Importance of Discrete Mathematics in Computer Science

Discrete mathematics is the formal language of computer science.

The importance of discrete mathematics and its applications has increased dramatically in recent years.

Discrete mathematics is vital in studying and describing objects and problems in branches of computer science.

Such as

• Computer algorithms
• Programming languages
• Cryptography
• Automated theorem proving
• Software development

Inversely, computer applications are predominant in applying ideas from discrete mathematics to real-world problems, like Operations research.

Discrete mathematics deals with distinct or separated values.

The term varies in contrast with continuous mathematics, which deals with real numbers.

The study of discrete structures and how they combine is known as Combinatorics.

Combinatorics also studies the probabilities of various outcomes of such structures.

Other fields of Mathematics that deal with discrete mathematics include graph theory and theory of computation.

To achieve the working knowledge of computer science principles requires specific mathematical skills.

Such as a strong conceptual understanding of De Morgan’s law to expedite Boolean expression

The basic concept of combinational circuits including knowledge of the growth of functions and summations for analysis of loop control structures

And an introduction to proof techniques for program correctness helps a long way.

Some notable Discrete Mathematic topics include (but not limited to):

• Propositional and predicate logic
• Boolean algebra
• Sequence and summations
• Number theory
• Proof techniques
• Matrices
• Counting
• Pigeon hole principle
• Permutations and combinations
• Discrete probability
• Relations
• Graphs

Applications of Discrete Mathematics

Theoretical computer science

Theoretical computer science deals mainly with graph theory and logic.

It is the core aspect of discrete mathematics that deals with computing.

Theoretical computer science is the study of algorithms, such as

• Computability study can be integrated into principles with a close tie to logic
• While complexity studies the time taken by the computations
• Automata theory and formal language theory is used in computability.
• Petri Nets and process algebras are used in model computer systems
• Discrete mathematical methods are used to analyze VLSI electronic circuits.

Theoretical computer science also includes the study of many continuous computational topics.

    Information theory

Information theory quantifies information.

It is used to design efficient and reliable data transmissions.

Information theory includes a study on

• Analog signals.
• Analog coding
• Analog encryptions
•  Mathematical logic.

     Set theory

Set theory is the part of mathematics that studies Set.

The sets are a collection of objects, or it can be a set of prime numbers.

That is, it is a set of a finite number.

In discrete mathematics, countable sets are the prime focus.

    Combinatorics

    Combinatorics studies the way discrete structures are arranged or combined.

    Some levels of Combinatorics include: Enumerative Combinatorics counts the number of particular

    combinatorial objects.

      Analytic Combinatorics determines the number of combinatorial structures.
Enumerative Combinatorics uses formulas and functions to describe results
Analytic Combinatorics aims to obtain the asymptotic method.
Design theory is the study of combinatorial structures, while partition theory studies various enumeration and asymptotic problems.

    Graph theory

It is the study of the graph and its networks.

It is often considered as a part of Combinatorics.

However, graph theory has grown large enough to have its problems.

Graphs are one of the prime objects to discrete mathematics.

In mathematics, they are essential in geometry and some parts of topology.

But the major part of graph theory falls under discrete mathematics.

Discrete probability theory

Discrete probability theory study events that occur in countable spaces

For example, observations such as the number of birds in a flock comprise natural numbers

On the other hand, the weights of birds include real values and can be categorized by a continuous probability distribution.

Discrete probability distributions are used to approximate continuous ones and vice versa.

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