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The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is NP-complete with the discretized Euclidean metric and rectilinear metric. The problem is known to be NP-hard with the (non-discretized) Euclidean metric. [3]: ND22, ND23
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.
Calculus. In mathematics education, precalculus is a course, or a set of courses, that includes algebra and trigonometry at a level which is designed to prepare students for the study of calculus, thus the name precalculus. Schools often distinguish between algebra and trigonometry as two separate parts of the coursework. [1]
A typical sequence of secondary-school (grades 6 to 12) courses in mathematics reads: Pre-Algebra (7th or 8th grade), Algebra I, Geometry, Algebra II, Pre-calculus, and Calculus or Statistics. However, some students enroll in integrated programs [3] while many complete high school without passing Calculus or Statistics.
Fundamental theorem of arithmetic. Gauss–Markov theorem (brief pointer to proof) Gödel's incompleteness theorem. Gödel's first incompleteness theorem. Gödel's second incompleteness theorem. Goodstein's theorem. Green's theorem (to do) Green's theorem when D is a simple region. Heine–Borel theorem.
The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US $1 million prize for the first correct solution to each problem. The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved ...
[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. [8] [9]
The following are the headers for Hilbert's 23 problems as they appeared in the 1902 translation in the Bulletin of the American Mathematical Society. [1] 1. Cantor's problem of the cardinal number of the continuum. 2. The compatibility of the arithmetical axioms. 3. The equality of the volumes of two tetrahedra of equal bases and equal altitudes.
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