But now he knows `` that an intellectual is not only a man to whom books are necessary, he is any man whose reasoning, however elementary it may be, affects and directs his life ''.

RCA Victor has an ambitious and useful project in a stereo series called `` Adventures In Music '', which is an instructional record library for elementary schools.

It has already been reported in your newspapers that the East Greenwich School Committee is considering additions to at least one elementary school and to the high school to insure future accommodations for a school population that we know will increase.

To appreciate the nature of the gamble, it should be realized that while college teaching is almost a public symbol of security, that security does not come as quickly or as automatically as it does in an elementary school system or in the Civil Service.

Since a coulomb is approximately equal to elementary charges ( such as electrons ), one ampere is approximately equivalent to elementary charges moving past a boundary in one second, or the reciprocal of the value of the elementary charges in coulombs.

But humans can do something equally useful, in the case of certain enumerably infinite sets: They can give explicit instructions for determining the nth member of the set, for arbitrary finite n. Such instructions are to be given quite explicitly, in a form in which they could be followed by a computing machine, or by a human who is capable of carrying out only very elementary operations on symbols.

The gluon is a member of the family of gauge bosons, which are elementary particles that mediate physical forces.

Thus, an axiom is an elementary basis for a formal logic system that together with the rules of inference define a deductive system.

where e is the elementary charge and I is the average current.

The elementary theory of optical systems leads to the theorem: Rays of light proceeding from any object point unite in an image point ; and therefore an object space is reproduced in an image space.

However, in quantum physics, there is another type of angular momentum, called spin angular momentum, represented by the spin operator S. Almost all elementary particles have spin.

Arithmetic or arithmetics ( from the Greek word ἀριθμός, arithmos " number ") is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations.

This is an elementary example of the family of advantage play techniques known as card counting.

Indeed, the most elementary definition of bipolar disorder is an often " violent " or " jarring " state of essentially uncontrollable oscillation between hyperthymia and dysthymia.

An " elementary " proof can be given using the fact that geometric mean of positive numbers is less than arithmetic mean

Bézout's identity ( also called Bezout's lemma ) is a theorem in the elementary theory of numbers: let a and b be integers, not both zero, and let d be their greatest common divisor.

Specifically it is the amount of a substance that contains as many elementary entities ( atoms, molecules or ions ) as there are atoms in 0. 012 kilogram ( or 12 grams ) of carbon-12, where the carbon-12 atoms are unbound, at rest and in their ground state.

The number of k-combinations from a given set S of n elements is often denoted in elementary combinatorics texts by C ( n, k ), or by a variation such as,, or even ( the latter form is standard in French, Russian, and Polish texts ).

When this linear draft is completed, I dust it down to a faint image.

The theory predicts a linear dependence of Af on Af, where J is the experimentally determined Curie-Weiss constant.

If the Af bond is linear then there are three reasonable positions for the hydrogen atoms: ( 1 ) The hydrogen atoms are centered and hence all lie on a sheet midway between the oxygen sheets ; ;

If Af are the projections associated with the primary decomposition of T, then each Af is a polynomial in T, and accordingly if a linear operator U commutes with T then U commutes with each of the Af, i.e., each subspace Af is invariant under U.

From these results, one sees that the study of linear operators on vector spaces over an algebraically closed field is essentially reduced to the study of nilpotent operators.

We have chosen to give it at the end of the section since it deals with differential equations and thus is not purely linear algebra.

If T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.

that is, one must know something about D other than the fact that it is a linear operator.

UTC is a discontinuous time scale composed from segments that are linear transformations of atomic time, the discontinuities being arranged so that UTC approximated UT2 until the end of 1971, and UT1 thereafter.

# As exploratory data analysis, an ANOVA is an organization of an additive data decomposition, and its sums of squares indicate the variance of each component of the decomposition ( or, equivalently, each set of terms of a linear model ).

# Closely related to the ANOVA is a linear model fit with coefficient estimates and standard errors.

Even when the statistical model is nonlinear, it can be approximated by a linear model for which an analysis of variance may be appropriate.

Since the randomization-based analysis is complicated and is closely approximated by the approach using a normal linear model, most teachers emphasize the normal linear model approach.

ANOVA is considered to be a special case of linear regression

which in turn is a special case of the general linear model.

** On every infinite-dimensional topological vector space there is a discontinuous linear map.

* In linear algebra, an endomorphism of a vector space V is a linear operator V → V. An automorphism is an invertible linear operator on V. When the vector space is finite-dimensional, the automorphism group of V is the same as the general linear group, GL ( V ).

has no zero in F. By contrast, the fundamental theorem of algebra states that the field of complex numbers is algebraically closed.

In the context of abstract algebra, for example, a mathematical object is an algebraic structure such as a group, ring, or vector space.

The same definition holds in any unital ring or algebra where a is any invertible element.

In addition to its obvious importance in geometry and calculus, area is related to the definition of determinants in linear algebra, and is a basic property of surfaces in differential geometry.

Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry.

His notion of abelian category is now the basic object of study in homological algebra.

With the existence of an alpha channel, it is possible to express compositing image operations, using a compositing algebra.

In mathematics, an associative algebra A is an associative ring that has a compatible structure of a vector space over a certain field K or, more generally, of a module over a commutative ring R. Thus A is endowed with binary operations of addition and multiplication satisfying a number of axioms, including associativity of multiplication and distributivity, as well as compatible multiplication by the elements of the field K or the ring R.

Explicitly, is an associative algebra homomorphism if

* Given any Banach space X, the continuous linear operators A: X → X form a unitary associative algebra ( using composition of operators as multiplication ); this is a Banach algebra.

* An example of a non-unitary associative algebra is given by the set of all functions f: R → R whose limit as x nears infinity is zero.

* Any ring of characteristic n is a ( Z / nZ )- algebra in the same way.

* Any ring A is an algebra over its center Z ( A ), or over any subring of its center.

* Any commutative ring R is an algebra over itself, or any subring of R.

Other important Arabic astrologers include Albumasur and Al Khwarizmi, the Persian mathematician, astronomer and astrologer, who is considered the father of algebra and the algorithm.