The diffraction theory of point-spread functions was first studied by Airy in the nineteenth century.

This is a very abstract definition since, in category theory, morphisms aren't necessarily functions and objects aren't necessarily sets.

Computational complexity theory deals with the relative computational difficulty of computable functions.

In category theory, n-ary functions generalise to n-ary morphisms in a multicategory.

The cell theory, first developed in 1839 by Matthias Jakob Schleiden and Theodor Schwann, states that all organisms are composed of one or more cells, that all cells come from preexisting cells, that vital functions of an organism occur within cells, and that all cells contain the hereditary information necessary for regulating cell functions and for transmitting information to the next generation of cells.

Partition theory studies various enumeration and asymptotic problems related to integer partitions, and is closely related to q-series, special functions and orthogonal polynomials.

However it is important to note that the objects of a category need not be sets nor the arrows functions ; any way of formalising a mathematical concept such that it meets the basic conditions on the behaviour of objects and arrows is a valid category, and all the results of category theory will apply to it.

A similar type of investigation occurs in many mathematical theories, such as the study of continuous maps ( morphisms ) between topological spaces in topology ( the associated category is called Top ), and the study of smooth functions ( morphisms ) in manifold theory.

If one axiomatizes relations instead of functions, one obtains the theory of allegories.

Although a " bijection " seems a more advanced concept than a number, the usual development of mathematics in terms of set theory defines functions before numbers, as they are based on much simpler sets.

The basic theory behind all business organizations is that, by combining certain functions within a single entity, a business ( usually called a firm by economists ) can operate more efficiently, and thereby realize a greater profit.

In computability theory, the Church – Turing thesis ( also known as the Turing-Church thesis, the Church – Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis ) is a combined hypothesis (" thesis ") about the nature of functions whose values are effectively calculable ; or, in more modern terms, functions whose values are algorithmically computable.

In the course of studying the problem, Church and his student Stephen Kleene introduced the notion of λ-definable functions, and they were able to prove that several large classes of functions frequently encountered in number theory were λ-definable.

Proofs in computability theory often invoke the Church – Turing thesis in an informal way to establish the computability of functions while avoiding the ( often very long ) details which would be involved in a rigorous, formal proof.

* Conjugate pairing of probability distributions, in the Fourier-analytic theory of characteristic functions and statistical mechanics

then used these equations to construct his theory of functions.

Riemann's dissertation on the theory of functions appeared in 1851.

* Harris Hancock Lectures on the theory of Elliptic functions ( New York, J. Wiley & sons, 1910 )

Classical analog filters are IIR filters, and classical filter theory centers on the determination of transfer functions given by low order rational functions, which can be synthesized using the same small number of reactive components.

In the context of decision theory, an estimator is a type of decision rule, and its performance may be evaluated through the use of loss functions.

A theory about some topic is usually first-order logic together with: a specified domain of discourse over which the quantified variables range, finitely many functions which map from that domain into it, finitely many predicates defined on that domain, and a recursive set of axioms which are believed to hold for those things.

Historically, the concept of fundamental group first emerged in the theory of Riemann surfaces, in the work of Bernhard Riemann, Henri Poincaré and Felix Klein, where it describes the monodromy properties of complex functions, as well as providing a complete topological classification of closed surfaces.

Selective investment theory proposes that close social bonds, and associated emotional, cognitive, and neurohormonal mechanisms, evolved in order to facilitate long-term, high-cost altruism between those closely depending on one another for survival and reproductive success.

In that setting one can use birational geometry, techniques from number theory, Galois theory and commutative algebra, and close analogues of the methods of algebraic topology, all in an integrated way.

Chinese astrology has a close relation with Chinese philosophy ( theory of the three harmonies: heaven, earth and man ) and uses concepts such as yin and yang, the Five phases, the 10 Celestial stems, the 12 Earthly Branches, and shichen ( 時辰 a form of timekeeping used for religious purposes ).

In three papers which were published in 1952 – 53, Bohr and Mottelson demonstrated close agreement between theory and experiment ; for example, showing that the energy levels of certain nuclei could be described by a rotation spectrum.

In 1930, England captain Douglas Jardine, together with Nottinghamshire's captain Arthur Carr and his bowlers Harold Larwood and Bill Voce, developed a variant of leg theory in which the bowlers bowled fast, short-pitched balls that would rise into the batsman's body, together with a heavily stacked ring of close fielders on the leg side.

In combinatorial game theory dots and boxes is very close to being an impartial game and many positions can be analyzed using Sprague – Grundy theory.

While many mathematicians before Galois gave consideration to what are now known as groups, it was Galois who was the first to use the word group ( in French groupe ) in a sense close to the technical sense that is understood today, making him among the founders of the branch of algebra known as group theory.

The subject has a close relationship with the discipline of financial economics, which is concerned with much of the underlying theory.

Their motivations are consistent with the convictions of James Daniel Bjorken and Sidney Drell: ” The Feynman graphs and rules of calculation summarize quantum field theory in a form in close contact with the experimental numbers one wants to understand.

Algebraic graph theory has close links with group theory.

It makes a close link between model theory that deals with what is true in different models, and proof theory that studies what can be formally proved in particular formal systems.

This theory is confusing as Gurmukhi characters have a very close resemblance with " Siddh Matrika " inscriptions found at some sacred wells in Punjab as G. B Singh notes, one being the hathur inscription dating to just before the brith of Guru Nanak.

This connection between both physical and human properties of geography is most apparent in the theory of Environmental determinism, made popular in the 19th century by Carl Ritter and others, and with close links to evolutionary biology of the time.

Because of its close relation to the time-evolution of a system, it is of fundamental importance in most formulations of quantum theory.

Another theory is that Wimsey was based, at least in part, on Eric Whelpton, who was a close friend of Sayers at Oxford.

During these years Trotsky began developing his theory of permanent revolution, which led to a close working relationship with Alexander Parvus in 1904 – 1907.

Since the 1960s, a theory based on Linear B phonetic values suggests that Linear A language could be an Anatolian language, close to Luwian.

Only the subjects with autism — who lack the degree of inferential capacity normally associated with aspects of theory of mind — came close to functioning as " meme machines ".

For objects traveling at speeds close to the speed of light, Newton ’ s laws were superseded by Albert Einstein ’ s theory of relativity.

Covers logics in close relation with computability theory and complexity theory