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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 [1] – do not vary smoothly in this way, but have distinct, separated values. [2]
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions).
Discrete integral calculus is the study of the definitions, properties, and applications of the Riemann sums. The process of finding the value of a sum is called integration . In technical language, integral calculus studies a certain linear operator .
Discrete mathematics, also called finite mathematics, is the study of mathematical structures that are fundamentally discrete, in the sense of not supporting or requiring the notion of continuity. Most, if not all, of the objects studied in finite mathematics are countable sets , such as integers , finite graphs , and formal languages .
Dichotomization is the special case of discretization in which the number of discrete classes is 2, which can approximate a continuous variable as a binary variable (creating a dichotomy for modeling purposes, as in binary classification). Discretization is also related to discrete mathematics, and is an important component of granular computing.
In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums. It is also called Abel's lemma or Abel transformation , named after Niels Henrik Abel who introduced it in 1826.
The GATE is used as a requirement for financial assistance (e.g. scholarships) for a number of programs, though criteria differ by admitting institution. [2] In December 2015, the University Grants Commission and MHRD announced that the scholarship for GATE-qualified master's degree students is increased by 56% from ₹ 8,000 (US$92) per month to ₹ 12,400 (US$140) per month.
The journal includes articles on pure and applied discrete mathematics. It was established in 1988, along with the SIAM Journal on Matrix Analysis and Applications, to replace the SIAM Journal on Algebraic and Discrete Methods. The journal is indexed by Mathematical Reviews and Zentralblatt MATH. Its 2009 MCQ was 0.57.