Theoretical computer scienceTheoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory. It is difficult to circumscribe the theoretical areas precisely. The ACM's Special Interest Group on Algorithms and Computation Theory (SIGACT) provides the following description: History of computer science While logical inference and mathematical proof had existed previously, in 1931 Kurt Gödel proved with his incompleteness theorem that there are fundamental limitations on what statements could be proved or disproved.
Computational scienceComputational science, also known as scientific computing, technical computing or scientific computation (SC), is a division of science that uses advanced computing capabilities to understand and solve complex physical problems. This includes Algorithms (numerical and non-numerical): mathematical models, computational models, and computer simulations developed to solve sciences (e.
Computer scienceComputer science is the study of computation, information, and automation. Computer science spans theoretical disciplines (such as algorithms, theory of computation, and information theory) to applied disciplines (including the design and implementation of hardware and software). Though more often considered an academic discipline, computer science is closely related to computer programming. Algorithms and data structures are central to computer science.
Group representationIn the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used to represent group elements as invertible matrices so that the group operation can be represented by matrix multiplication. In chemistry, a group representation can relate mathematical group elements to symmetric rotations and reflections of molecules.
Irreducible representationIn mathematics, specifically in the representation theory of groups and algebras, an irreducible representation or irrep of an algebraic structure is a nonzero representation that has no proper nontrivial subrepresentation , with closed under the action of . Every finite-dimensional unitary representation on a Hilbert space is the direct sum of irreducible representations. Irreducible representations are always indecomposable (i.e. cannot be decomposed further into a direct sum of representations), but the converse may not hold, e.
Western EuropeWestern Europe is the western region of Europe. The region's extent varies depending on context. The concept of "the West" appeared in Europe in juxtaposition to "the East" and originally applied to the ancient Mediterranean world, the Roman Empire (Western Roman Empire and Eastern Roman Empire), and medieval "Christendom" (Western Christianity and Eastern Christianity). Beginning with the Renaissance and the Age of Discovery, roughly from the 15th century, the concept of Europe as "the West" slowly became distinguished from and eventually replaced the dominant use of "Christendom" as the preferred endonym within the region.
Northwestern EuropeNorthwestern Europe, or Northwest Europe, is a loosely defined subregion of Europe, overlapping Northern and Western Europe. The term is used in geographic, history, and military contexts. Geographically, Northwestern Europe is given by some sources as a region which includes Great Britain, Ireland, Belgium, the Netherlands, Luxembourg, Northern France, parts of Germany, Denmark, Norway, Sweden, and Iceland. In some works, Switzerland, Finland, and Austria are also included as part of Northwestern Europe.
Lie algebra representationIn the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms of a vector space) in such a way that the Lie bracket is given by the commutator. In the language of physics, one looks for a vector space together with a collection of operators on satisfying some fixed set of commutation relations, such as the relations satisfied by the angular momentum operators.
InbreedingInbreeding is the production of offspring from the mating or breeding of individuals or organisms that are closely related genetically. By analogy, the term is used in human reproduction, but more commonly refers to the genetic disorders and other consequences that may arise from expression of deleterious recessive traits resulting from incestuous sexual relationships and consanguinity. Animals avoid incest only rarely. Inbreeding results in homozygosity, which can increase the chances of offspring being affected by recessive traits.
Languages of EuropeMost languages of Europe belong to the Indo-European language family. Out of a total European population of 744 million as of 2018, some 94% are native speakers of an Indo-European language. Within Indo-European, the three largest phyla in Europe are Romance, Germanic, and Slavic; they have more than 200 million speakers each and together account for close to 90% of Europeans.
Regions of EuropeEurope, the westernmost portion of Eurasia, is often divided into regions and subregions based on geographical, cultural or historical factors. Since there is no universal agreement on Europe's regional composition, the placement of individual countries may vary based on criteria being used. For instance, the Balkans is a distinct geographical region within Europe but individual countries may alternatively be grouped into South-eastern Europe, Southern Europe or less commonly, Eastern Europe.
Inbreeding avoidanceInbreeding avoidance, or the inbreeding avoidance hypothesis, is a concept in evolutionary biology that refers to the prevention of the deleterious effects of inbreeding. Animals only rarely exhibit inbreeding avoidance. The inbreeding avoidance hypothesis posits that certain mechanisms develop within a species, or within a given population of a species, as a result of assortative mating and natural and sexual selection, in order to prevent breeding among related individuals.
Inbreeding depressionInbreeding depression is the reduced biological fitness which has the potential to result from inbreeding (the breeding of related individuals). Biological fitness refers to an organism's ability to survive and perpetuate its genetic material. Inbreeding depression is often the result of a population bottleneck. In general, the higher the genetic variation or gene pool within a breeding population, the less likely it is to suffer from inbreeding depression, though inbreeding and outbreeding depression can simultaneously occur.
DoctorateA doctorate (from Latin doctor, meaning "teacher") or doctoral degree is a postgraduate academic degree awarded by universities and some other educational institutions, derived from the ancient formalism licentia docendi ("licence to teach"). In most countries, a research degree qualifies the holder to teach at university level in the degree's field or work in a specific profession. There are a number of doctoral degrees; the most common is the Doctor of Philosophy (PhD), awarded in many different fields, ranging from the humanities to scientific disciplines.
Weight (representation theory)In the mathematical field of representation theory, a weight of an algebra A over a field F is an algebra homomorphism from A to F, or equivalently, a one-dimensional representation of A over F. It is the algebra analogue of a multiplicative character of a group. The importance of the concept, however, stems from its application to representations of Lie algebras and hence also to representations of algebraic and Lie groups. In this context, a weight of a representation is a generalization of the notion of an eigenvalue, and the corresponding eigenspace is called a weight space.
ProfessorProfessor (commonly abbreviated as Prof.) is an academic rank at universities and other post-secondary education and research institutions in most countries. Literally, professor derives from Latin as a "person who professes." Professors are usually experts in their field and teachers of the highest rank. In most systems of academic ranks, "professor" as an unqualified title refers only to the most senior academic position, sometimes informally known as "full professor.
Doctor of PhilosophyA Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: philosophiae doctor or doctor philosophiae) is the most common degree at the highest academic level, awarded following a course of study and research. PhDs are awarded for programs across the whole breadth of academic fields. Because it is an earned research degree, those studying for a PhD are required to produce original research that expands the boundaries of knowledge, normally in the form of a dissertation, and defend their work before a panel of other experts in the field.
Coefficient of relationshipThe coefficient of relationship is a measure of the degree of consanguinity (or biological relationship) between two individuals. The term coefficient of relationship was defined by Sewall Wright in 1922, and was derived from his definition of the coefficient of inbreeding of 1921. The measure is most commonly used in genetics and genealogy. A coefficient of inbreeding can be calculated for an individual, and is typically one-half the coefficient of relationship between the parents.
Algebra representationIn abstract algebra, a representation of an associative algebra is a module for that algebra. Here an associative algebra is a (not necessarily unital) ring. If the algebra is not unital, it may be made so in a standard way (see the adjoint functors page); there is no essential difference between modules for the resulting unital ring, in which the identity acts by the identity mapping, and representations of the algebra.
Postgraduate educationPostgraduate education, graduate education, or grad school, refers to academic or professional degrees, certificates, diplomas, or other qualifications usually pursued by post-secondary students who have earned an undergraduate (bachelor's) degree. The organization and structure of postgraduate education varies in different countries, as well as in different institutions within countries.
