What is Discrete: Definition and 895 Discussions

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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  1. I

    Discrete math textbook problem

    Homework Statement find the domain and image of f such that f(x) = {(x,y) \in R \times R \vert x = \sqrt{y+3} and domain and image of g such that g = { (\alpha,\beta) \vert \alpha is a person, \beta is a person, \alpha is the father of \beta Homework Equations the domain and image...
  2. T

    Discrete math - equivalence relation

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  3. hxtasy

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  4. F

    Discrete mathematics (PMI, composition, onto)

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  5. N

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  6. M

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  7. M

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  8. Z

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  9. Z

    What is the 15th term of (X3 + Y)25?

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  10. G

    Discrete Dynamical Systems Proof Help.

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  11. S

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  12. S

    Is a Discrete Group of Rotations Cyclic?

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  13. T

    Discrete energy states (explanations in QFT?)

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  14. F

    Discrete mathematics induction

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  15. L

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  16. G

    Help with a proof with discrete dynamical sysmtes / chaos theory.

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  17. G

    Discrete mathematics: incursion

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  18. M

    Proving NTG Relation on S x S: Reflexive, Non-Transitive, and Non-Antisymmetric

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  19. M

    Discrete Mathematics again

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  20. F

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  21. M

    Logics and Proof - Discrete Mathematics

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  22. M

    2.2 Set Operations: Discrete Mathematics and its application

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  23. W

    A Problem in Discrete Probability

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  24. E

    Exploring Binomial Theorem through Discrete Math

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  25. E

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  26. L

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  27. H

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  28. M

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  29. C

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  30. S

    Discrete Mathematics (confused and help wanted)

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  31. F

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  32. A

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  33. O

    Discrete Probability and Distribution to understand the topic.

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  34. T

    Where can I find a comprehensive resource for learning discrete mathematics?

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  35. A

    Finding Solutions to a Discrete Math Function Problem

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  36. S

    Unit Pulse Response for a discrete time system

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  37. P

    Equations of Lines: How to Find, Solve, and Verify Intersection Points

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  38. P

    Discrete systems possible mistake in answers

    starting with the iterated map derived in the notes for calculating rootp(p>0) Xn+1=1/2(Xn+(p)/(Xn) calculate root 7 starting with x0=1 so ok starting with that i get x0=1 x1=4 and then something strange happens the sub in looks like this X2=1/2(4+2/4)=9/4 i was under the...
  39. W

    Which Major Would Benefit Me More: Applied Math or Discrete? (Link Included)

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  40. P

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  41. T

    I have the possibility of taking Calculus 1 and Discrete Math next semester.

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  42. F

    Having some trouble with Discrete Math.

    Hey all, I just started my Junior year at Florida International University this summer and decided to start light by taking Programming I and Discrete Math to kick things off with and get used to the university. Programming class is going fine, but Discrete Math class is really giving me a...
  43. Fra

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  44. F

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  45. N

    Mathematica Discrete Fourier Transform to find phase shift - Mathematica

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  46. I

    Discrete probability distribution

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  47. W

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  48. C

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  49. C

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  50. L

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