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The variant where variables are required to be 0 or 1, called zero-one linear programming, and several other variants are also NP-complete [2] [3]: MP1 Some problems related to Job-shop scheduling Knapsack problem , quadratic knapsack problem , and several variants [ 2 ] [ 3 ] : MP9
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.
For example, the batik of Cirebon has a fractal dimension of 1.1; the batiks of Yogyakarta and Surakarta (Solo) in Central Java have a fractal dimension of 1.2 to 1.5; and the batiks of Lasem on the north coast of Java and of Tasikmalaya in West Java have a fractal dimension between 1.5 and 1.7. [86]
[1] Topics introduced in the New Math include set theory, modular arithmetic, algebraic inequalities, bases other than 10, matrices, symbolic logic, Boolean algebra, and abstract algebra. [2] All of the New Math projects emphasized some form of discovery learning. [3] Students worked in groups to invent theories about problems posed in the ...
Microsoft Mathematics 4.0 (removed): The first freeware version, released in 32-bit and 64-bit editions in January 2011; [8] features a ribbon GUI Microsoft Math for Windows Phone (removed): A branded mobile application for Windows Phone released in 2015 specifically for South African and Tanzanian students; also known as Nokia Mobile ...
Problems 1, 2, 5, 6, [a] 9, 11, 12, 15, and 22 have solutions that have partial acceptance, but there exists some controversy as to whether they resolve the problems. That leaves 8 (the Riemann hypothesis), 13 and 16 [b] unresolved. Problems 4 and 23 are considered as too vague to ever be described as solved; the withdrawn 24 would also be in ...
It was originally known as "HECKE and Manin". After a short while it was renamed SAGE, which stands for ‘’Software of Algebra and Geometry Experimentation’’. Sage 0.1 was released in 2005 and almost a year later Sage 1.0 was released. It already consisted of Pari, GAP, Singular and Maxima with an interface that rivals that of Mathematica.
In mathematical logic, Tarski's high school algebra problem was a question posed by Alfred Tarski.It asks whether there are identities involving addition, multiplication, and exponentiation over the positive integers that cannot be proved using eleven axioms about these operations that are taught in high-school-level mathematics.