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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). Objects studied in discrete mathematics include integers, graphs, and statements in logic.
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.
Discrete modelling is the discrete analogue of continuous modelling. In discrete modelling, formulae are fit to discrete data —data that could potentially take on only a countable set of values, such as the integers , and which are not infinitely divisible.
Discrete optimization is a branch of optimization in applied mathematics and computer science. As opposed to continuous optimization , some or all of the variables used in a discrete optimization problem are restricted to be discrete variables —that is, to assume only a discrete set of values, such as the integers .
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]
In signal processing and machine learning, discrete calculus allows for appropriate definitions of operators (e.g., convolution), level set optimization and other key functions for neural network analysis on graph structures. [3] Discrete calculus can be used in conjunction with other mathematical disciplines.
According to the preface, the topics in Concrete Mathematics are "a blend of CONtinuous and disCRETE mathematics". Calculus is frequently used in the explanations and exercises. The term "concrete mathematics" also denotes a complement to "abstract mathematics". The book is based on a course begun in 1970 by Knuth at Stanford University.
In contrast, a variable is a discrete variable if and only if there exists a one-to-one correspondence between this variable and a subset of , the set of natural numbers. [8] In other words, a discrete variable over a particular interval of real values is one for which, for any value in the range that the variable is permitted to take on, there ...