In mathematics, a Fuchsian group is a discrete subgroup of PSL ( 2, R ).

Pelageya Yakovlevna Polubarinova-Kochina (; May 13, 1899 – July 3, 1999 ) was a Soviet applied mathematician, known for her work on fluid mechanics and hydrodynamics, particularly, the application of Fuchsian equations, as well in the history of mathematics.

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.

Note that unlike Hypatia he did not study ' mathematics, philosophy and astronomy ', thus he and his followers came into conflict with the ancient University of Alexandria which pursued all forms of knowledge including science and human anatomy, politics and history according to the model inaugurated by Alexander the Great, the founder of Alexandria.

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

In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects from a certain collection.

In Indian astronomy, Aryabhata's Aryabhatiya ( 499 CE ) proposed the Earth's rotation, while Nilakantha Somayaji ( 1444 – 1544 ) of the Kerala school of astronomy and mathematics proposed a semi-heliocentric model resembling the Tychonic system.

With amplification, logic gates can be cascaded in the same way that Boolean functions can be composed, allowing the construction of a physical model of all of Boolean logic, and therefore, all of the algorithms and mathematics that can be described with Boolean logic.

Intuitionistic logic substitutes constructability for abstract truth and is associated with a transition from the proof to model theory of abstract truth in modern mathematics.

The method of forcing is employed in set theory, model theory, and recursion theory, as well as in the study of intuitionistic mathematics.

In mathematics, model theory is the study of ( classes of ) mathematical structures ( e. g. groups, fields, graphs, universes of set theory ) using tools from mathematical logic.

In a similar way to proof theory, model theory is situated in an area of interdisciplinarity between mathematics, philosophy, and computer science.

The ambition of geometric model theory is to provide a geography of mathematics by embarking on a detailed study of definable sets in various mathematical structures, aided by the substantial tools developed in the study of pure model theory.

Due to its simplicity, the model allows insight into quantum effects without the need for complicated mathematics.

In both mathematics and the relational database model, a set is an unordered collection of unique, non-duplicated items, although some DBMSs impose an order to their data.

In theoretical computer science and mathematics, the theory of computation is the branch that deals with whether and how efficiently problems can be solved on a model of computation, using an algorithm.

This result is both hard to model mathematically and quite counterintuitive to people who lack experience with mathematics or real networks.

With advances in origami mathematics however, the basic structure of a new origami model can be theoretically plotted out on paper before any actual folding even occurs.

CA ) is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling.

The colon is used in mathematics, cartography, model building and other fields to denote a ratio or a scale, as in 3: 1 ( pronounced “ three to one ”).

The mathematics behind this problem led to a well-known cryptographic attack called the birthday attack, which uses this probabilistic model to reduce the complexity of cracking a hash function.

This model, which can be represented by the Friedmann equations, provides a curvature ( often referred to as geometry ) of the universe based on the mathematics of fluid dynamics, i. e. it models the matter within the universe as a perfect fluid.

Under the assumption that the universe is homogeneous and isotropic, the curvature of the observable universe, or the local geometry, is described by one of the three " primitive " geometries ( in mathematics these are called the model geometries ):

Some Greek astronomers ( e. g., Aristarchus of Samos ) speculated that the planets ( Earth included ) orbited the Sun, but the optics ( and the specific mathematics – Newton's Law of Gravitation for example ) necessary to provide data that would convincingly support the heliocentric model did not exist in Ptolemy's time and would not come around for over fifteen hundred years after his death.

In applied mathematics, the Wiener process is used to represent the integral of a Gaussian white noise process, and so is useful as a model of noise in electronics engineering, instrument errors in filtering theory and unknown forces in control theory.

Now we can say that mathematics has a clear and satisfying foundation made of set theory and model theory.

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.

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

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

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

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.