Algebraic groupIn mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory. Many groups of geometric transformations are algebraic groups; for example, orthogonal groups, general linear groups, projective groups, Euclidean groups, etc. Many matrix groups are also algebraic. Other algebraic groups occur naturally in algebraic geometry, such as elliptic curves and Jacobian varieties.
Right to privacyThe right to privacy is an element of various legal traditions that intends to restrain governmental and private actions that threaten the privacy of individuals. Over 150 national constitutions mention the right to privacy. On 10 December 1948, the United Nations General Assembly adopted the Universal Declaration of Human Rights (UDHR), originally written to guarantee individual rights of everyone everywhere; while right to privacy does not appear in the document, many interpret this through Article 12, which states: "No one shall be subjected to arbitrary interference with his privacy, family, home or correspondence, nor to attacks upon his honour and reputation.
Privacy lawPrivacy law is the body of law that deals with the regulating, storing, and using of personally identifiable information, personal healthcare information, and financial information of individuals, which can be collected by governments, public or private organisations, or other individuals. It also applies in the commercial sector to things like trade secrets and the liability that directors, officers, and employees have when handing sensitive information.
Permutation groupIn mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G (which are thought of as bijective functions from the set M to itself). The group of all permutations of a set M is the symmetric group of M, often written as Sym(M). The term permutation group thus means a subgroup of the symmetric group. If M = {1, 2, ..., n} then Sym(M) is usually denoted by Sn, and may be called the symmetric group on n letters.
PrivacyPrivacy (UK, US) is the ability of an individual or group to seclude themselves or information about themselves, and thereby express themselves selectively. The domain of privacy partially overlaps with security, which can include the concepts of appropriate use and protection of information. Privacy may also take the form of bodily integrity. There have been many different conceptions of privacy throughout history. Most cultures recognize the right of an individual to withhold aspects of their personal lives from public record.
EngineeringEngineering is the practice of using natural science, mathematics, and the engineering design process to solve problems, increase efficiency and productivity, and improve systems. Modern engineering comprises many subfields which include designing and creating infrastructure, machinery, vehicles, electronics, materials, and energy. The discipline of engineering encompasses a broad range of more specialized fields of engineering, each with a more specific emphasis on particular areas of applied mathematics, applied science, and types of application.
MathematicsMathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them.
Privacy engineeringPrivacy engineering is an emerging field of engineering which aims to provide methodologies, tools, and techniques to ensure systems provide acceptable levels of privacy. In the US, an acceptable level of privacy is defined in terms of compliance to the functional and non-functional requirements set out through a privacy policy, which is a contractual artifact displaying the data controlling entities compliance to legislation such as Fair Information Practices, health record security regulation and other privacy laws.
Personal dataPersonal data, also known as personal information or personally identifiable information (PII), is any information related to an identifiable person. The abbreviation PII is widely accepted in the United States, but the phrase it abbreviates has four common variants based on personal or personally, and identifiable or identifying. Not all are equivalent, and for legal purposes the effective definitions vary depending on the jurisdiction and the purposes for which the term is being used.
Parity of a permutationIn mathematics, when X is a finite set with at least two elements, the permutations of X (i.e. the bijective functions from X to X) fall into two classes of equal size: the even permutations and the odd permutations. If any total ordering of X is fixed, the parity (oddness or evenness) of a permutation of X can be defined as the parity of the number of inversions for σ, i.e., of pairs of elements x, y of X such that x < y and σ(x) > σ(y). The sign, signature, or signum of a permutation σ is denoted sgn(σ) and defined as +1 if σ is even and −1 if σ is odd.
PermutationIn mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set. Permutations differ from combinations, which are selections of some members of a set regardless of order. For example, written as tuples, there are six permutations of the set {1, 2, 3}, namely (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1).
Cyclic permutationIn mathematics, and in particular in group theory, a cyclic permutation is a permutation consisting of a single cycle. In some cases, cyclic permutations are referred to as cycles; if a cyclic permutation has k elements, it may be called a k-cycle. Some authors widen this definition to include permutations with fixed points in addition to at most one non-trivial cycle. In cycle notation, cyclic permutations are denoted by the list of their elements enclosed with parentheses, in the order to which they are permuted.
Internet privacyInternet privacy involves the right or mandate of personal privacy concerning the storage, re-purposing, provision to third parties, and display of information pertaining to oneself via the Internet. Internet privacy is a subset of data privacy. Privacy concerns have been articulated from the beginnings of large-scale computer sharing and especially relate to mass surveillance enabled by the emergence of computer technologies. Privacy can entail either personally identifiable information (PII) or non-PII information such as a site visitor's behaviour on a website.
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.
Materials scienceMaterials science is an interdisciplinary field of researching and discovering materials. Materials engineering is an engineering field of finding uses for materials in other fields and industries. The intellectual origins of materials science stem from the Age of Enlightenment, when researchers began to use analytical thinking from chemistry, physics, and engineering to understand ancient, phenomenological observations in metallurgy and mineralogy. Materials science still incorporates elements of physics, chemistry, and engineering.
Privacy by designPrivacy by design is an approach to systems engineering initially developed by Ann Cavoukian and formalized in a joint report on privacy-enhancing technologies by a joint team of the Information and Privacy Commissioner of Ontario (Canada), the Dutch Data Protection Authority, and the Netherlands Organisation for Applied Scientific Research in 1995. The privacy by design framework was published in 2009 and adopted by the International Assembly of Privacy Commissioners and Data Protection Authorities in 2010.
AlgebraAlgebra () is the study of variables and the rules for manipulating these variables in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variables (commonly represented by Roman letters) as if they were numbers and is therefore essential in all applications of mathematics. Abstract algebra is the name given, mostly in education, to the study of algebraic structures such as groups, rings, and fields.
Algebraic structureIn mathematics, an algebraic structure consists of a nonempty set A (called the underlying set, carrier set or domain), a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities, known as axioms, that these operations must satisfy. An algebraic structure may be based on other algebraic structures with operations and axioms involving several structures.
Systems engineeringSystems engineering is an interdisciplinary field of engineering and engineering management that focuses on how to design, integrate, and manage complex systems over their life cycles. At its core, systems engineering utilizes systems thinking principles to organize this body of knowledge. The individual outcome of such efforts, an engineered system, can be defined as a combination of components that work in synergy to collectively perform a useful function.
Civil engineeringCivil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads, bridges, canals, dams, airports, sewage systems, pipelines, structural components of buildings, and railways. Civil engineering is traditionally broken into a number of sub-disciplines. It is considered the second-oldest engineering discipline after military engineering, and it is defined to distinguish non-military engineering from military engineering.
