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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.
Open problems around exact algorithms by Gerhard J. Woeginger, Discrete Applied Mathematics 156 (2008) 397–405. The RTA list of open problems – open problems in rewriting. The TLCA List of Open Problems – open problems in area typed lambda calculus
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
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]
These range from "Algorithmica", where P = NP and problems like SAT can be solved efficiently in all instances, to "Cryptomania", where P ≠ NP and generating hard instances of problems outside P is easy, with three intermediate possibilities reflecting different possible distributions of difficulty over instances of NP-hard problems.
If the answer is yes, many important problems can be shown to have more efficient solutions. These include various types of integer programming problems in operations research, many problems in logistics, protein structure prediction in biology, [5] and the ability to find formal proofs of pure mathematics theorems. [6]
The Diffie–Hellman problem is stated informally as follows: Given an element and the values of and , what is the value of ?. Formally, is a generator of some group (typically the multiplicative group of a finite field or an elliptic curve group) and and are randomly chosen integers.
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