Discrete mathematics Definition and 106 Threads

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. 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. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus or Euclidean geometry. Discrete objects can often be enumerated by integers. 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). 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.
The set of objects studied in discrete mathematics can be finite or infinite. 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.
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. 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. Conversely, computer implementations are significant in applying ideas from discrete mathematics to real-world problems, such as in operations research.
Although the main objects of study in discrete mathematics are discrete objects, analytic methods from continuous mathematics are often employed 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. 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. Some high-school-level discrete mathematics textbooks have appeared as well. At this level, discrete mathematics is sometimes seen as a preparatory course, not unlike precalculus in this respect.The Fulkerson Prize is awarded for outstanding papers in discrete mathematics.

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    Discrete Mathematics - Logics Puzzles

    I ran into this logic puzzle and have been working on it for couple hours now but i can't seem to explain clearly why the answer i came up with is the answer. Heres the question: The police have three suspects for the murder of Mr. Cooper: Smith, Jones, and Williams. Smith, Jones, and...
  2. C

    Why is ~(P v Q) equivalent to (~P & ~Q)?

    Hi, For one of the questions in my Discrete Mathematics course, I have to find what property of a formula makes its dual formula also its negative. With a dual formula, the logical operators of "^" and "v" are reversed, the former meaning "and" and the latter meaning "or". With its negative...
  3. C

    Decision and discrete mathematics

    Decision and discrete mathematics... Why is Decision maths called "Decision maths"? :smile: Thanks.
  4. E

    How to Find the Normal Vector for a Plane Perpendicular to Another?

    Find the scalar eq'n of a plane that is perpendicular to the plane with normal vector [3,1,2] and passes through points A(2,-6,-1) and B(1,2,-4). I think that the normal vector can be the direction vector of this new plane. But then, in order to find the scalar eq'n I need a normal vector...
  5. Link

    Discrete Math Definition - What Is Discrete Math?

    Can someone give me a definition of discrete mathematics?
  6. C

    Geometry and Discrete Mathematics (Matrix)

    Hey all, I'm having some problems with this one homework question... We just did The Intersection of Three Planes using The augmented matrix... and here's my question... For what value of k will the following set of planes intersect in a line? x - 2y - z = 0 x + 9y - 5z = 0 kx - y + z = 0
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