This would provide for long-term Federal loans for construction of parochial and other private-school facilities for teaching science, languages and mathematics.

The term " arithmetic mean " is preferred in mathematics and statistics because it helps distinguish it from other means such as the geometric and harmonic mean.

In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number.

Two aspects of this attitude deserve to be mentioned: 1 ) he did not only study science from books, as other academics did in his day, but actually observed and experimented with nature ( the rumours starting by those who did not understand this are probably at the source of Albert's supposed connections with alchemy and witchcraft ), 2 ) he took from Aristotle the view that scientific method had to be appropriate to the objects of the scientific discipline at hand ( in discussions with Roger Bacon, who, like many 20th century academics, thought that all science should be based on mathematics ).

* Absorbing element, in mathematics, an element that does not change when it is combined in a binary operation with some other element

His influence spilled over into many other branches of mathematics, for example the contemporary theory of D-modules.

Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.

This is philosophically unsatisfying to some and has motivated additional work in set theory and other methods of formalizing the foundations of mathematics such as New Foundations by Willard Van Orman Quine.

A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis.

In mathematics, a Cauchy sequence ( pronounced ), named after Augustin-Louis Cauchy, is a sequence whose elements become arbitrarily close to each other as the sequence progresses.

" In addition, the element Earth is associated with Budha or Mercury who represents communication, business, mathematics and other practical matters.

Most frequently, sophisticated mathematics is used to manipulate complex three dimensional polygons, apply “ textures ”, lighting and other effects to the polygons and finally rendering the complete image.

These can include shi ( 史, historical works ), zi ( 子, philosophical works belonging to schools of thought other than the Confucian, but also works of agriculture, medicine, mathematics, astronomy, divination, art criticism, and all sorts of miscellaneous writings ) and ji ( 集, literary works ) as well as jing.

The originality of Descartes ' thinking, therefore, is not so much in expressing the cogito — a feat accomplished by other predecessors, as we shall see — but on using the cogito as demonstrating the most fundamental epistemological principle, that science and mathematics are justified by relying on clarity, distinctiveness, and self-evidence.

The classification theorem has applications in many branches of mathematics, as questions about the structure of finite groups ( and their action on other mathematical objects ) can sometimes be reduced to questions about finite simple groups.

Computational complexity theory is a branch of the theory of computation in theoretical computer science and mathematics that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.

Cartesian coordinates are the foundation of analytic geometry, and provide enlightening geometric interpretations for many other branches of mathematics, such as linear algebra, complex analysis, differential geometry, multivariate calculus, group theory, and more.

This activity is performed through the verbal impersonation of the characters by the players, while also employing a variety of social and other useful cognitive skills, such as logic, basic mathematics and imagination.

In mathematics, a directed set ( or a directed preorder or a filtered set ) is a nonempty set A together with a reflexive and transitive binary relation ≤ ( that is, a preorder ), with the additional property that every pair of elements has an upper bound: In other words, for any a and b in A there must exist a c in A with a ≤ c and b ≤ c.

For Husserl this is not the case: mathematics ( with the exception of geometry ) is the ontological correlate of logic, and while both fields are related, neither one is strictly reducible to the other.

In modern mathematics, Euclidean spaces form the prototypes for other, more complicated geometric objects.

This proved to be a fertile approach, which later mathematicians adapted to many other fields of mathematics besides the theory of equations to which Galois originally applied it.

In mathematics, more specifically algebraic topology, the fundamental group ( defined by Henri Poincaré in his article Analysis Situs, published in 1895 ) is a group associated to any given pointed topological space that provides a way of determining when two paths, starting and ending at a fixed base point, can be continuously deformed into each other.

The field is largely focused on the modelling of derivatives, although other important subfields include insurance mathematics and quantitative portfolio problems.

Greek words have been widely borrowed into other languages, including English: mathematics, physics, astronomy, democracy, philosophy, thespian, athletics, theatre, rhetoric, baptism, evangelist etc.

Though respected for their contributions to various academic disciplines ( respectively mathematics, linguistics, and literature ), the three men became known to the general public only by making often-controversial and disputed pronouncements on politics and public policy that would not be regarded as noteworthy if offered by a medical doctor or skilled tradesman.

On the inside, a renderer is a carefully engineered program, based on a selective mixture of disciplines related to: light physics, visual perception, mathematics and software development.

Certain forms treat all knowledge as empirical, while some regard disciplines such as mathematics and logic as exceptions.

