* Reflections and Refractions in Ray Tracing, a simple but thorough discussion of the mathematics behind refraction and reflection.

In physics and mathematics, a pseudovector ( or axial vector ) is a quantity that transforms like a vector under a proper rotation, but gains an additional sign flip under an improper rotation such as a reflection.

A reflection through an axis followed by a reflection across a second axis parallel to the first one results in a total motion which is a translation ( mathematics ) | translation.

A reflection across an axis followed by a reflection in a second axis not parallel to the first one results in a total motion that is a Rotation ( mathematics ) | rotation around the point of intersection of the axes.

In mathematics, extendible cardinals are large cardinals introduced by, who was partly motivated by reflection principles.

A reflection ( mathematics ) | reflection against an axis followed by a reflection against a second axis not parallel to the first one results in a total motion that is a rotation around the point of intersection of the axes.

In their activities and in reflection, they come to new insights and integrate diverse knowledge from fields such as English, political science, mathematics, and sociology.

A reflection against an axis followed by a reflection against a second axis parallel to the first one results in a total motion which is a translation ( mathematics ) | translation.

For bilateral symmetry in mathematics, see reflection symmetry.

A molecule is achiral ( not chiral ) when an improper rotation, that is a combination of a rotation and a reflection in a plane, perpendicular to the axis of rotation, results in the same molecule-see chirality ( mathematics ).

In transformation geometry, the elemental concept of transformation is the reflection ( mathematics ).

In physics and mathematics, a pseudotensor is usually a quantity that transforms like a tensor under an orientation preserving coordinate transformation ( e. g., a proper rotation ), but additionally changes sign under an orientation reversing coordinate transformation ( e. g., an improper rotation, which is a transformation that can be expressed as a proper rotation followed by reflection ).

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.

In number theory, a branch of mathematics, two integers a and b are said to be coprime ( also spelled co-prime ) or relatively prime if the only positive integer that evenly divides both of them is 1.

Mikhail Leonidovich Gromov ( also spelled Mikhael Gromov or Michael Gromov ; ; born 23 December 1943 ), is a French-Russian mathematician known for important contributions in many different areas of mathematics.

The band sometimes spelled their name as " N ∅ thing Painted Blue " ( abbreviated "∅ PB "), a use of notation for the empty set in mathematics.

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.

Next September, after receiving a degree from Yale's Master of Arts in Teaching Program, I will be teaching somewhere -- that much is guaranteed by the present shortage of mathematics teachers.

But because science is based on mathematics doesn't mean that a hot rodder must necessarily be a mathematician.

Like primitive numbers in mathematics, the entire axiological framework is taken to rest upon its operational worth.

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.

So, too, is the mathematical competence of a college graduate who has majored in mathematics.

The principal of the school announced that -- despite the help of private tutors in Hollywood and Philadelphia -- Fabian is a 10-o'clock scholar in English and mathematics.

In mathematics and statistics, the arithmetic mean, or simply the mean or average when the context is clear, is the central tendency of a collection of numbers taken as the sum of the numbers divided by the size of the collection.

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 addition to mathematics and statistics, the arithmetic mean is used frequently in fields such as economics, sociology, and history, though it is used in almost every academic field to some extent.

The use of the soroban is still taught in Japanese primary schools as part of mathematics, primarily as an aid to faster mental calculation.

In mathematics and computer science, an algorithm ( originating from al-Khwārizmī, the famous Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī ) is a step-by-step procedure for calculations.

In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that " the product of a collection of non-empty sets is non-empty ".

The axiom of choice is avoided in some varieties of constructive mathematics, although there are varieties of constructive mathematics in which the axiom of choice is embraced.

:" A choice function exists in constructive mathematics, because a choice is implied by the very meaning of existence.

One of the most interesting aspects of the axiom of choice is the large number of places in mathematics that it shows up.

There is no prize awarded for mathematics, but see Abel Prize.