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Learn about the basic concepts and topics of discrete mathematics, the study of mathematical structures that are fundamentally discrete rather than continuous. Find definitions, examples, and links to related disciplines and fields of discrete mathematics.
Discrete mathematics is the study of mathematical structures that can be considered discrete, such as integers, graphs, and logic statements. It has applications in computer science, information theory, and theoretical computer science.
Mathematics is a field of study that discovers and organizes methods, theories and theorems for various sciences and mathematics itself. It involves the description and manipulation of abstract objects using pure reason and proofs, and has many areas such as number theory, geometry, algebra, calculus, and set theory.
A lattice is a partially ordered set with a unique supremum and infimum for every pair of elements. Learn how to define and characterize lattices as order-theoretic or algebraic structures, and see some examples of bounded and unbounded lattices.
The discrete Fourier transform (DFT) is a mathematical operation that converts a finite sequence of samples of a function into a sequence of complex numbers representing the frequency components. The DFT is widely used in signal processing, image processing, and fast Fourier transform algorithms.
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Learn about its origins, basic notation, operations, paradoxes, and applications in mathematics and other fields.
The pigeonhole principle is a mathematical statement that if n items are put into m containers, with n > m, then at least one container must contain more than one item. Learn the history, examples, generalizations and applications of this counting argument.
Mathematical analysis formally developed in the 17th century during the Scientific Revolution, [3] but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were implicitly present in the early days of ancient Greek mathematics.