Some high-school-level discrete mathematics textbooks have appeared as well. The curriculum has thereafter developed in conjunction with efforts by ACM and MAA into a course that is basically intended to develop mathematical maturity in first-year students therefore, it is nowadays a prerequisite for mathematics majors in some universities as well. In university curricula, "Discrete Mathematics" appeared in the 1980s, initially as a computer science support course its contents were somewhat haphazard at the time. Conversely, computer implementations are significant in applying ideas from discrete mathematics to real-world problems, such as in operations research.Īlthough the main objects of study in discrete mathematics are discrete objects, analytic methods from continuous mathematics are often employed as well.
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Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development.
Research in discrete mathematics increased in the latter half of the twentieth century partly due to the development of digital computers which operate in discrete steps and store data in discrete bits. The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to business. The set of objects studied in discrete mathematics can be finite or infinite. However, there is no exact definition of the term "discrete mathematics." Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets (finite sets or sets with the same cardinality as the natural numbers). Discrete objects can often be enumerated by integers. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus or Euclidean geometry. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values. Graphs like this are among the objects studied by discrete mathematics, for their interesting mathematical properties, their usefulness as models of real-world problems, and their importance in developing computer algorithms.ĭiscrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.
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