Discrete mathematics is the study of mathematics confined to the set of integers. While the applications of fields of continuous mathematics such as calculus and algebra are obvious to many, the applications of discrete mathematics may at first be obscure. Nevertheless, discrete math forms the basis of many real-world scientific fields -- especially computer science. The primary techniques learned in a discrete math course can be applied to many different fields.
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. This is partly because computers send information in discrete -- or separate and distinct -- bits. Number theory, one important part of discrete math, allows cryptographers to create and break numerical passwords. 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.
Relational databases play a part in almost every organization that must keep track of employees, clients or resources. A relational database connects the traits of a certain piece of information. For example, in a database containing client information, the relational aspect of this database allows the computer system to know how to link the client’s name, address, phone number and other pertinent information. This is all done through the discrete math concept of sets. Sets allow information to be grouped and put in order. 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.
Uses for Discrete Math in Logistics
Logistics is the study of organizing the flow of information, goods and services. Without discrete mathematics, logistics would not exist. This is because logistics makes heavy use of graphs and graph theory, a sub-field of discrete math. Graph theory allows complex logistical problems to simplify into graphs consisting of nodes and lines. 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.
Algorithms are the rules by which a computer operates. These rules are created through the laws of discrete mathematics. A computer programmer uses discrete math to design efficient algorithms. This design includes applying discrete math to determine the number of steps an algorithm needs to complete, which implies the speed of the algorithm. Because of discrete mathematical applications in algorithms, today’s computers run faster than ever before.
- A Logical Approach to Discrete Math; David Gries and Fred Schneider
- A First Course in Scientific Computing; Rubin Landau et. al.