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.

George W. Snedecor, the head of Iowa State's Statistics Department, was very likely the first user of an electronic digital computer to solve real world mathematics problems.

Stroustrup has a master's degree in mathematics and computer science ( 1975 ) from the University of Aarhus, Denmark, and a Ph. D. in computer science ( 1979 ) from the University of Cambridge, England, where he was a student at Churchill College.

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.

These connections shed the boundaries between combinatorics and parts of mathematics and theoretical computer science, but at the same time led to a partial fragmentation of the field.

A variant of counting-out game, known as Josephus problem, represents a famous theoretical problem in mathematics and computer science.

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.

* Computational complexity theory, a field in theoretical computer science and 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 ).

Much of the work on computer music has drawn on the relationship between music theory and mathematics.

Although Xenakis could well have composed this music by hand, the intensity of the calculations needed to transform probabilistic mathematics into musical notation was best left to the number-crunching power of the computer.

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.

In 1970, longtime professor of mathematics and computer science John George Kemeny became president of Dartmouth.

Graph ( mathematics ) | Graphs like this are among the objects studied by discrete mathematics, for their interesting graph property | mathematical properties, their usefulness as models of real-world problems, and their importance in developing computer algorithm s.

Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development.

Conversely, computer implementations are significant in applying ideas from discrete mathematics to real-world problems, such as in operations research.

Several fields of discrete mathematics, particularly theoretical computer science, graph theory, and combinatorics, are important in addressing the challenging bioinformatics problems associated with understanding the tree of life.

Theoretical computer science includes areas of discrete mathematics relevant to computing.

Petri nets and process algebras are used to model computer systems, and methods from discrete mathematics are used in analyzing VLSI electronic circuits.

* Numerical digit, as used in mathematics or computer science

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

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

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

Ethics cannot be based on the authoritative certainty given by mathematics and logic, or prescribed directly from the empirical findings of science.

The Ionian School of philosophers were the first natural philosophers ( φυσιολόγοι: physiologoi ) who tried to explain phenomena according to non-supernatural laws, and Pythagoras introduced the abstract mathematical-relations which formed the basis of the science of mathematics.

He stressed training in awareness of abstracting, using techniques that he had derived from his study of mathematics and science.

In later life Ampère claimed that he knew as much about mathematics and science when he was eighteen as ever he knew ; but, a polymath, his reading embraced history, travels, poetry, philosophy, and the natural sciences.

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.

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 ).

Arithmetic or arithmetics ( from the Greek word ἀριθμός, arithmos " number ") is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations.

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 ".

The young Pascal showed an amazing aptitude for mathematics and science.

Their cognitive science of mathematics was a study of the embodiment of basic symbols and properties including those studied in the philosophy of mathematics, via embodied philosophy, using cognitive science.

These Greek city-states reached great levels of prosperity that resulted in an unprecedented cultural boom, that of classical Greece, expressed in architecture, drama, science, mathematics and philosophy, and nurtured in Athens under a democratic government.

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.

Binary relations are used in many branches of mathematics to model concepts like " is greater than ", " is equal to ", and " divides " in arithmetic, " is congruent to " in geometry, " is adjacent to " in graph theory, " is orthogonal to " in linear algebra and many more.

A convex function | function is convex if and only if its Epigraph ( mathematics ) | epigraph, the region ( in green ) above its graph of a function | graph ( in blue ), is a convex set.

The telecommunication industry has also motivated advances in discrete mathematics, particularly in graph theory and information theory.

A graph may be undirected, meaning that there is no distinction between the two vertices associated with each edge, or its edges may be directed from one vertex to another ; see graph ( mathematics ) for more detailed definitions and for other variations in the types of graph that are commonly considered.

The fusion of the ideas coming from mathematics with those coming from chemistry is at the origin of a part of the standard terminology of graph theory.

* Core ( graph theory ), in mathematics, the homomorphically minimal subgraph of a graph

In mathematics, more specifically graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one simple path.

In mathematics, Tait's conjecture states that " Every 3-connected planar cubic graph has a Hamiltonian cycle ( along the edges ) through all its vertices ".

* The degree ( graph theory ), or valency, of a vertex in graph theory ( mathematics )

Some chess problems, like Eight queens puzzle or Knight's Tour has connection to mathematics, especially to graph theory and combinatorics.

Petersen's interests in mathematics were manifold ( geometry, function theory, number theory, mathematical physics, mathematical economics, cryptography and graph theory ).

Many fundamental tasks in mathematics, geometry, trigonometry, graph theory and graphing are performed in a two-dimensional space, or in other words, in the plane.

Tomaž ( Tomo ) Pisanski ( b. May 24, 1949 in Ljubljana, Slovenia ) is a Slovenian mathematician working mainly in discrete mathematics and graph theory.

In mathematics, the graph of a function f is the collection of all ordered pairs ( x, f ( x )).

It is interdisciplinary in nature, borrowing, adapting and enhancing method and theory from numerous other disciplines such as computer science ( e. g. algorithm and software design, database design and theory ), geoinformation science ( spatial statistics and modeling, geographic information systems ), artificial intelligence research ( supervised classification, fuzzy logic ), ecology ( point pattern analysis ), applied mathematics ( graph theory, probability theory ) and statistics.