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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).
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]
Commonly expressed today as Force = Mass × Acceleration, it invokes discrete calculus when the change is incremental because acceleration is the difference quotient of velocity with respect to time or second difference quotient of the spatial position.
Today’s mathematicians would probably agree that the Riemann Hypothesis is the most significant open problem in all of math. It’s one of the seven Millennium Prize Problems , with $1 million ...
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 .
Theoretical computer science is a subfield of computer science and mathematics that focuses on the abstract and mathematical foundations of computation. It is difficult to circumscribe the theoretical areas precisely. The ACM's Special Interest Group on Algorithms and Computation Theory (SIGACT) provides the following description: [1]
The four color theorem and optimal sphere packing were two major problems of discrete mathematics solved in the second half of the 20th century. [44] The P versus NP problem, which remains open to this day, is also important for discrete mathematics, since its solution would potentially impact a large number of computationally difficult ...
The Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) is a collaboration between Rutgers University, Princeton University, and the research firms AT&T, Bell Labs, Applied Communication Sciences, and NEC. It was founded in 1989 with money from the National Science Foundation. Its offices are located on the Rutgers campus ...