It can be applied in the study of classical concepts of mathematics, such as real numbers, complex variables, trigonometric functions, and algorithms, or of non-classical concepts like constructivism, harmonics, infinity, and vectors.

These Greek city-states reached great levels of prosperity that resulted in an unprecedented cultural boom, that of classical Greece, expressed in architecture, drama, science, mathematics and philosophy, and nurtured in Athens under a democratic government.

A term dating from the 1940s, " general abstract nonsense ", refers to its high level of abstraction, compared to more classical branches of mathematics.

Students of control engineering may start with a linear control system course dealing with the time and complex-s domain, which requires a thorough background in elementary mathematics and Laplace transform ( called classical control theory ).

After re-working the foundations of classical geometry, Hilbert could have extrapolated to the rest of mathematics.

In the early modern age, Victorian schools were reformed to teach commercially useful topics, such as modern languages and mathematics, rather than classical subjects, such as Latin and Greek.

The 900-page book, titled Elementorum physicae mathematicae, written in Latin by Jesuit Father Andrea Caraffa, a professor at the Collegio Romano, covered subjects like mathematics, classical mechanics, astronomy, optics, and acoustics.

Anne-Marie moved back to her parents ' house in Meudon, where she raised Sartre with help from her father, a teacher of German, who taught Sartre mathematics and introduced him to classical literature at a very early age.

The classical thinkers who studied, wrote, and experimented at the museum include the fathers of mathematics, engineering, physiology, geography, and medicine.

The development of algebraic geometry from its classical to modern forms is a particularly striking example of the way an area of mathematics can change radically in its viewpoint, without making what was correctly proved before in any way incorrect ; of course mathematical progress clarifies gaps in previous proofs, often by exposing hidden assumptions, which progress has revealed worth conceptualizing.

However, because the intuitionistic notion of truth is more restrictive than that of classical mathematics, the intuitionist must reject some assumptions of classical logic to ensure that everything he proves is in fact intuitionistically true.

The changes that took place at the beginning of the 20th-century are emphasized by the fact that many modern disciplines, including sciences such as physics, mathematics, neuroscience and economics, and arts such as ballet and architecture, call their pre-20th century forms classical.

With the advent of the BHK interpretation and Kripke models, intuitionism became easier to reconcile with classical mathematics.

Heisenberg's matrix mechanics formulation was based on algebras of infinite matrices, a very radical formulation in light of the mathematics of classical physics, although he started from the index-terminology of the experimentalists of that time, not even aware that his " index-schemes " were matrices, as Born soon pointed out to him.

Equally proficient in mathematics and geography as well as classical languages, he produced the first woodcut map of Silesia made on the basis of surveys and data collected from local inhabitants, which he published in 1561 under the title " Silesiae Typus " and dedicated to Nicolaus II.

Much constructive mathematics uses intuitionistic logic, which is essentially classical logic without the law of the excluded middle which states that for any proposition, either that proposition is true, or its negation is.

In this sense, propositions restricted to the finite are still regarded as being either true or false, as they are in classical mathematics, but this bivalence does not extend to propositions which refer to infinite collections.

* Errett Bishop ( promoted a version of constructivism which is consistent with classical mathematics )

Non-standard analysis is a branch of classical mathematics that formulates analysis using a rigorous notion of an infinitesimal number.

: It is shown in this book that Leibniz's ideas can be fully vindicated and that they lead to a novel and fruitful approach to classical Analysis and to many other branches of mathematics.

Ottoman science and technology had been highly regarded in medieval times, as a result of Ottoman scholars ' synthesis of classical learning with Islamic philosophy and mathematics, and knowledge of such Chinese advances in technology as gunpowder and the magnetic compass.

Here Spengler received a classical education at the local Gymnasium ( academically oriented secondary school ), studying Greek, Latin, mathematics and natural sciences.

After the use of classical theories since the end of the scientific revolution, various fields substituted mathematics studies for experimental studies and examining equations to build a theoretical structure.

In terms of analytic geometry, the restriction of classical geometry to compass and straightedge constructions means a restriction to first-and second-order equations, e. g., y

A proof theoretical abduction method for first order classical logic based on the sequent calculus and a dual one, based on semantic tableaux ( analytic tableaux ) have been proposed ( Cialdea Mayer & Pirri 1993 ).

