This is an unsolved problem which probably has never been seriously investigated, although one frequently hears the comment that we have insufficient specialists of the kind who can compete with the Germans or Swiss, for example, in precision machinery and mathematics, or the Finns in geochemistry.

In the new situation, philosophy is able to provide the social sciences with the same guidance that mathematics offers the physical sciences, a reservoir of logical relations that can be used in framing hypotheses having explanatory and predictive value.

Blind students also complete mathematical assignments using a braille-writer and Nemeth code ( a type of braille code for mathematics ) but large multiplication and long division problems can be long and difficult.

It can be applied in the study of classical concepts of mathematics, such as real numbers, complex variables, trigonometric functions, and algorithms, or of non-classical concepts like constructivism, harmonics, infinity, and vectors.

It can also be used in topics as diverse as mathematics, gastronomy, fashion and website design.

It can also be used to denote abstract vectors and linear functionals in mathematics.

The term can also be applied to some degree to functions in mathematics, referring to the anatomy of curves.

The contributions of Kurt Gödel in 1940 and Paul Cohen in 1963 showed that the hypothesis can neither be disproved nor be proved using the axioms of Zermelo – Fraenkel set theory, the standard foundation of modern mathematics, provided ZF set theory is consistent.

Many significant areas of mathematics can be formalised as categories, and the use of category theory allows many intricate and subtle mathematical results in these fields to be stated, and proved, in a much simpler way than without the use of categories.

Categories now appear in most branches of mathematics, some areas of theoretical computer science where they correspond to types, and mathematical physics where they can be used to describe vector spaces.

Many important constructions in mathematics can be studied in this context.

Certain categories called topoi ( singular topos ) can even serve as an alternative to axiomatic set theory as a foundation of mathematics.

From these four, a multitude of equations, relating the thermodynamic properties of the thermodynamic system can be derived using relatively simple mathematics.

In mathematics, particularly theoretical computer science and mathematical logic, the computable numbers, also known as the recursive numbers or the computable reals, are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm.

In mathematics and computer science, currying is the technique of transforming a function that takes multiple arguments ( or an n-tuple of arguments ) in such a way that it can be called as a chain of functions each with a single argument ( partial application ).

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 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.

In mathematics, any vector space, V, has a corresponding dual vector space ( or just dual space for short ) consisting of all linear functionals on V. Dual vector spaces defined on finite-dimensional vector spaces can be used for defining tensors.

In the essay a blind English mathematician named Saunderson argues that since knowledge derives from the senses, then mathematics is the only form of knowledge that both he and a sighted person can agree about.

The set of objects studied in discrete mathematics can be finite or infinite.

In mathematics, one can often define a direct product of objects

Modern mathematics defines an " elliptic integral " as any function which can be expressed in the form

In mathematics, more specifically in abstract algebra and ring theory, a Euclidean domain ( also called a Euclidean ring ) is a ring that can be endowed with a certain structure – namely a Euclidean function, to be described in detail below – which allows a suitable generalization of the Euclidean division of the integers.

In logic and the foundations of mathematics, formal languages are used to represent the syntax of axiomatic systems, and mathematical formalism is the philosophy that all of mathematics can be reduced to the syntactic manipulation of formal languages in this way.

The axiom of choice has also been thoroughly studied in the context of constructive mathematics, where non-classical logic is employed.

Although the axiom of countable choice in particular is commonly used in constructive mathematics, its use has also been questioned.

It is also commonly used in mathematics in algebraic solutions representing quantities such as angles.

The term may be also used loosely or metaphorically to denote highly skilled people in any non -" art " activities, as well — law, medicine, mechanics, or mathematics, for example.

He also applied mathematics in generalizing physical laws from these experimental results.

Despite being quite religious, he was also interested in mathematics and science, and sometimes is claimed to have contradicted the teachings of the Church in favour of scientific theories.

He was educated at the Collège des Quatre-Nations ( also known as Collège Mazarin ) from 1754 to 1761, studying chemistry, botany, astronomy, and mathematics.

His criticisms of the scientific community, and especially of several mathematics circles, are also contained in a letter, written in 1988, in which he states the reasons for his refusal of the Crafoord Prize.

He is also noted for his mastery of abstract approaches to mathematics and his perfectionism in matters of formulation and presentation.

In mathematics, the axiom of regularity ( also known as the axiom of foundation ) is one of the axioms of Zermelo – Fraenkel set theory and was introduced by.

In classical mathematics, analytic geometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system and the principles of algebra and analysis.

He won a scholarship to the University and majored in mathematics, and also studied astronomy, physics and chemistry.

His father, Étienne Pascal ( 1588 – 1651 ), who also had an interest in science and mathematics, was a local judge and member of the " Noblesse de Robe ".

In chemistry, physics, and mathematics, the Boltzmann distribution ( also called the Gibbs Distribution ) is a certain distribution function or probability measure for the distribution of the states of a system.

Bioinformatics also deals with algorithms, databases and information systems, web technologies, artificial intelligence and soft computing, information and computation theory, structural biology, software engineering, data mining, image processing, modeling and simulation, discrete mathematics, control and system theory, circuit theory, and statistics.

In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers which at the same time is also a Banach space.

Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, and combinatorics also has many applications in optimization, computer science, ergodic theory and statistical physics.

It has also given rise to a new theory of the philosophy of mathematics, and many theories of artificial intelligence, persuasion and coercion.

Most undergraduate programs emphasize mathematics and physics as well as chemistry, partly because chemistry is also known as " the central science ", thus chemists ought to have a well-rounded knowledge about science.

Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows ( also called morphisms, although this term also has a specific, non category-theoretical meaning ), where these collections satisfy some basic conditions.