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MacMahon Master theorem (enumerative combinatorics) Maharam's theorem (measure theory) Mahler's compactness theorem (geometry of numbers) Mahler's theorem (p-adic analysis) Maier's theorem (analytic number theory) Malgrange preparation theorem (singularity theory) Malgrange–Ehrenpreis theorem (differential equations)
Sections 4.3 (The master method) and 4.4 (Proof of the master theorem), pp. 73–90. Michael T. Goodrich and Roberto Tamassia. Algorithm Design: Foundation, Analysis, and Internet Examples. Wiley, 2002. ISBN 0-471-38365-1. The master theorem (including the version of Case 2 included here, which is stronger than the one from CLRS) is on pp. 268 ...
In geometry, an isosceles triangle (/ aɪ ˈ s ɒ s ə l iː z /) is a triangle that has two sides of equal length or two angles of equal measure. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.
In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle. Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid 's Elements . [ 1 ]
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.
Absolute geometry is a geometry based on an axiom system consisting of all the axioms giving Euclidean geometry except for the parallel postulate or any of its alternatives. [69] The term was introduced by János Bolyai in 1832. [70] It is sometimes referred to as neutral geometry, [71] as it is neutral with respect to the parallel postulate.
[1] [2] [3] This theorem is best known in Russia, where it is called the trillium theorem (теорема трилистника) or trident lemma (лемма о трезубце), based on the geometric figure's resemblance to a trillium flower or trident; [4] [5] these names have sometimes also been adopted in English.
In some cases, there may be more sums then variables. For example, if the integrand is a product of 3 functions of a common single variable, and each function is converted to a series expansion sum, the integrand is now a product of 3 sums, each sum corresponding to a distinct series expansion.
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