of it.

## Courses in Discrete Mathematics for Computer Science

Discrete mathematics is widely used in mathematical operations (branch of mathematics) and in computer science as a language. Both aspects of it contain their own importance and having their own specialization of course. It is a very versatile subject that provides knowledge for maths and computer science together. More on, discrete objects can be identified by integers. Notations and concepts from DS are useful in describing and studying problems and objects in branches of computer science for instance programming languages, software development, automated theorem proving, and computer algorithms.

#### Discrete Mathematics for CS

There are 5 most popular specializations in this course such as mathematical thinking in computer science, introduction to graph theory, combinatorics and probability, delivery problem and number theory, and cryptography

• Mathematical thinking in computer science:- It is paramount in all domains of computer science such as bioinformatics, computer graphics, machine learning, and data science. Here students will learn the most vital tools that are used in it like logic, invariants, and induction.
• Introduction to graph theory:- It is an area of CS that joins the elegance of painting and the rigor of mathematics. It provides both a simple way to graphically represent many important mathematical results and shows the deep theories behind it.
• Combinatorics and probability:- Consumers of combinatorics is the main probability theory. This sector is related to various sides of everyday life and indispensable tools in such important and modern fields as machine learning and statistics.
• Delivery problem:- In Python, we will apply together systematic programs for a problem needed by delivery firms all over the globe millions of times/day. The motive in this problem is to reach all the given places as soon as possible and how to search for the best solution to such a problem fastly?
• Number theory and cryptography:- Number theory is a wide and attractive area of mathematics, similarly known as higher arithmetic. It consists of studying the whole number’s properties. Whereas cryptography is the procedure of securely transferring information, in such a way that no 3rd party will be able to get the information.

## List of Famous Universities Providing this Course

The excessive use of informative technology and mathematical operation in computer science increase the demand for young professionals who can easily deal and manage the whole work process. At the university level, universities allow the learner to use the tools and teach new techniques that students will later use for growth. Here are some prominent names of the universities that provide a good platform for the students who want to learn discrete mathematics:

• HSE University (Russia)
• Peking University(China)
• Goldsmith, University of London
• Duke University (North Carolina)
• Imperial College of London
• Stanford University (California)
• University of Zurich (Switzerland)
• University of London
• EIT Digital (Belgium)
• University of Pennsylvania
• Shanghai Jiao Tong University (China)

## Outcomes of the Course

After the successful completion of the course, the student will be able to;

• Recognize the basic method of particularly induction, proof, and bid them solve it.
• Complications in computer science and mathematics.
• Handle relations, functions sets, and their related concepts, and apply them to solve hurdles of computer science and mathematics.
• Operate and analyze simple 1st and 2nd order recurrence relations.
• Use graphs and trees to resolve complications in computer science.
• Try counting principles in combinatorics.
• Learn the concepts of elementary probability.

### Conclusion

Discrete mathematics creates the mathematical fundamentals of information science and computers. This is also an interesting subject in itself. In this subject, students will learn the language of computer science, learn the advanced maths that also define CS, and work on applying it through numerical evidence and Python code.

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