His closest friend, Sándor Ferenczi, with whom Rank collaborated in the early Twenties on new experiential, object-relational and " here-and-now " approaches to therapy, vacillated on the significance of Rank's pre-Oedipal theory but not on Rank's objections to classical analytic technique.

The only known analytic solutions to the classical equations of motion are marginal deformations.

Analytic vectors are dense by a classical argument of Edward Nelson, amplified by Roe Goodman, since vectors in the image of a heat operator e < sup >– tD </ sup >, corresponding to an elliptic differential operator D in the universal enveloping algebra of G, are analytic.

The first “ modern ” social theories ( known as classical theories ) that begin to resemble the analytic social theory of today developed almost simultaneously with the birth of the science of sociology.

Analysis may be performed through classical mathematical techniques, analytic mathematical modelling or computational simulation, through experimental testing techniques, or a combination of methods.

His early work was in classical analytic number theory.

Their area of study was primarily classical analysis, differential equations and analytic functions.

Using this powerful tool one may then prove Cauchy's integral formula, and, just like in the classical case, that any vector-valued holomorphic function is analytic.

The name has been in continuous use ever since, as Socrates ' argument provides the foundation for classical propositional logic and hence much of traditional western philosophy ( or analytic philosophy ).

Abstract analytic number theory is a branch of mathematics which takes the ideas and techniques of classical analytic number theory and applies them to a variety of different mathematical fields.

* Jesus Guillera and Jonathan Sondow, " Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent ", Ramanujan Journal 16 ( 2008 ), 247 – 270 ( Provides an integral and a series representation ).

In classical geometry, the tangent line to the graph of the function f at a real number a was the unique line through the point ( a, f ( a )) that did not meet the graph of f transversally, meaning that the line did not pass straight through the graph.

Some classical construction problems of geometry are impossible using compass and straightedge, but can be solved using origami.

Euclid frequently used the method of proof by contradiction, and therefore the traditional presentation of Euclidean geometry assumes classical logic, in which every proposition is either true or false, i. e., for any proposition P, the proposition " P or not P " is automatically true.

Some predictions of general relativity differ significantly from those of classical physics, especially concerning the passage of time, the geometry of space, the motion of bodies in free fall, and the propagation of light.

The preferred inertial motions are related to the geometry of space and time: in the standard reference frames of classical mechanics, objects in free motion move along straight lines at constant speed.

Phenomena that in classical mechanics are ascribed to the action of the force of gravity ( such as free-fall, orbital motion, and spacecraft trajectories ), correspond to inertial motion within a curved geometry of spacetime in general relativity ; there is no gravitational force deflecting objects from their natural, straight paths.

The term is also used as a collective term for the approach to classical, computational and relativistic geometry that makes heavy use of such algebras.

In fact, his interest in the geometry of differential equations was first motivated by the work of Carl Gustav Jacobi, on the theory of partial differential equations of first order and on the equations of classical mechanics.

In general, separability is a technical hypothesis on a space which is quite useful and — among the classes of spaces studied in geometry and classical analysis — generally considered to be quite mild.

Many theorems from classical geometry hold true for this spherical geometry as well, but many do not ( see parallel postulate ).

In the classical geometry of space, a vector exhibits a certain behavior when it is acted upon by a rotation or reflected in a hyperplane.

In classical geometry, axioms are general statements while postulates are statements about geometrical objects.

In classical geometry, a proposition may be a construction that satisfies given requirements ; for example, Proposition 1 in Book I of Euclid's elements is the construction of an equilateral triangle.

While he is best known for the Kolmogorov – Arnold – Moser theorem regarding the stability of integrable Hamiltonian systems, he made important contributions in several areas including dynamical systems theory, catastrophe theory, topology, algebraic geometry, classical mechanics and singularity theory, including posing the ADE classification problem, since his first main result — the partial solution of Hilbert's thirteenth problem in 1957 at the age of 19.

Using this, it becomes relatively easy to answer such classical problems of geometry as

The design studies for precast concrete units or for the moulds for in situ shuttering, prompted by the need to obtain a large number of different forms from the combination of a very limited number of units contributed, in the 1980s, to the Taller ’ s affirmation of the validity of classical forms and geometry in contemporary architecture.