These keys are the working principles of physics, mathematics and astronomy, principles which are then extrapolated, or projected, to explain phenomena of which we have little or no direct knowledge.

Connes has applied his work in areas of mathematics and theoretical physics, including number theory, differential geometry and particle physics.

Another possibility, raised in an essay by the Swedish fantasy writer and editor Rickard Berghorn, is that the name Alhazred was influenced by references to two historical authors whose names were Latinized as Alhazen: Alhazen ben Josef, who translated Ptolemy into Arabic ; and Abu ' Ali al-Hasan ibn al-Haytham, who wrote about optics, mathematics and physics.

Overall, his contributions are considered the most important in advancing chemistry to the level reached in physics and mathematics during the 18th century.

Francesco Lana de Terzi, a 17th century Jesuit professor of physics and mathematics from Brescia, Lombardy, has been referred to as the Father of Aeronautics.

Akio, however, found his true calling in mathematics and physics, and in 1944 he graduated from Osaka Imperial University with a degree in physics.

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

Born in Jerusalem in 1937 to secular parents, Steinsaltz studied mathematics, physics, and chemistry at the Hebrew University, in addition to rabbinical studies.

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.

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.

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.

* Theoretical chemistry is the study of chemistry via theoretical reasoning ( usually within mathematics or physics ).

On November 29, 1921, the trustees declared it to be the express policy of the Institute to pursue scientific research of the greatest importance and at the same time " to continue to conduct thorough courses in engineering and pure science, basing the work of these courses on exceptionally strong instruction in the fundamental sciences of mathematics, physics, and chemistry ; broadening and enriching the curriculum by a liberal amount of instruction in such subjects as English, history, and economics ; and vitalizing all the work of the Institute by the infusion in generous measure of the spirit of research.

Caltech requires students to take a core curriculum of 30 classes: five terms of mathematics, five terms of physics, two terms of chemistry, one term of biology, a freshman elective " menu " course, two terms of introductory lab courses, 2 terms of science writing, and 12 terms of humanities.

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.

* nLab, a wiki project on mathematics, physics and philosophy with emphasis on the n-categorical point of view

Chemical engineering is the branch of engineering that deals with physical science ( e. g., chemistry and physics ), and life sciences ( e. g., biology, microbiology and biochemistry ) with mathematics and economics, to the process of converting raw materials or chemicals into more useful or valuable forms.

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.

* Theoretical chemistry – study of chemistry via fundamental theoretical reasoning ( usually within mathematics or physics ).

After completing high school Doppler studied philosophy in Salzburg and mathematics and physics at the k. k. Polytechnisches Institut ( now Vienna University of Technology ) where he worked as an assistant since 1829.

In Doppler's time in Prague as a professor he published over 50 articles on mathematics, physics and astronomy.

In 1847 he left Prague for the professorship of mathematics, physics, and mechanics at the Academy of Mines and Forests in Schemnitz ( Banská Štiavnica, Slovakia ), and in 1849 he moved to Vienna.

In 1954, he was awarded the top open scholarship to Trinity College, Cambridge University in chemistry and physics, and went on to read mathematics.

They are known in mathematics as the first Chern numbers and are closely related to Berry's phase.

In mathematics and physics, " phase diagram " is used with a different meaning: a synonym for a phase space.

In engineering, agriculture, mathematics, and the natural sciences, 120 credits are always required, while in ( veterinary ) medicine or pharmacy the master's phase requires 180 credits ( 3 years ).

In mathematics, in the area of dynamical systems, a limit cycle on a plane or a two-dimensional manifold is a closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity or as time approaches negative infinity.

* Phase space for information about phase state ( like continuous state space ) in physics and mathematics.

In mathematics and its applications, particularly to phase transitions in matter, a Stefan problem ( also Stefan task ) is a particular kind of boundary value problem for a partial differential equation ( PDE ), adapted to the case in which a phase boundary can move with time.

In mathematics and classical mechanics, canonical coordinates are particular sets of coordinates on the phase space, or equivalently, on the cotangent bundle of a manifold.

A pure phase shift affects the eccentricity ( mathematics ) | eccentricity of the Lissajous oval.

This combination of mathematics and physical chemistry expertise enabled them to tackle head-on the phase problem of X-ray crystallography.

For the full mathematics on directing beams using amplitude and phase shifts, see the mathematical section in phased array.

In mathematics, the stationary phase approximation is a basic principle of asymptotic analysis, applying to oscillatory integrals

From the mathematics of complexity and game theory they use the idea of phase space and talk about extelligence space.

In applied mathematics, in particular the context of nonlinear system analysis, a phase plane is a visual display of certain characteristics of certain kinds of differential equations ; a coordinate plane with axes being the values of the two state variables, say ( x, y ), or ( q, p ) etc.

* Stationary phase approximation in the evaluation of integrals in mathematics

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.

In mathematics, more specifically in functional analysis, a Banach space ( pronounced ) is a complete normed vector space.

In mathematics, specifically in measure theory, a Borel measure is defined as follows: let X be a locally compact Hausdorff space, and let be the smallest σ-algebra that contains the open sets of X ; this is known as the σ-algebra of Borel sets.

In mathematics, a bilinear operator is a function combining elements of two vector spaces to yield an element of a third vector space that is linear in each of its arguments.

In mathematics terminology, the vector space of bras is the dual space to the vector space of kets, and corresponding bras and kets are related by the Riesz representation theorem.

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.

In mathematics, specifically general topology and metric topology, a compact space is a mathematical space in which any infinite collection of points sampled from the space must — as a set — be arbitrarily close to some point of the space.

In mathematics, a contraction mapping, or contraction, on a metric space ( M, d ) is a function f from M to itself, with the property that there is some nonnegative real number < math > k < 1 </ math > such that for all x and y in M,

In mathematics, compactification is the process or result of making a topological space compact.

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 physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it.

High-dimensional spaces occur in mathematics and the sciences for many reasons, frequently as configuration spaces such as in Lagrangian or Hamiltonian mechanics ; these are abstract spaces, independent of the physical space we live in.

In mathematics, the dimension of an object is an intrinsic property independent of the space in which the object is embedded.

A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space.

In mathematics, Euclidean space is the Euclidean plane and three-dimensional space of Euclidean geometry, as well as the generalizations of these notions to higher dimensions.

In modern mathematics, it is more common to define Euclidean space using Cartesian coordinates and the ideas of analytic geometry.