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The history of discrete mathematics has involved a number of challenging problems which have focused attention within areas of the field. In graph theory, much research was motivated by attempts to prove the four color theorem , first stated in 1852, but not proved until 1976 (by Kenneth Appel and Wolfgang Haken, using substantial computer ...
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 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 .
The discrete logarithm problem is considered to be computationally intractable. That is, no efficient classical algorithm is known for computing discrete logarithms in general. A general algorithm for computing log b a in finite groups G is to raise b to larger and larger powers k until the desired a is found.
This problem concerns the issue of whether questions that are easy to verify (a class of queries called NP) also have solutions that are easy to find (a class called P). Hosch, William L (11 August 2009). "P versus NP problem mathematics". Encyclopædia Britannica "P vs NP Problem". www.claymath.org (Cook, Levin)
[7] Jeffrey Lagarias stated in 2010 that the Collatz conjecture "is an extraordinarily difficult problem, completely out of reach of present day mathematics". [8] However, though the Collatz conjecture itself remains open, efforts to solve the problem have led to new techniques and many partial results.
A college student just solved a seemingly paradoxical math problem—and the answer came from an incredibly unlikely place. Skip to main content. 24/7 Help. For premium support please call: 800 ...
Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete: An optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must be found from a countable set.
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