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.

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.

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

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.

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

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.

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

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.

The most general setting in which these words have meaning is an abstract branch of mathematics called category theory.

In mathematics, a binary operation on a set is a calculation involving two elements of the set ( called operands ) and producing another element of the set ( more formally, an operation whose arity is two ).

Following Desargues ' thinking, the sixteen-year-old Pascal produced, as a means of proof, a short treatise on what was called the " Mystic Hexagram ", Essai pour les coniques (" Essay on Conics ") and sent it — his first serious work of mathematics — to Père Mersenne in Paris ; it is known still today as Pascal's theorem.

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.

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

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 ).

Students of control engineering may start with a linear control system course dealing with the time and complex-s domain, which requires a thorough background in elementary mathematics and Laplace transform ( called classical control theory ).

This program is still recognizable in the most popular philosophy of mathematics, where it is usually called formalism.

Instructors in primary and secondary institutions are often called teachers, and they direct the education of students and might draw on many subjects like reading, writing, mathematics, science and history.

Note that congruences alter some properties, such as location and orientation, but leave others unchanged, like distance and angle s. The latter sort of properties are called invariant ( mathematics ) | invariant s and studying them is the essence of geometry.

Then he moved to the Humboldt University of Berlin ( then called the Friedrich William University ) in 1878 where he continued his study of mathematics under Leopold Kronecker and the renowned Karl Weierstrass.

The reason why we do not deal with sensible objects in mathematics is because of another faculty of understanding called " categorial abstraction.

In mathematics and abstract algebra, a group is the algebraic structure, where is a non-empty set and denotes a binary operation called the group operation.

The physicist Richard Feynman called Euler's formula " our jewel " and " one of the most remarkable, almost astounding, formulas in all of mathematics.

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 mathematics, the four color theorem, or the four color map theorem states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color.

A number representation ( called a numeral system in mathematics ) specifies some way of storing a number that may be encoded as a string of digits.

This period has been called the Golden Age of India and was marked by extensive achievements in science, technology, engineering, art, dialectic, literature, logic, mathematics, astronomy, religion, and philosophy that crystallized the elements of what is generally known as Hindu culture.

In mathematics, the harmonic mean ( sometimes called the subcontrary mean ) is one of several kinds of average.

In mathematics, an inner product space is a vector space with an additional structure called an inner product.

In mathematics, an identity function, also called identity map or identity transformation, is a function that always returns the same value that was used as its argument.

In mathematics, the inverse limit ( also called the projective limit ) is a construction which allows one to " glue together " several related objects, the precise manner of the gluing process being specified by morphisms between the objects.

In mathematics, a linear map, linear mapping, linear transformation, or linear operator ( in some contexts also called linear function ) is a function between two modules ( including vector spaces ) that preserves the operations of module ( or vector ) addition and scalar multiplication.