Real analysisIn mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued sequences and functions that real analysis studies include convergence, limits, continuity, smoothness, differentiability and integrability. Real analysis is distinguished from complex analysis, which deals with the study of complex numbers and their functions.
PermutationIn mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set. Permutations differ from combinations, which are selections of some members of a set regardless of order. For example, written as tuples, there are six permutations of the set {1, 2, 3}, namely (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1).
Differential analyserThe differential analyser is a mechanical analogue computer designed to solve differential equations by integration, using wheel-and-disc mechanisms to perform the integration. It was one of the first advanced computing devices to be used operationally. The original machines could not add, but then it was noticed that if the two wheels of a rear differential are turned, the drive shaft will compute the average of the left and right wheels.
Series (mathematics)In mathematics, a series is, roughly speaking, the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures (such as in combinatorics) through generating functions. In addition to their ubiquity in mathematics, infinite series are also widely used in other quantitative disciplines such as physics, computer science, statistics and finance.
GenevaGeneva (dʒəˈniːvə ; Genève ʒənɛv) is the second-most populous city in Switzerland (after Zürich) and the most populous city of Romandy, the French-speaking part of Switzerland. Situated in the south west of the country, where the Rhône exits Lake Geneva, it is the capital of the Republic and Canton of Geneva, and a center for international diplomacy. The city of Geneva (ville de Genève) had a population of 203,951 in 2020 (Jan. estimate) within its small municipal territory of , but the Canton of Geneva (the city and its closest Swiss suburbs and exurbs) had a population of 504,128 (Jan.
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