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The UAEH was the first university established in the state of Hidalgo, tracing its origins to the Instituto Literario y Escuela de Artes y Oficios (Literary Institute and School of Arts and Crafts), founded in Pachuca in February 1869 by various businessmen and promptly absorbed by the state government under Governor Juan C. Doria. In 1875, the ...
The term is derived from the Latin word docēns, which is the present active participle of docēre ('to teach, to lecture'). Becoming a docent is often referred to as habilitation or doctor of science and is an academic qualification that shows that the holder is qualified to be employed at the level of associate or full professor.
Modulo is a mathematical jargon that was introduced into mathematics in the book Disquisitiones Arithmeticae by Carl Friedrich Gauss in 1801. [3] Given the integers a, b and n, the expression "a ≡ b (mod n)", pronounced "a is congruent to b modulo n", means that a − b is an integer multiple of n, or equivalently, a and b both share the same remainder when divided by n.
In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a (not necessarily commutative) ring.The concept of a module also generalizes the notion of an abelian group, since the abelian groups are exactly the modules over the ring of integers.
For a given positive integer , two integers and are called congruent modulo , written a ≡ b ( mod n ) {\displaystyle a\equiv b{\pmod {n}}} if a − b {\displaystyle a-b} is divisible by n {\displaystyle n} (or equivalently if a {\displaystyle a} and b {\displaystyle b} have the same remainder when divided by n {\displaystyle n} ).
A plot of the modulus of (in red) for in the unit disk centered at the origin (shown in blue). As predicted by the theorem, the maximum of the modulus cannot be inside of the disk (so the highest value on the red surface is somewhere along its edge).
We can find quadratic residues or verify them using the above formula. To test if 2 is a quadratic residue modulo 17, we calculate 2 (17 − 1)/2 = 2 8 ≡ 1 (mod 17), so it is a quadratic residue. To test if 3 is a quadratic residue modulo 17, we calculate 3 (17 − 1)/2 = 3 8 ≡ 16 ≡ −1 (mod 17), so it is not a quadratic residue.
In algebra, a module homomorphism is a function between modules that preserves the module structures. Explicitly, if M and N are left modules over a ring R, then a function : is called an R-module homomorphism or an R-linear map if for any x, y in M and r in R,