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In computational number theory, the index calculus algorithm is a probabilistic algorithm for computing discrete logarithms.Dedicated to the discrete logarithm in (/) where is a prime, index calculus leads to a family of algorithms adapted to finite fields and to some families of elliptic curves.
In mathematics education, calculus is an abbreviation of both infinitesimal calculus and integral calculus, which denotes courses of elementary mathematical analysis.. In Latin, the word calculus means “small pebble”, (the diminutive of calx, meaning "stone"), a meaning which still persists in medicine.
The calculus of variations began with the work of Isaac Newton, such as with Newton's minimal resistance problem, which he formulated and solved in 1685, and later published in his Principia in 1687, [2] which was the first problem in the field to be formulated and correctly solved, [2] and was also one of the most difficult problems tackled by variational methods prior to the twentieth century.
We are free to choose components as infinitesimally small as we wish as long as they remain nonzero. Since the outer product of these terms can be interpreted as a k {\displaystyle k} -volume, a natural way to define a measure is
The first published statement and proof of a rudimentary form of the fundamental theorem, strongly geometric in character, [2] was by James Gregory (1638–1675). [ 3 ] [ 4 ] Isaac Barrow (1630–1677) proved a more generalized version of the theorem, [ 5 ] while his student Isaac Newton (1642–1727) completed the development of the ...
Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, . [1] The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration.
For example, in 3-D Euclidean space and using Cartesian coordinates; the coordinate vector A = (A 1, A 2, A 3) = (A x, A y, A z) shows a direct correspondence between the subscripts 1, 2, 3 and the labels x, y, z. In the expression A i, i is interpreted as an index ranging over the values 1, 2, 3, while the x, y, z subscripts are only labels ...
Plankalkül (German pronunciation: [ˈplaːnkalkyːl]) is a programming language designed for engineering purposes by Konrad Zuse between 1942 and 1945. It was the first high-level programming language to be designed for a computer.