The major advance in integration came in the 17th century with the independent discovery of the fundamental theorem of calculus by Newton and Leibniz.

The fundamental principles established at the Institute by Blau and the late Corrigan included ideas like “ no technique in advance of need ,” and that a curriculum should be cyclical rather than sequential, returning to root principles at regular intervals, and that “ we ’ re a community of artists here, some of us called faculty and some called students.

* In 2012, a new Division was formed the Laboratory Astrophysics Division ( LAD ) to advance our understanding of the Universe through the promotion of fundamental theoretical and experimental research into the underlying processes that drive the Universe.

“ Indeed, the courts advance democratic bargaining only when assured that such democracy will not disadvantage more fundamental policy interests, such as harmony between employers and “ unions ” ( read union elites ) or control of inflation ”.

It was the most fundamental cryptanalytic advance until WWII.

As a " field of inquiry with a diverse scope " its " fundamental goal ... is to advance management and policies so that government can function.

The fundamental powers of the Bank were limited to lending in small amounts, making advance payments to the Government and discounting some Treasury bills.

The AAUP's stated mission is to advance academic freedom and shared governance, to define fundamental professional values and standards for higher education, and to ensure higher education's contribution to the common good.

Such information will advance understanding of the fundamental high-energy processes at the core of the solar flare problem.

Even the fundamental questions of existence, uniqueness, and extendability of solutions for nonlinear differential equations, and well-posedness of initial and boundary value problems for nonlinear PDEs are hard problems and their resolution in special cases is considered to be a significant advance in the mathematical theory ( cf.

Professor Martin Nowak, Director of the Program for Evolutionary Dynamics at Harvard University, was awarded a grant for the “ Foundational Questions in Evolutionary Biology ” initiative, which seeks to advance fundamental questions in the context of evolutionary biology and to generate new understanding in the origins of biological creativity, the deep logics of biological dynamics and ontology, and the concepts of teleology and ultimate purpose in the context of evolutionary biology.

Glaciologists consider that trends in mass balance for glaciers are more fundamental than the advance or retreat of the termini of individual glaciers.

Decoupling the sender from communications sent was a fundamental advance of the Actor model enabling asynchronous communication and control structures as patterns of passing messages.

and Nagaoka himself recognized a fundamental defect in the theory even at its conception, namely that a classical charged object cannot sustain orbital motion because it is accelerating and therefore loses energy due to electromagnetic radiation.

Lavoisier's fundamental contributions to chemistry were a result of a conscious effort to fit all experiments into the framework of a single theory.

He also provided an algebraic definition of fundamental groups of schemes and more generally the main structures of a categorical Galois theory.

Lavoisier's fundamental contributions to chemistry were a result of a conscious effort to fit all experiments into the framework of a single theory.

Some, such as computational complexity theory, which studies fundamental properties of computational problems, are highly abstract, while others, such as computer graphics, emphasize real-world applications.

Some fields, such as computational complexity theory ( which explores the fundamental properties of computational problems ), are highly abstract, whilst fields such as computer graphics emphasise real-world applications.

* the equivalence principle, whether or not Einstein's general theory of relativity is the correct theory of gravitation, and if the fundamental laws of physics are the same everywhere in the universe.

Ronald Dworkin ( 2005 ) rejects Hart's theory and proposes that all individuals should expect the equal respect and concern of those who govern them as a fundamental political right.

This work was fundamental in consolidating number theory as a discipline and has shaped the field to the present day.

Although Bohr, Fowler, Pauli, and other physicists agreed with Chandrasekhar's analysis, at the time, owing to Eddington's status, they were unwilling to publicly support Chandrasekhar .< sup >, pp. 110 – 111 </ sup > Through the rest of his life, Eddington held to his position in his writings, including his work on his fundamental theory.

Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry.

Ecological theory suggests that in order to coexist, species must have some level of limiting similarity — they must be different from one another in some fundamental way, otherwise one species would competitively exclude the other.

It was at around the same time that he began making fundamental discoveries in the theory of polynomial equations.

( Compare this with the modern theory of quantum physics, which postulates a non-deterministic random motion of fundamental particles, which do not swerve absent an external force ; randomness originates in interaction of particles in incompatible eigenstates.

Finally, it is a basic tool for proving theorems in modern number theory, such as Lagrange's four-square theorem and the fundamental theorem of arithmetic ( unique factorization ).

He maintained, however, that it was not replicability, or even a fundamental theory of ESP that would evolve research, but only a greater interest in unconscious mental processes and a more complete understanding of human personality.

Fundamental groups can be studied using the theory of covering spaces, since a fundamental group coincides with the group of deck transformations of the associated universal covering space.

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.

Since the fundamental group is a homotopy invariant, the theory of the winding number for the complex plane minus one point is the same as for the circle.

However, the Standard Model is widely considered to be a provisional theory rather than a truly fundamental one, since it is not known if it is compatible with Einstein's general relativity.

In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 is either prime itself or is the product of prime numbers, and that, although the order of the primes in the second case is arbitrary, the primes themselves are not.

However, unanswered questions remain, the most fundamental being how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity.

Georg Ferdinand Ludwig Philipp Cantor ( ; ; – January 6, 1918 ) was a German mathematician, best known as the inventor of set theory, which has become a fundamental theory in mathematics.

The fundamental assertion is that there is a maximum amount that " a consumer will give up, of one commodity, to get one unit of another good, in that amount which will leave the consumer indifferent between the new and old situations " The negative slope of the indifference curves represents the willingness of the consumer to make a trade off.

* The special case where one of the curves is a line can be derived from the fundamental theorem of algebra.

He then claims that, in Books i – iv, he only works out the generation of the curves and their fundamental properties presented in Book i more fully and generally than did earlier treatises, and that a number of theorems in Book iii and the greater part of Book iv are new.

It is the form of the fundamental property ( expressed in terms of the " application of areas ") that leads him to give these curves their names: parabola, ellipse, and hyperbola.

The fundamental theorem of curves asserts that the knowledge of these invariants completely determines the curve.

If the Darboux derivatives of two frames are equal, then a version of the fundamental theorem of calculus asserts that the curves are congruent.

This is not really good enough, given the steep rise in loudness ( rising to as much as 24 dB per octave ) with frequency revealed by the equal-loudness curves below about 100 Hz, and a good experimenter must ensure that trial subjects really are hearing the fundamental and not harmonics, especially the third harmonic which will be especially pronounced as speaker cones become limited in travel as their suspensions reach the limit of compliance.

In differential geometry, the fundamental theorem of curves states that any regular curve with non-zero curvature has its shape ( and size ) completely determined by its curvature and torsion.

We can pick two oriented simple closed curves m and ℓ on the boundary torus of the 3-manifold that generate the fundamental group of the torus.

The Riemann-Roch theorem for algebraic curves is a fundamental identity involving the dimension of complete linear systems in the setup of projective curves.

* Max Noether's residual intersection theorem ( Fundamentalsatz or fundamental theorem ) is a result on algebraic curves in the projective plane, on the residual sets of intersections ; see AF + BG theorem.

Age determination of fish and shellfish is a fundamental step in generating basic biological data such as growth curves, and is needed for many stock assessment methods.