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The Interactive Mathematics Program (IMP) is a four-year, problem-based mathematics curriculum for high schools. It was one of several curricula funded by the National Science Foundation and designed around the 1989 National Council of Teachers of Mathematics (NCTM) standards .
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.
Rule 110 - most questions involving "can property X appear later" are undecidable. The problem of determining whether a quantum mechanical system has a spectral gap. [8] [9] Finding the capacity of an information-stable finite state machine channel. [10] In network coding, determining whether a network is solvable. [11] [12]
For example, an event in spacetime may be represented as a position four-vector, with coherent derived unit of meters: it includes a position Euclidean vector and a timelike component, t ⋅ c 0 (involving the speed of light). In that case, the Minkowski metric is adopted instead of the Euclidean metric.
A unit of measurement, or unit of measure, is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. [1] Any other quantity of that kind can be expressed as a multiple of the unit of measurement. [2] For example, a length is a physical quantity.
Conceptual questions or conceptual problems in science, technology, engineering, and mathematics (STEM) education are questions that can be answered based only on the knowledge of relevant concepts, rather than performing extensive calculations. They contrast with most homework and exam problems in science and engineering that typically require ...
A physical quantity can be expressed as a value, which is the algebraic multiplication of a numerical value and a unit of measurement. For example, the physical quantity mass, symbol m, can be quantified as m=n kg, where n is the numerical value and kg is the unit symbol (for kilogram). Quantities that are vectors have, besides numerical value ...
The unit interval is a subset of the real numbers. However, it has the same size as the whole set: the cardinality of the continuum . Since the real numbers can be used to represent points along an infinitely long line , this implies that a line segment of length 1, which is a part of that line, has the same number of points as the whole line.