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Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
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]
The general class of questions that some algorithm can answer in polynomial time is "P" or "class P". For some questions, there is no known way to find an answer quickly, but if provided with an answer, it can be verified quickly. The class of questions where an answer can be verified in polynomial time is "NP", standing for "nondeterministic ...
Some math problems have been challenging us for centuries, and while brain-busters like these hard math problems may seem impossible, someone is bound to solve ’em eventually. Well, m aybe .
The question of whether P equals NP is one of the most important open questions in theoretical computer science because of the wide implications of a solution. [3] If the answer is yes, many important problems can be shown to have more efficient solutions.
Kawasaki's theorem (mathematics of paper folding) Kelvin's circulation theorem ; Kempf–Ness theorem (algebraic geometry) Kepler conjecture (discrete geometry) Kharitonov's theorem (control theory) Khinchin's theorem (probability) Killing–Hopf theorem (Riemannian geometry) Kinoshita–Lee–Nauenberg theorem (quantum field theory)
Until that time, the concept of an NP-complete problem did not even exist. The proof shows how every decision problem in the complexity class NP can be reduced to the SAT problem for CNF [a] formulas, sometimes called CNFSAT. A useful property of Cook's reduction is that it preserves the number of accepting answers.