History of scienceThe history of science covers the development of science from ancient times to the present. It encompasses all three major branches of science: natural, social, and formal. Science's earliest roots can be traced to Ancient Egypt and Mesopotamia around 3000 to 1200 BCE. These civilizations' contributions to mathematics, astronomy, and medicine influenced later Greek natural philosophy of classical antiquity, wherein formal attempts were made to provide explanations of events in the physical world based on natural causes.
CalculusCalculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. It has two major branches, differential calculus and integral calculus; the former concerns instantaneous rates of change, and the slopes of curves, while the latter concerns accumulation of quantities, and areas under or between curves.
Differential geometryDifferential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky.
Industrial and organizational psychologyIndustrial and organizational psychology (I-O psychology) is the science of human behavior in the workplace and work-life interface. It is an applied discipline within psychology. Depending on the country or region of the world, I-O psychology is also known as occupational psychology in the United Kingdom, organisational psychology in Australia and New Zealand, and work and organizational (WO) psychology throughout Europe and Brazil. Industrial, work, and organizational (IWO) psychology is the broader, more global term for the science and profession.
Reinforcement learningReinforcement learning (RL) is an area of machine learning concerned with how intelligent agents ought to take actions in an environment in order to maximize the notion of cumulative reward. Reinforcement learning is one of three basic machine learning paradigms, alongside supervised learning and unsupervised learning. Reinforcement learning differs from supervised learning in not needing labelled input/output pairs to be presented, and in not needing sub-optimal actions to be explicitly corrected.
EquationsIn mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign . The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. Solving an equation containing variables consists of determining which values of the variables make the equality true.
Bayesian inferenceBayesian inference (ˈbeɪziən or ˈbeɪʒən ) is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law.
Quality managementQuality management ensures that an organization, product or service consistently functions well. It has four main components: quality planning, quality assurance, quality control and quality improvement. Quality management is focused not only on product and service quality, but also on the means to achieve it. Quality management, therefore, uses quality assurance and control of processes as well as products to achieve more consistent quality. Quality control is also part of quality management.
Software designSoftware design is the process by which an agent creates a specification of a software artifact intended to accomplish goals, using a set of primitive components and subject to constraints. The term is sometimes used broadly to refer to "all the activity involved in conceptualizing, framing, implementing, commissioning, and ultimately modifying" the software, or more specifically "the activity following requirements specification and before programming, as ... [in] a stylized software engineering process.
Topics in number theoryNumber theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example, rational numbers), or defined as generalizations of the integers (for example, algebraic integers).
Business process managementBusiness process management (BPM) is the discipline in which people use various methods to discover, model, analyze, measure, improve, optimize, and automate business processes. Any combination of methods used to manage a company's business processes is BPM. Processes can be structured and repeatable or unstructured and variable. Though not required, enabling technologies are often used with BPM. As an approach, BPM sees processes as important assets of an organization that must be understood, managed, and developed to announce and deliver value-added products and services to clients or customers.
Mathematical formulation of quantum mechanicsThe mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional analysis, especially Hilbert spaces, which are a kind of linear space. Such are distinguished from mathematical formalisms for physics theories developed prior to the early 1900s by the use of abstract mathematical structures, such as infinite-dimensional Hilbert spaces (L2 space mainly), and operators on these spaces.
