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Eigenvalue problems occur naturally in the vibration analysis of mechanical structures with many degrees of freedom. The eigenvalues are the natural frequencies(or eigenfrequencies) of vibration, and the eigenvectors are the shapes of these vibrational modes.
Mathematics in Nazi Germany was heavily affected by Nazi policies. Though Jews had previously faced discrimination in academic institutions, the Civil Service Law of 1933 led to the dismissal of many Jewish mathematics professors and lecturers at German universities. During this time, many Jewish mathematicians left Germany and took positions at American universities.
Al-Khwārizmī's contributions to mathematics, geography, astronomy, and cartography established the basis for innovation in algebra and trigonometry. His systematic approach to solving linear and quadratic equations led to algebra, a word derived from the title of his book on the subject, Al-Jabr. [40]
Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. [1] [2] It is generally divided into two subfields: discrete optimization and continuous optimization.
The programs developed in the years after the Dartmouth Workshop were, to most people, simply "astonishing": [79] computers were solving algebra word problems, proving theorems in geometry and learning to speak English.
In mathematics, reduction refers to the rewriting of an expression into a simpler form. For example, the process of rewriting a fraction into one with the smallest whole-number denominator possible (while keeping the numerator a whole number) is called "reducing a fraction". Rewriting a radical (or "root") expression with the smallest possible ...
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