Gottlob Frege, founder of the analytic tradition in philosophy, famously argued for the analysis of language in terms of sense and reference.

In the early 1920s Rolf Nevanlinna, partly in collaboration with his brother Frithiof, extended the theory to cover meromorphic functions, i. e. functions analytic in the plane except for isolated points in which the Laurent series of the function has a finite number of terms with a negative power of the variable.

In more analytic terms, it is " the representational faithfulness of information to the true state of the object that the information represents, where representational faithfulness is composed of four essential qualities or core attributes: completeness, currency / timeliness, accuracy / correctness and validity / authorization.

( Note that running time is measured in terms of the size of the input, which in this case is ~ log n, that being the number of bits needed to represent the number n .) The elliptic curve primality test can be proven to run in O (( log n )< sup > 6 </ sup >), but only if some still unproven ( but widely assumed to be true ) statements of analytic number theory are used.

Developments within analytic number theory are often refinements of earlier techniques, which reduce the error terms and widen their applicability.

Where analytic philosophy tends to treat philosophy in terms of discrete problems, capable of being analyzed apart from their historical origins ( much as scientists consider the history of science inessential to scientific inquiry ), continental philosophy typically suggests that " philosophical argument cannot be divorced from the textual and contextual conditions of its historical emergence ".

When all the terms of the series are defined and it has a non-zero radius of convergence, then the series defines an analytic function.

Since for even s the Riemann zeta function has an analytic expression in terms of a rational multiple of, then for even exponents, this infinite product evaluates to a rational number.

Taking a finite sum of such terms avoids difficulties of analytic continuation to the region σ < 1.

In terms of sheaf theory, this difference can be stated as follows: the sheaf of differentiable functions on a differentiable manifold is fine, in contrast with the analytic case.

In terms of the inverse global analytic function ƒ < sup >− 1 </ sup >, branch points are those points around which there is nontrivial monodromy.

On the other hand, where the study of conversational talk is divorced from its situated context, and de-linked from its reflexive character in terms of constituting a specific social order-that is, as it takes on the character of a purely " technical method ", and, " formal analytic enterprise in its own right "-it is not a form of ethnomethodology understood in any orthodox sense.

Many results and properties in algebraic geometry and complex analytic geometry are formulated in terms of coherent sheaves and their cohomology.

" An analytic philosopher, Stevenson suggested in his 1937 essay " The Emotive Meaning of Ethical Terms " that any ethical theory should explain three things: that intelligent disagreement can occur over moral questions, that moral terms like good are " magnetic " in encouraging action, and that the scientific method is insufficient for verifying moral claims.

These make analytic integrals often easier to evaluate, and Gaussian quadrature tables are often presented in terms of area coordinates.

It seems that the only way to assert the synonymy is by supposing that the terms ' bachelor ' and ' unmarried man ' are synonymous and that the sentence " All and only all bachelors are unmarried men " is analytic.

This wavelet is formulated in terms of its Fourier transform as the Hilbert analytic function of the conventional Mexican hat wavelet:

* The Borel – Carathéodory theorem, which bounds an analytic function in terms of its real part.

In computer science, a parsing expression grammar, or PEG, is a type of analytic formal grammar, i. e. it describes a formal language in terms of a set of rules for recognizing strings in the language.

Otto F. Kernberg and Heinz Kohut regard the analytic process as well as the role of the analyst in quite different terms.

This is the expression in analytic terms of the uniqueness of prime factorization of the ideals I in O < sub > K </ sub >.

He was the first to propose that by positing analytic equivalencies ( or " bridge laws ") between the terms of different sciences, one could eliminate all ontological commitments except those required by the most basic science.

In Geert Hofstede ’ s terms Europe can, to a large extend, be considered an individualistic civilization ( i. e. a rather direct and analytic style is preferred, important points are mentioned before an explanation or illustration in an argument, decisions are based on compromise or the majority ’ s vote ); in contrast, the Sinic ( Chinese ), Japanese, Arabic and Hindu ( Indian ) civilizations are collectivistic ( i. e. a rather indirect and synthetic style is used, explanations and illustrations are mentioned before the essential point of an argument, decisions are reached through consent ).

In analytic terms, is a d-dimensional copula if

Initially a study of systems of polynomial equations in several variables, the subject of algebraic geometry starts where equation solving leaves off, and it becomes even more important to understand the intrinsic properties of the totality of solutions of a system of equations, than to find a specific solution ; this leads into some of the deepest areas in all of mathematics, both conceptually and in terms of technique.

* Glossary of archaic terms in algebraic geometry

The cartoonist liked to joke about how he failed geometry for nine straight terms.

Near the beginning of the first book of the Elements, Euclid gives five postulates ( axioms ) for plane geometry, stated in terms of constructions ( as translated by Thomas Heath ):

The Elements began with definitions of terms, fundamental geometric principles ( called axioms or postulates ), and general quantitative principles ( called common notions ) from which all the rest of geometry could be logically deduced.

This new class of preferred motions, too, defines a geometry of space and time — in mathematical terms, it is the geodesic motion associated with a specific connection which depends on the gradient of the gravitational potential.

The geometric mean can also be understood in terms of geometry.

The electrostatic potential can be expressed in terms of the inter-ionic separation and a constant ( Madelung constant ) that takes account of the geometry of the crystal.

Verifying this relationship throughout the orbital cycle, however, required very extensive calculation ; to simplify this task, by late 1602 Kepler reformulated the proportion in terms of geometry: planets sweep out equal areas in equal times — Kepler's second law of planetary motion.

The Kaluza – Klein theory is striking because it has a particularly elegant presentation in terms of geometry.

One may say that Diophantus was studying rational points — i. e., points whose coordinates are rational — on curves and algebraic varieties ; however, unlike the Greeks of the Classical period, who did what we would now call basic algebra in geometrical terms, Diophantus did what we would now call basic algebraic geometry in purely algebraic terms.

Among some of the old words that were replaced are terms in geometry, cardinal directions, some months ' names, and many nouns and adjectives.

* In differential geometry, a web permits an intrinsic characterization in terms of Riemannian geometry of the additive separation of variables in the Hamilton – Jacobi equation

Lovecraft's celebrated short story, The Call of Cthulhu ( 1928 ), the titular entity emerges from the vast and ancient alien city of R ' lyeh, which is described in terms of " non-Euclidean geometry " and contains angles which are " all wrong " ( appearing acute but behaving as if obtuse, for example ) and planes which could be horizontal or slanted depending on how the observer looks at them.

This difference is too minute to measure on an actual honeycomb, and irrelevant to the hive economy in terms of efficient use of wax, considering that wild comb varies considerably from any mathematical notion of " ideal " geometry.

Klein is responsible for the terms " hyperbolic " and " elliptic " ( in his system he called Euclidean geometry " parabolic ", a term which has not survived the test of time ).

Other systems, using different sets of undefined terms obtain the same geometry by different paths.

* Definitiones, containing definitions of terms for geometry.

In addition to his writings on geometry, Posidonius was credited for creating some mathematical definitions, or for articulating views on technical terms, for example ' theorem ' and ' problem '.

Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry.