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Discrete Math Homework

Discrete Mathematics is a set of branches of mathematics that all have been in common in the feature that they are discrete rather than continuous. It dealt with objects that only assumed to be distinct and having separated values. Discrete mathematics is a contemporary field of mathematics that is widely used in business and industry. It is sometimes called the mathematics of computers, or the mathematics used to optimize finite systems. Discrete Mathematics is the study of topics in discrete mathematics usually includes the study of algorithms, their implementations, and efficiencies. Discrete mathematics is the mathematical language of computer science, and as such, its importance has increased dramatically in recent decades. Although there is no agreed-upon definition of discrete mathematics, there is a general agreement that discrete mathematics includes three important areas: combinatorics, iteration and recursion, and vertex-edge graphs. Discrete mathematics includes sets, functions and relations, matrix algebra, combinatorics and finite probability, graph theory, finite differences and recurrence relations, logic, mathematical induction, and algorithmic thinking. Other topics often considered part of discrete mathematics are Boolean algebra, the mathematics of social choice, linear programming, and number theory. Discrete Mathematics is mathematics that deals with discrete objects and operations, often using computable and/or iterative methods. It is usually opposed to continuous mathematics (e.g. classical calculus). It 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. Because of this diversity of topics, it is perhaps preferable to view discrete mathematics simply as the mathematics that is necessary for decision making in noncontinuous situations. As there are two basic types of data "continuous" and discrete. So, in discrete mathematics we study discrete data which is not continuous or in some regular pattern. Topics in discrete maths are integers, graphs and statements in logic. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. More simply, we can say that discrete maths deals with countable sets.

Discrete Mathematics is a rapidly growing area of mathematics and includes topics such as graph theory, algorithms and optimisation which are all closely connected with computing. Discrete mathematics is the kind of mathematics one needs to know to communicate with a computer as designer, programmer, or user. It is necessary for all students, regardless of their choice of career path, to receive some instruction in discrete mathematics so that they will be able to function as informed citizens of an increasingly technological society. Its importance lies not only in deep theoretical results and methods but in its many practical applications. The design of efficient internet routing protocols, cryptography, electronic banking, security, telecommunications and web search engines all commonly utilise discrete mathematics. It is central to computer science and to operational research. The study of how discrete objects combine with one another and the probabilities of various outcomes is known as combinatorics. Other fields of mathematics that are considered to be part of discrete mathematics include graph theory and the theory of computation. Topics in number theory such as congruences and recurrence relations are also considered part of discrete mathematics.

In fact, discrete mathematics affords many students a new opportunity to experience success and enjoyment in mathematics classes. Those who have encountered numerous difficulties with computation and the complexities of mathematics in the past can be reached with appealing problems from discrete mathematics that have few formal skills as requisites. Discreteness here refers to a property of subjects of discourse. Some collection of things is called discrete if these things are distinguishable and not continuously transformable into each other.