In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed.

This was particularly important because it shows that Cotton Mather had influence in mathematics during the time of Puritan New England.

In mathematics, particularly in the area of abstract algebra known as group theory, a characteristic subgroup is a subgroup that is invariant under all automorphisms of the parent group.

The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to business accounts.

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

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.

Another definition of the GCD is helpful in advanced mathematics, particularly ring theory.

An example of such a finite field is the ring Z / pZ, which is essentially the set of integers from 0 to p − 1 with integer addition and multiplication modulo p. It is also sometimes denoted Z < sub > p </ sub >, but within some areas of mathematics, particularly number theory, this may cause confusion because the same notation Z < sub > p </ sub > is used for the ring of p-adic integers.

Al-Kindi wrote De Gradibus, in which he demonstrated the application of mathematics to medicine, particularly in the field of pharmacology.

Hutton's mother-Sarah Balfour-insisted on his education at the High School of Edinburgh where he was particularly interested in mathematics and chemistry, then when he was 14 he attended the University of Edinburgh as a " student of humanity " i. e. Classics ( Latin and Greek ).

Gödel attended the Evangelische Volksschule, a Lutheran school in Brünn from 1912 to 1916, and was enrolled in the Deutsches Staats-Realgymnasium from 1916 to 1924, excelling with honors in all his subjects, particularly in mathematics, languages and religion.

The development of algebraic geometry from its classical to modern forms is a particularly striking example of the way an area of mathematics can change radically in its viewpoint, without making what was correctly proved before in any way incorrect ; of course mathematical progress clarifies gaps in previous proofs, often by exposing hidden assumptions, which progress has revealed worth conceptualizing.

The Fourier transform is useful in applied mathematics, particularly physics and signal processing.

This makes Prolog ( and other logic programming languages ) particularly useful for database, symbolic mathematics, and language parsing applications.

In mathematics, particularly in differential geometry and global analysis, spinors have since found broad applications to algebraic and differential topology, symplectic geometry, gauge theory, complex algebraic geometry, index theory, and special holonomy.

Meanwhile, however, significant progress in geometry, mathematics, and astronomy was made in the medieval era, particularly in the Islamic world as well as Europe.

This was particularly appropriate because Onsager, like Willard Gibbs, had been involved primarily in the application of mathematics to problems in physics and chemistry and, in a sense, could be considered to be continuing in the same areas Gibbs had pioneered.

In 1868 after a short stint in Kherson gymnasium worked as a gymnasium teacher of physics and mathematics at gymnasiums of Taganrog, particularly the Chekhov Gymnasium.

The status of abstract entities, particularly numbers, is a topic of discussion in mathematics.

In mathematics, particularly in measure theory, measurable functions are structure-preserving functions between measurable spaces ; as such, they form a natural context for the theory of integration.

He is particularly famous for his association with the concept of the embodied mind, which he has written about in relation to mathematics.

He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics.

In mathematics, particularly topology, one describes

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

This is reinforced by his theoretical treatises, which involve principles of mathematics, perspective and ideal proportions.

In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right.

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.

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

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

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

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.

His attempt to support axiomatized mathematics with definitive principles, which could banish theoretical uncertainties, was however to end in failure.

In May 2006 he became a professor at Wuhan University's international school of software, teaching graduate level pure mathematics, theoretical physics and computer science.

) ( English: Institute of Advanced Scientific Studies ) is a French institute supporting advanced research in mathematics and theoretical physics.

Although initially intending to study theoretical physics, he also attended courses on mathematics and philosophy.

Lie groups represent the best-developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics.

An alternative view is that certain scientific fields ( such as theoretical physics ) are mathematics with axioms that are intended to correspond to reality.

In fact, the theoretical physicist, J. M. Ziman, proposed that science is public knowledge and thus includes mathematics.

Likewise, analysis, geometry and topology, although considered pure mathematics, find applications in theoretical physics — string theory, for instance.

Mathematical logic ( also known as symbolic logic ) is a subfield of mathematics with close connections to the foundations of mathematics, theoretical computer science and philosophical logic.

While the mathematics permits calculation of many quantities that can be measured experimentally, there is a definite theoretical limit to values that can be simultaneously measured.

In the early 1960s he began his studies in Uppsala University, initially in mathematics, and thereafter theoretical physics, aesthetics, history of ideas and astronomy.

After the use of classical theories since the end of the scientific revolution, various fields substituted mathematics studies for experimental studies and examining equations to build a theoretical structure.