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).
Mathematical logicMathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.
Mathematical modelling of infectious diseasesMathematical models can project how infectious diseases progress to show the likely outcome of an epidemic (including in plants) and help inform public health and plant health interventions. Models use basic assumptions or collected statistics along with mathematics to find parameters for various infectious diseases and use those parameters to calculate the effects of different interventions, like mass vaccination programs. The modelling can help decide which intervention(s) to avoid and which to trial, or can predict future growth patterns, etc.
Mathematical economicsMathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity.
Mathematical psychologyMathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior (in practice often constituted by task performance). The mathematical approach is used with the goal of deriving hypotheses that are more exact and thus yield stricter empirical validations.
Mathematical and theoretical biologyMathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories. The field is sometimes called mathematical biology or biomathematics to stress the mathematical side, or theoretical biology to stress the biological side.
Basque nationalismBasque nationalism (eusko abertzaletasuna eus̺ko abeɾts̻aletas̺una; nacionalismo vasco; nationalisme basque) is a form of nationalism that asserts that Basques, an ethnic group indigenous to the western Pyrenees, are a nation and promotes the political unity of the Basques, today scattered between Spain and France. Since its inception in the late 19th century, Basque nationalism has included separatist movements.
Basque Country (autonomous community)The Basque Country (bæsk,_bɑːsk; Euskadi eus̺kadi; País Vasco paˈiz ˈβasko; Pays Basque), also called Basque Autonomous Community (Euskal Autonomia Erkidegoa, EAE; Comunidad Autónoma Vasca, CAV), is an autonomous community in northern Spain. It includes the Basque provinces of Álava, Biscay, and Gipuzkoa. The Basque Country or Basque Autonomous Community was granted the status of nationality within Spain, attributed by the Spanish Constitution of 1978.
BasquesThe Basques (bɑːsks or bæsks ; euskaldunak eus̺kaldunak; vascos ˈbaskos; basques bask) are a Southwestern European ethnic group, characterised by the Basque language, a common culture and shared genetic ancestry to the ancient Vascones and Aquitanians. Basques are indigenous to, and primarily inhabit, an area traditionally known as the Basque Country (Euskal Herria)—a region that is located around the western end of the Pyrenees on the coast of the Bay of Biscay and straddles parts of north-central Spain and south-western France.
Singularity (mathematics)In mathematics, a singularity is a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved in some particular way, such as by lacking differentiability or analyticity. For example, the function has a singularity at , where the value of the function is not defined, as involving a division by zero. The absolute value function also has a singularity at , since it is not differentiable there. The algebraic curve defined by in the coordinate system has a singularity (called a cusp) at .