Examples of broad areas of academic disciplines include the natural sciences, mathematics, computer science, social sciences, humanities and applied sciences.

Thus, contrary to the first impression its name might convey, and as realized in specific approaches and disciplines ( e. g. Fuzzy Sets and Systems ), intuitionist mathematics is more rigorous than conventionally founded mathematics, where, ironically, the foundational elements which Intuitionism attempts to construct / refute / refound are taken as intuitively given.

The changes that took place at the beginning of the 20th-century are emphasized by the fact that many modern disciplines, including sciences such as physics, mathematics, neuroscience and economics, and arts such as ballet and architecture, call their pre-20th century forms classical.

In the broad definition, the parent disciplines of musicology include history ; cultural studies and gender studies ; philosophy, aesthetics and semiotics ; ethnology and cultural anthropology ; archeology and prehistory ; psychology and sociology ; physiology and neuroscience ; acoustics and psychoacoustics ; and computer / information sciences and mathematics.

However, it is currently an interdisciplinary science that collaborates with other fields such as chemistry, computer science, engineering, linguistics, mathematics, medicine and allied disciplines, philosophy, physics, and psychology.

Parameter ( from Ancient Greek παρά also “ para ” meaning “ beside, subsidiary ” and μέτρον also “ metron ” meaning “ measure ”) can be interpreted in mathematics, logic, linguistics, environmental science and other disciplines.

Degrees are traditionally used in navigation, surveying, and many applied disciplines, while radians are more common in mathematics and mathematical physics.

In specific disciplines, Stanford was ranked in English ( in the United States ), in modern languages ( 7 ), in history ( 8 ), in philosophy ( 4 ), in geography & area studies ( 4 ), in linguistics ( 3 ), in computer science ( 2 ), in civil & structural engineering ( 2 ), in chemical engineering ( 3 ), in electrical engineering ( 2 ), in mechanical, aeronautical, & manufacturing engineering, in medicine ( 3 ), in biological sciences ( 3 ), in chemistry ( 4 ), in physics and astronomy ( 4 ), in metallurgy ( 4 ), in mathematics ( 3 ), in environmental sciences ( 4 ), in earth and marine sciences ( 6 ), in psychology ( 2 ), in sociology ( 4 ), in statistics, in politics and international studies ( 4 ), in law ( 3 ), in economics ( 3 ), and in account and finance.

Approximately one-third of the laboratory's technical staff members are physicists, one quarter are engineers, one-sixth are chemists and materials scientists, and the remainder work in mathematics and computational science, biology, geoscience, and other disciplines.

The applied tools of the mathematics disciplines of Celestial mechanics or its subfield Orbital mechanics ( both predict orbital paths and positions ) about a center of gravity are used to generate an ephemeris ( plural: ephemerides ; from the Greek word ephemeros = daily ) which is a table of values that gives the positions of astronomical objects in the sky at a given time or times, or a formula to calculate such given the proper time offset from the epoch.

The Han applied mathematics to various diverse disciplines.

In mathematics, the phrase up to is useful for modeling fundamental concepts within a realm of mathematical inquiry, and can be compared with the phrase " all other things being equal " in other disciplines.

These terms are used in scientific disciplines from mathematics and logic to economics and psychology to denote similar investigative procedures.

Other than the associated disciplines just mentioned, cognitive neuroscientists may have backgrounds in these disciplines: neurobiology, bioengineering, psychiatry, neurology, physics, computer science, linguistics, philosophy and mathematics.

As with most engineering disciplines, having a sound knowledge of mathematics and sciences is necessary for computer engineers.

Grenoble is also a major scientific centre, especially in the fields of physics, computer science, and applied mathematics: Joseph Fourier University ( UJF ) is one of the leading French scientific universities while the Grenoble Institute of Technology trains more than 5, 000 engineers every year in key technology disciplines.

Most IEEE members are electrical and electronics engineers, but the organization's wide scope of interests has attracted people in other disciplines as well ( e. g., computer science, mechanical engineering, civil engineering, biology, physics, and mathematics ).

Also, a person can gain the skills required to become a professional economist in other related disciplines, such as statistics or some types of applied mathematics, such as mathematical finance or game theory.

Various disciplines within mathematics have given the term different meanings depending on the area of study, so the precise meaning depends on context.

Ridgewood Avenue School offers an academic curriculum in the major disciplines of language arts literacy, mathematics, social studies, and science, and students are exposed to art, instrumental and vocal music, physical education, health, library skills and Spanish.