Importance of discrete mathematics in computer science

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Coursera introduction to discrete mathematics for computer science

In , Yuri Matiyasevich proved that this could not be done. While undoubtedly the subject matter being taught is important, the material at least at the introductory level does not lend itself to a great deal of creative mathematical thinking. Discrete math shows up on most middle and high school math contests. Design theory is a study of combinatorial designs , which are collections of subsets with certain intersection properties. Formal verification of statements in logic has been necessary for software development of safety-critical systems , and advances in automated theorem proving have been driven by this need. Discrete Math in Cryptography The field of cryptography, which is the study of how to create security structures and passwords for computers and other electronic systems, is based entirely on discrete mathematics. It draws heavily on graph theory and mathematical logic. This is partly because computers send information in discrete -- or separate and distinct -- bits. Main article: Information theory The ASCII codes for the word "Wikipedia", given here in binary , provide a way of representing the word in information theory , as well as for information-processing algorithms. Algebra is often taught as a series of formulas and algorithms for students to memorize for example, the quadratic formula, solving systems of linear equations by substitution, etc. Information theory involves the quantification of information. About the Author Having obtained a Master of Science in psychology in East Asia, Damon Verial has been applying his knowledge to related topics since

In real-world applications, the set of objects of interest are mainly finite, the study of which is often called finite mathematics. Since each piece of information and each trait belonging to that piece of information is discrete, the organization of such information in a database requires discrete mathematical methods.

What is discrete mathematics quora

Logical formulas are discrete structures, as are proofs , which form finite trees [14] or, more generally, directed acyclic graph structures [15] [16] with each inference step combining one or more premise branches to give a single conclusion. Discrete Math in Cryptography The field of cryptography, which is the study of how to create security structures and passwords for computers and other electronic systems, is based entirely on discrete mathematics. More than half of the problems in the high level math contests, such as the AIME American Invitational Mathematics Examination , are associated with discrete mathematics. This is all done through the discrete math concept of sets. Discrete math shows up on most middle and high school math contests. Originally a part of number theory and analysis , partition theory is now considered a part of combinatorics or an independent field. Main article: Mathematical logic Logic is the study of the principles of valid reasoning and inference , as well as of consistency , soundness , and completeness.

Relational Databases Relational databases play a part in almost every organization that must keep track of employees, clients or resources. Updated March 13, By Damon Verial Discrete mathematics is the study of mathematics confined to the set of integers.

essential maths for computer science

These rules are created through the laws of discrete mathematics. Computer Algorithms Algorithms are the rules by which a computer operates.

Importance of discrete mathematics in information technology

Because of the quantity of money and the amount of confidential information involved, cryptographers must first have a solid background in number theory to show they can provide secure passwords and encryption methods. Uses for Discrete Math in Logistics Logistics is the study of organizing the flow of information, goods and services. Computer Algorithms Algorithms are the rules by which a computer operates. The beginning of set theory as a branch of mathematics is usually marked by Georg Cantor 's work distinguishing between different kinds of infinite set , motivated by the study of trigonometric series, and further development of the theory of infinite sets is outside the scope of discrete mathematics. Formal verification of statements in logic has been necessary for software development of safety-critical systems , and advances in automated theorem proving have been driven by this need. Theoretical computer science also includes the study of various continuous computational topics. Discrete math teaches mathematical reasoning and proof techniques. The primary techniques learned in a discrete math course can be applied to many different fields. Petri nets and process algebras are used to model computer systems, and methods from discrete mathematics are used in analyzing VLSI electronic circuits. A mathematician can analyze these graphs according to the methods of graph theory to determine the best routes for shipping or solving other logistical problems. Main article: Combinatorics Combinatorics studies the way in which discrete structures can be combined or arranged. Main article: Mathematical logic Logic is the study of the principles of valid reasoning and inference , as well as of consistency , soundness , and completeness. About the Author Having obtained a Master of Science in psychology in East Asia, Damon Verial has been applying his knowledge to related topics since

However, discrete math has become increasingly important in recent years, for a number of reasons: Discrete math is essential to college-level mathematics and beyond. Computational geometry has been an important part of the computer graphics incorporated into modern video games and computer-aided design tools.

Importance of discrete mathematics in computer science

Discrete mathematics produces a significant collection of powerful methods, including mathematical tools for understanding and managing very high-dimensional data, inference systems for drawing sound conclusions from large and noisy data sets, and algorithms for scaling computations up to very large sizes. A mathematician can analyze these graphs according to the methods of graph theory to determine the best routes for shipping or solving other logistical problems. Rarely is this the case with most discrete math topics. A computer programmer uses discrete math to design efficient algorithms. Automata theory and formal language theory are closely related to computability. The truth values of logical formulas usually form a finite set, generally restricted to two values: true and false, but logic can also be continuous-valued, e. Partition theory studies various enumeration and asymptotic problems related to integer partitions , and is closely related to q-series , special functions and orthogonal polynomials. This is all done through the discrete math concept of sets. The mathematics of modern computer science is built almost entirely on discrete math, in particular combinatorics and graph theory. Included within theoretical computer science is the study of algorithms for computing mathematical results. Closely related is coding theory which is used to design efficient and reliable data transmission and storage methods. It draws heavily on graph theory and mathematical logic.

The truth values of logical formulas usually form a finite set, generally restricted to two values: true and false, but logic can also be continuous-valued, e.

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The Importance of Discrete Mathematics