Mathematical modelA mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).
Development theoryDevelopment theory is a collection of theories about how desirable change in society is best achieved. Such theories draw on a variety of social science disciplines and approaches. In this article, multiple theories are discussed, as are recent developments with regard to these theories. Depending on which theory that is being looked at, there are different explanations to the process of development and their inequalities. Modernization theory Modernization theory is used to analyze the processes in which modernization in societies take place.
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.
Reaction mechanismIn chemistry, a reaction mechanism is the step by step sequence of elementary reactions by which overall chemical reaction occurs. A chemical mechanism is a theoretical conjecture that tries to describe in detail what takes place at each stage of an overall chemical reaction. The detailed steps of a reaction are not observable in most cases. The conjectured mechanism is chosen because it is thermodynamically feasible and has experimental support in isolated intermediates (see next section) or other quantitative and qualitative characteristics of the reaction.
Collective animal behaviorCollective animal behaviour is a form of social behavior involving the coordinated behavior of large groups of similar animals as well as emergent properties of these groups. This can include the costs and benefits of group membership, the transfer of information, decision-making process, locomotion and synchronization of the group. Studying the principles of collective animal behavior has relevance to human engineering problems through the philosophy of biomimetics.
Dynamical systems theoryDynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle.
Chemical reactionA chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking of chemical bonds between atoms, with no change to the nuclei (no change to the elements present), and can often be described by a chemical equation. Nuclear chemistry is a sub-discipline of chemistry that involves the chemical reactions of unstable and radioactive elements where both electronic and nuclear changes can occur.
Collective consciousnessCollective consciousness, collective conscience, or collective conscious (conscience collective) is the set of shared beliefs, ideas, and moral attitudes which operate as a unifying force within society. In general, it does not refer to the specifically moral conscience, but to a shared understanding of social norms. The modern concept of what can be considered collective consciousness includes solidarity attitudes, memes, extreme behaviors like group-think and herd behavior, and collectively shared experiences during collective rituals and dance parties.
Ecological designEcological design or ecodesign is an approach to designing products and services that gives special consideration to the environmental impacts of a product over its entire lifecycle. Sim Van der Ryn and Stuart Cowan define it as "any form of design that minimizes environmentally destructive impacts by integrating itself with living processes." Ecological design can also be defined as the process of integrating environmental considerations into design and development with the aim of reducing environmental impacts of products through their life cycle.
Collective intelligenceCollective intelligence (CI) is shared or group intelligence (GI) that emerges from the collaboration, collective efforts, and competition of many individuals and appears in consensus decision making. The term appears in sociobiology, political science and in context of mass peer review and crowdsourcing applications. It may involve consensus, social capital and formalisms such as voting systems, social media and other means of quantifying mass activity.
Aldol reactionThe aldol reaction (aldol addition) is a reaction that combines two carbonyl compounds (aldehydes or ketones) to form a new β-hydroxy carbonyl compound. These products are known as aldols, from the aldehyde + alcohol, a structural motif seen in many of the products. The use of aldehyde in the name comes from its discovery history, where aldehydes were first used in the reaction and not ketones. Aldol structural units are found in many important molecules, whether naturally occurring or synthetic.
Mathematical beautyMathematical beauty is the aesthetic pleasure derived from the abstractness, purity, simplicity, depth or orderliness of mathematics. Mathematicians may express this pleasure by describing mathematics (or, at least, some aspect of mathematics) as beautiful or describe mathematics as an art form, (a position taken by G. H. Hardy) or, at a minimum, as a creative activity. Comparisons are made with music and poetry. Mathematicians describe an especially pleasing method of proof as elegant.
