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| series = ...|first=Albrecht |authorlink=Albrecht Beutelspacher |year=1994 |publisher=[[Mathematical Association of America]] |isbn=0-88385-504-6 |pages=9–11 }}</ref> While sol ...

...mmation|sigma summation notation]] the sum of the first ''m'' terms of the series can be expressed as :<math alt="Summation from n equals 1 to m of the series n * (-1)^(n-1)">\sum_{n=1}^m n(-1)^{n-1}.</math> ...

...</ref><ref>{{cite book|title=Nets, Puzzles, and Postmen: An Exploration of Mathematical Connections|author=Peter M. Higgins|year=2007|publisher=Oxford University P ...tician) | title = Euler: The Master of Us All| year = 1999| publisher =The Mathematical Association of America | pages = 17}}</ref> He is also renowned for his wor ...

...f the problem involving these and other assumptions have been published in mathematical literature. ...statement of the Monty Hall problem, explanations, simulations, and formal mathematical proofs, many people still meet the correct answer with disbelief. ...

...g—that it encountered [[Controversy over Cantor's theory|resistance]] from mathematical contemporaries such as [[Leopold Kronecker]] and [[Henri Poincaré]]<ref>Dau ...ngen|University of Göttingen]], then and later a very important center for mathematical research. In 1867, Berlin granted him the [[Doctor of Philosophy|PhD]] for ...

...mathematical proof|Proofs]] have been formulated with varying degrees of [[mathematical rigour]], taking into account preferred development of the real numbers, ba ...generally unrelated to 0.999…, but they are of considerable interest in [[mathematical analysis]]. ...

...of a [[parabola]] with the [[Series (mathematics)|summation of an infinite series]], and gave a remarkably accurate approximation of [[pi]].<ref>{{cite web | ...cluding the bases of the latter), and regarded this as the greatest of his mathematical achievements. ...

...p and its operation. This allows one to handle entities of very different mathematical origins in a flexible way, while retaining essential structural aspects of ...and firmly established around 1870. Modern [[group theory]]—a very active mathematical discipline—studies groups in their own right.{{cref|a}} To explore groups, ...

...n domain]]s. The Euclidean algorithm has been generalized further to other mathematical structures, such as [[knot (mathematics)|knots]] and [[multivariate polynom ...ef>Stark, p. 16.</ref> although the latter notation is also used for other mathematical concepts, such as two-dimensional [[coordinate vector|vectors]]. ...

...>{{cite book| author = [[Isaac Newton|Newton I]]| year = 1974| title = The Mathematical Papers of Isaac Newton, Volume VI: 1684–1691| editor = DT Whiteside| publis ...uthors.<ref name="alt_reconstructions">[[Robert Simson|Simson R]] (1734) ''Mathematical Collection'', volume VII, p. 117.<br>{{cite book| author = Zeuthen HG| year ...

...department at the [[University of Göttingen]], a world-renowned center of mathematical research. The philosophical faculty objected, however, and she spent four y ...s]], ''[[Noether's theorem]]'', has been called "one of the most important mathematical theorems ever proved in guiding the development of modern physics".<ref nam ...

...description had in turn been generalized to higher-dimensional spaces in a mathematical formalism introduced by [[Bernhard Riemann]] in the 1850s. With the help of ...gravity: they are how matter tells spacetime how to curve. In the theory's mathematical formulation, all these quantities are but aspects of a more general physica ...

These mathematical techniques, combined with material supplied by Captain [[Gustave Bertrand]] ...t cryptanalysts of all time".<ref>Kahn, 1996, p. 974</ref> Rejewski used a mathematical theorem that one mathematics professor has since described as "the theorem ...

...er is the sum of the two directly above it. The triangle demonstrates many mathematical properties in addition to showing [[binomial coefficients]].]] ...l=http://www.math.rutgers.edu/courses/436/Honors02/leibniz.html |title=The Mathematical Leibniz |publisher=Math.rutgers.edu |date= |accessdate=2009-08-16}}</ref> ...

...will limit the overall speed-up available from parallelization. Any large mathematical or engineering problem will typically consist of several parallelizable par ...pologies. Logics such as Lamport's [[Temporal logic of actions|TLA+]], and mathematical models such as [[Trace theory|traces]] and [[Actor model theory|Actor event ...

...lgorithm was, to the best of their knowledge, free from any statistical or mathematical weakness."<ref>{{cite book|first=D.W.|last=Davies|coauthors=W.L. Price|titl | Second workshop, discussing mathematical foundation of DES ...

In this context, "[[almost surely]]" is a mathematical term with a precise meaning, and the "monkey" is not an actual monkey; rath ...tal state of a person who can identify the 'works' of Shakespeare with the series of letters printed on the pages of a book…<ref>p.126 of ''The Principles of ...

...own as '''Bridge Formula B''' and the '''Federal Bridge Formula''') is a [[mathematical formula]] used by [[truck drivers]] and [[United States Department of Trans ...ation of State Highway and Transportation Officials]] (AASHTO) conducted a series of extensive [[AASHO Road Test|field tests]] of roads and bridges to determ ...

...w class of preferred motions, too, defines a geometry of space and time—in mathematical terms, it is the [[geodesic]] motion associated with a specific [[connectio ...time's semi-Riemannian metric, at least up to a positive scalar factor. In mathematical terms, this defines a [[conformal structure]].<ref>E.g. {{Harvnb|Ehlers|197 ...

...the court, officials and candidates were asked to provide comments about a series of recent earthquakes which could be interpreted as signs of displeasure fr ...er, the ''[[Book of Later Han]]'' hints that Zhang was the first to make a mathematical grid reference, stating that he "cast a network of coordinates about heaven ...