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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.
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]
The notion of a BDD is now generally used to refer to that particular data structure. In his video lecture Fun With Binary Decision Diagrams (BDDs), [12] Donald Knuth calls BDDs "one of the only really fundamental data structures that came out in the last twenty-five years" and mentions that Bryant's 1986 paper was for some time one of the most ...
There are several equivalent definitions of a Riemann surface. A Riemann surface X is a connected complex manifold of complex dimension one. This means that X is a connected Hausdorff space that is endowed with an atlas of charts to the open unit disk of the complex plane: for every point x ∈ X there is a neighbourhood of x that is homeomorphic to the open unit disk of the complex plane, and ...
Discrete calculus or the calculus of discrete functions, is the mathematical study of incremental change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.
A final discrete system is often modeled with a directed graph and is analyzed for correctness and complexity according to computational theory. Because discrete systems have a countable number of states, they may be described in precise mathematical models. A computer is a finite-state machine that may be viewed as a discrete system. Because ...
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points , lines , planes , circles , spheres , polygons , and so forth.
This quality of unpredictability and apparent randomness led the logistic map equation to be used as a pseudo-random number generator in early computers. [ 4 ] At r = 2, the function r x ( 1 − x ) {\displaystyle rx(1-x)} intersects y = x {\displaystyle y=x} precisely at the maximum point, so convergence to the equilibrium point is on the ...