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.
C*-algebraIn mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties of the adjoint. A particular case is that of a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties: A is a topologically closed set in the norm topology of operators. A is closed under the operation of taking adjoints of operators.
*-algebraIn mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra) is a mathematical structure consisting of two involutive rings R and A, where R is commutative and A has the structure of an associative algebra over R. Involutive algebras generalize the idea of a number system equipped with conjugation, for example the complex numbers and complex conjugation, matrices over the complex numbers and conjugate transpose, and linear operators over a Hilbert space and Hermitian adjoints.
Lie algebraIn mathematics, a Lie algebra (pronounced liː ) is a vector space together with an operation called the Lie bracket, an alternating bilinear map , that satisfies the Jacobi identity. Otherwise said, a Lie algebra is an algebra over a field where the multiplication operation is now called Lie bracket and has two additional properties: it is alternating and satisfies the Jacobi identity. The Lie bracket of two vectors and is denoted . The Lie bracket does not need to be associative, meaning that the Lie algebra can be non associative.
Associative algebraIn mathematics, an associative algebra A is an algebraic structure with compatible operations of addition, multiplication (assumed to be associative), and a scalar multiplication by elements in some field K. The addition and multiplication operations together give A the structure of a ring; the addition and scalar multiplication operations together give A the structure of a vector space over K. In this article we will also use the term [[algebra over a field|K-algebra]] to mean an associative algebra over the field K.
Algebra over a fieldIn mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure consisting of a set together with operations of multiplication and addition and scalar multiplication by elements of a field and satisfying the axioms implied by "vector space" and "bilinear". The multiplication operation in an algebra may or may not be associative, leading to the notions of associative algebras and non-associative algebras.
Jordan algebraIn abstract algebra, a Jordan algebra is a nonassociative algebra over a field whose multiplication satisfies the following axioms: (commutative law) (). The product of two elements x and y in a Jordan algebra is also denoted x ∘ y, particularly to avoid confusion with the product of a related associative algebra. The axioms imply that a Jordan algebra is power-associative, meaning that is independent of how we parenthesize this expression. They also imply that for all positive integers m and n.
Differential graded algebraIn mathematics, in particular in homological algebra, a differential graded algebra is a graded associative algebra with an added chain complex structure that respects the algebra structure. TOC A differential graded algebra (or DG-algebra for short) A is a graded algebra equipped with a map which has either degree 1 (cochain complex convention) or degree −1 (chain complex convention) that satisfies two conditions: A more succinct way to state the same definition is to say that a DG-algebra is a monoid object in the .
EmploymentEmployment is a relationship between two parties regulating the provision of paid labour services. Usually based on a contract, one party, the employer, which might be a corporation, a not-for-profit organization, a co-operative, or any other entity, pays the other, the employee, in return for carrying out assigned work. Employees work in return for wages, which can be paid on the basis of an hourly rate, by piecework or an annual salary, depending on the type of work an employee does, the prevailing conditions of the sector and the bargaining power between the parties.
Employment contractAn employment contract or contract of employment is a kind of contract used in labour law to attribute rights and responsibilities between parties to a bargain. The contract is between an "employee" and an "employer". It has arisen out of the old master-servant law, used before the 20th century. Employment contracts relies on the concept of authority, in which the employee agrees to accept the authority of the employer and in exchange, the employer agrees to pay the employee a stated wage (Simon, 1951).
Self-employmentSelf-employment is the state of working for oneself rather than an employer. Tax authorities will generally view a person as self-employed if the person chooses to be recognised as such or if the person is generating income for which a tax return needs to be filed. In the real world, the critical issue for the tax authorities is not whether a person is engaged in a business activity (called "trading" even when referring to the provision of a service) but whether the activity is profitable and therefore potentially taxable.
Full employmentFull employment is a situation in which there is no cyclical or deficient-demand unemployment. Full employment does not entail the disappearance of all unemployment, as other kinds of unemployment, namely structural and frictional, may remain. For instance, workers who are "between jobs" for short periods of time as they search for better employment are not counted against full employment, as such unemployment is frictional rather than cyclical.
Climate justiceClimate justice is a concept that addresses the just division, fair sharing, and equitable distribution of the burdens of climate change and its mitigation and responsibilities to deal with climate change. It has been described as encompassing "a set of rights and obligations, which corporations, individuals and governments have towards those vulnerable people who will be in a way significantly disproportionately affected by climate change.
Climate movementThe climate movement is a global social movement focused on pressuring governments and industry to take action (also called "climate action") addressing the causes and impacts of climate change. Environmental non-profit organizations have engaged in significant climate activism since the late 1980s and early 1990s, as they sought to influence the United Nations Framework Convention on Climate Change (UNFCCC). Climate activism has become increasingly prominent over time, gaining significant momentum during the 2009 Copenhagen Summit and particularly following the signing of the Paris Agreement in 2016.
LearningLearning is the process of acquiring new understanding, knowledge, behaviors, skills, values, attitudes, and preferences. The ability to learn is possessed by humans, animals, and some machines; there is also evidence for some kind of learning in certain plants. Some learning is immediate, induced by a single event (e.g. being burned by a hot stove), but much skill and knowledge accumulate from repeated experiences. The changes induced by learning often last a lifetime, and it is hard to distinguish learned material that seems to be "lost" from that which cannot be retrieved.
School Strike for ClimateSchool Strike for Climate (Skolstrejk för klimatet), also known variously as Fridays for Future (FFF), Youth for Climate, Climate Strike or Youth Strike for Climate, is an international movement of school students who skip Friday classes to participate in demonstrations to demand action from political leaders to prevent climate change and for the fossil fuel industry to transition to renewable energy.
Climate change vulnerabilityClimate change vulnerability (or climate vulnerability or climate risk vulnerability) is a concept that describes how strongly people or ecosystems are likely to be affected by climate change. It is defined as the "propensity or predisposition to be adversely affected" by climate change. It can apply to humans and also to natural systems (or ecosystems). Related concepts include climate sensitivity and the ability, or lack thereof, to cope and adapt. Vulnerability is a component of climate risk.
Machine learningMachine learning (ML) is an umbrella term for solving problems for which development of algorithms by human programmers would be cost-prohibitive, and instead the problems are solved by helping machines 'discover' their 'own' algorithms, without needing to be explicitly told what to do by any human-developed algorithms. Recently, generative artificial neural networks have been able to surpass results of many previous approaches.
Experiential learningExperiential learning (ExL) is the process of learning through experience, and is more narrowly defined as "learning through reflection on doing". Hands-on learning can be a form of experiential learning, but does not necessarily involve students reflecting on their product. Experiential learning is distinct from rote or didactic learning, in which the learner plays a comparatively passive role. It is related to, but not synonymous with, other forms of active learning such as action learning, adventure learning, free-choice learning, cooperative learning, service-learning, and situated learning.
Learning stylesLearning styles refer to a range of theories that aim to account for differences in individuals' learning. Although there is ample evidence that individuals express personal preferences for how they prefer to receive information, few studies have found any validity in using learning styles in education. Many theories share the proposition that humans can be classified according to their "style" of learning, but differ in how the proposed styles should be defined, categorized and assessed.
