Mathematics Dictionary

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unbiased estimator An statistic whose expected value is known to be identical to the value being estimated.

unbiased hypothesis test: A hypothesis test where the probability of rejecting the null hypothesis is not less than the significance level if the alternative hypothesis is true and is not greater than the significance level when the null hypothesis is true.

unbounded function: A function whose values (in the image) form an unbounded set.

unbounded set A set (with some sort of distance function defined) such that, for any real value, there are always two elements of the set whose "distance" is greater than the real value.

uncountable An infinite set for which a bijection to the set of integers is impossible.

underdetermined_system_of_equations A system of equations whose degree of freedom in the variables is greater than that of the degree of constraint imposed by the equations. For real equations in real variables, it is a system where the number of variables is greater than the number of equations.

uniform distribution A probability distribution where all elements have the same probability. In the case of a continuous function, all values have the same probability density.

uniformly continuous function Informally, a continuous function satisfying the weierstrass definition of limits in the same way, regardless of the point in the function. Formally, for all ε > 0 there exists a δ > 0 such that for all xy ∈ X |x − y| < δ implies |ƒ(x) − ƒ(y)| < ε.

uniform motion The motion of an object under no resultant external force - constantvelocity.

uniform polyhedron A polyhedron composed of regular polygonal faces with a high degree of reflective and rotational symmetry.

unilateral surface A two dimensional object with only one side. Notable examples are the Moebius strip, the Klein Bottle and the Real-Projective Plane (RP2).

unimodal distribution Any distribution with only one mode.

union (join, sum, cup): A set-building operation where the new set consists of all elements of each set. Alternatively, an object is a member of the union of the sets A and B if the object is an element of the set A, and, an object is a member of the union of the sets A and B if the object is an element of the set B.

unique factorisation theorem The descriptive name of the fundamental theorem of arithmetic.

unitary ratio A ratio in which one of the terms is reduced to 1. (Even if it means that the other term becomes a non-integer.)

unit circle A circle with a radius of 1. unit in length.

unit cube A cube whose edges are of length 1.

unit disc A disc with a radius of 1.

unit matrix Another name for the identity matrix

unit sphere A sphere with a radius of 1. unit in length.

unit square A square whose edges are of length 1.

unit vector A vector with magnitude of 1.

unity Of or related to the number 1. For example, the topic of the roots of unity concern complex numbers is the study of the multitude of roots of the real number 1.

universal set The set of all objects under consideration. As opposed to the concept of the empty set.

unknown A quantity that may take on different values. The presence of an unknown does not always implied that there is an answer to be found.

upper bound The upper bound of a set of values is a value that is greater than or equal to all other values in the set.

upper limit The value whose substitution into the anti-derivative forms the minuend of the calculation of a definite integral.

upper triangular matrix: A matrix where all elements "below" the main diagonal is zero. Alternatively, A matrix M is an upper triangular matrix if all elements mij is zero where i < j.

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It's not that I'm so smart, it's just that I stay with problems longer.
Albert Einstein

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