MAT 123 Discrete Mathematics

Discrete Mathematics has been described as the mathematical language of computer science. It is the branch of mathematics dealing with objects that can assume only distinct, separated values. Discrete means individual, separate, distinguishable implying discontinuous or not continuous, so integers are discrete in this sense even though they are countable in the sense that you can use them to count. The term “Discrete Mathematics” is therefore used in contrast with “Continuous Mathematics,” which is the branch of mathematics dealing with objects that can vary smoothly (and which includes, for example, calculus). Whereas discrete objects can often be characterized by integers, continuous objects require real numbers Discrete mathematics is of direct importance to the fields of Computer Science and Information Technology. Basically, discrete mathematics is the branch of mathematics that studies the underlying principles which govern discrete structures and the binary universe. Such principles are essential and effective in the implementation of algorithms, performance analysis, and information management. It has been described as the mathematical language of computer science. Some real-world applications of discrete mathematics are as follows: Cryptography: The art and science of converting data or information into an encoded form that can ideally only be decoded by an authorized entity. This field makes heavy use of number theory, the study of the counting numbers, and algorithms on base-n number systems. Logistics: This field makes use of graph theory to simplify complex logistical problems by converting them to graphs. These graphs can further be used to find the best routes for shipping goods and services, and so on. For example, airlines use graph theory to map their global airplane routing and scheduling. Machine Learning: This is the area that seeks to automate statistical and analytical methods so systems can find useful patterns in data, learn, and make decisions with minimal human intervention. This is frequently applied to predictive modeling and web searches. Analysis of Algorithms: Any set of instructions to accomplish a task is an algorithm. An effective algorithm must solve the problem, terminate in a useful amount of time, and not take up too much memory. Algorithms form one of the topics we cover in this course. Relational Databases: They help to connect the different traits between data fields. For example, in a database containing information about accidents in a city, the "relational feature" allows the user to link the location of the accident to the road condition, lighting condition, and other necessary information. A relational database makes use of the concept of set theory in order to group together relevant information.