Combinatorial optimizationCombinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the set of feasible solutions is discrete or can be reduced to a discrete set. Typical combinatorial optimization problems are the travelling salesman problem ("TSP"), the minimum spanning tree problem ("MST"), and the knapsack problem. In many such problems, such as the ones previously mentioned, exhaustive search is not tractable, and so specialized algorithms that quickly rule out large parts of the search space or approximation algorithms must be resorted to instead.
Proof assistantIn computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer. A recent effort within this field is making these tools use artificial intelligence to automate the formalization of ordinary mathematics.
Eigenvector centralityIn graph theory, eigenvector centrality (also called eigencentrality or prestige score) is a measure of the influence of a node in a network. Relative scores are assigned to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes. A high eigenvector score means that a node is connected to many nodes who themselves have high scores. Google's PageRank and the Katz centrality are variants of the eigenvector centrality.
CombinatoricsCombinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science. Combinatorics is well known for the breadth of the problems it tackles. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas.
Constructive proofIn mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object. This is in contrast to a non-constructive proof (also known as an existence proof or pure existence theorem), which proves the existence of a particular kind of object without providing an example. For avoiding confusion with the stronger concept that follows, such a constructive proof is sometimes called an effective proof.
CentralityIn graph theory and network analysis, indicators of centrality assign numbers or rankings to nodes within a graph corresponding to their network position. Applications include identifying the most influential person(s) in a social network, key infrastructure nodes in the Internet or urban networks, super-spreaders of disease, and brain networks. Centrality concepts were first developed in social network analysis, and many of the terms used to measure centrality reflect their sociological origin.
Dutch languageDutch (Nederlands ˈneːdərlɑnts), also known as Netherlandic or Netherlandish, is a West Germanic language spoken by about 25 million people as a first language and 5 million as a second language. It is the third most widely spoken Germanic language, after its close relatives German and English. Afrikaans is a separate but somewhat mutually intelligible daughter language spoken, to some degree, by at least 16 million people, mainly in South Africa and Namibia, evolving from the Cape Dutch dialects of Southern Africa.
Proof by contradictionIn logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition, by showing that assuming the proposition to be false leads to a contradiction. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof as universally valid. More broadly, proof by contradiction is any form of argument that establishes a statement by arriving at a contradiction, even when the initial assumption is not the negation of the statement to be proved.
ThiolIn organic chemistry, a thiol ('θaɪɒl; ), or thiol derivative, is any organosulfur compound of the form , where R represents an alkyl or other organic substituent. The functional group itself is referred to as either a thiol group or a sulfhydryl group, or a sulfanyl group. Thiols are the sulfur analogue of alcohols (that is, sulfur takes the place of oxygen in the hydroxyl () group of an alcohol), and the word is a blend of "thio-" with "alcohol". Many thiols have strong odors resembling that of garlic or rotten eggs.
AfrikaansAfrikaans (UKˌæfrᵻˈkɑːns, USˌɑːf-) is a West Germanic language that evolved in the Dutch Cape Colony from the Dutch vernacular of Holland proper (i.e., the Hollandic dialect) used by Dutch, French, and German settlers and people enslaved by them. Afrikaans gradually began to develop distinguishing characteristics during the course of the 18th century. Now spoken in South Africa, Namibia and (to a lesser extent) Botswana, Zambia and Zimbabwe, estimates 2010 of the total number of Afrikaans speakers range between 15 and 23 million.
Null graphIn the mathematical field of graph theory, the term "null graph" may refer either to the order-zero graph, or alternatively, to any edgeless graph (the latter is sometimes called an "empty graph"). The order-zero graph, K_0, is the unique graph having no vertices (hence its order is zero). It follows that K_0 also has no edges. Thus the null graph is a regular graph of degree zero. Some authors exclude K_0 from consideration as a graph (either by definition, or more simply as a matter of convenience).
LuxembourgishLuxembourgish (ˈlʌksəmbɜːrɡɪʃ ; also Luxemburgish, Luxembourgian, Letzebu(e)rgesch; Luxembourgish: Lëtzebuergesch ˈlətsəbuəjəʃ) is a West Germanic language that is spoken mainly in Luxembourg. About 400,000 people speak Luxembourgish worldwide. As a standard form of the Moselle Franconian language, Luxembourgish has similarities with other varieties of High German and the wider group of West Germanic languages.
