It provides a mathematical foundation of industrial organization, discussed above, to model different types of firm behavior, for example in an oligopolistic industry ( few sellers ), but equally applicable to wage negotiations, bargaining, contract design, and any situation where individual agents are few enough to have perceptible effects on each other.

Ørsted's work influenced Ampère to produce a theory of electromagnetism that set the subject on a mathematical foundation.

Kirchhoff's diffraction formula provides a rigorous mathematical foundation for diffraction, based on the wave equation.

Together with Newton's mathematical theories, they are part of the foundation of modern astronomy and physics.

In 1921, he laid the mathematical foundation of fiber diffraction analysis.

If one agrees that set theory is an appealing foundation of mathematics, then all mathematical objects must be defined as sets of some sort.

His laws of motion were to be the solid foundation of mechanics ; his law of universal gravitation combined terrestrial and celestial mechanics into one great system that seemed to be able to describe the whole world in mathematical formulae.

This concept is important in mathematical analysis as the foundation for Lebesgue integration, and in probability theory, where it is interpreted as the collection of events which can be assigned probabilities.

Some mathematical theorems and axioms are referred to as laws because they provide logical foundation to empirical laws.

As a formal concept, it has appeared in jurisprudence, commerce and scholasticism long before it was given a rigorous mathematical foundation.

In this view, logic is the proper foundation of mathematics, and all mathematical statements are necessary logical truths.

Asimov took varying positions on whether the Laws were optional: although in his first writings they were simply carefully engineered safeguards, in later stories Asimov stated that they were an inalienable part of the mathematical foundation underlying the positronic brain.

Constantin Carathéodory formulated thermodynamics on a purely mathematical axiomatic foundation.

managed, despite intense administrative pressures, to oversee a great deal of fundamental work on providing a mathematical foundation for the semantics of programming languages, the work for which Scott is best known.

Not our axioms, but the very real world of mathematical objects forms the foundation.

Green was the first person to create a mathematical theory of electricity and magnetism and his theory formed the foundation for the work of other scientists such as James Clerk Maxwell, William Thomson, and others.

One theme Stephenson explores in Quicksilver is the advancement of mathematical sciences which in turn led to important applications: Leibniz's theory of binary mathematic became the foundation upon which to develop computers.

They also form the mathematical foundation for the topological order in condensed matter.

" The 2007 National Medal of Science to Leonard Kleinrock for his fundamental contributions to the mathematical theory of modern data networks, and for the functional specification of packet switching, which is the foundation of Internet technology.

Logic is the foundation which underlies mathematical logic and the rest of mathematics.

His book, Information Theory and Reliable Communication, Wiley 1968, placed Information Theory on a sound mathematical foundation and is still considered by many as the standard textbook on information theory.

More general affine connections were then studied around 1920, by Hermann Weyl, who developed a detailed mathematical foundation for general relativity, and Élie Cartan, who made the link with the geometrical ideas coming from surface theory.

The mathematical foundation of thermoacoustics is by Nicolas Rott.

Their pioneering work " A Theory For Record Linkage " remains the mathematical foundation for many record linkage applications even today.

Some years ago Julian Huxley proposed to an audience made up of members of the British Association for the Advancement of Science that `` man's supernormal or extra-sensory faculties are ( now ) in the same case as were his mathematical faculties during the ice age ''.

A guy can be an active and successful hot rodder for years without becoming even remotely involved with mathematical problems ; ;

A mathematical formula is nothing more than a pattern for solving a specific problem.

The equation is used for the mathematical process of solving the problem.

We devote a chapter to the binomial distribution not only because it is a mathematical model for an enormous variety of real life phenomena, but also because it has important properties that recur in many other probability models.

It has become painfully clear that the very attempt to make the language of social research free of values by erecting mathematical and physical models, is itself a conditioned response to a world which pays a premium price for technological manipulation.

A mathematical block diagram for the leveling system is shown in Fig. 7-2.

Although modern scholars have expressed surprise that `` the simple magic square of three '', a mere `` mathematical puzzle '', was able to exert a considerable influence on the minds and imaginations of the cultured Chinese for so many centuries, they could have found most of the answers right within the square itself.

The tremendous emphasis on the 5 in the Lo Shu square -- for purely mathematical reasons -- and the fact that this number so neatly symbolized the heart and center of the universe, could well explain why the Old Chinese seem to have so revered the number 5, and why they put so much stress on the concept of Centrality.

Although the primary mathematical properties of the middle number at the center of the Lo Shu, and the interrelation of all the other numbers to it, might seem enough to account for the deep fascination which the Lo Shu held for the Old Chinese philosophers, this was actually only a beginning of wonders.

The Greek sculptors tried to clarify it by looking for mathematical proportions, just as they sought some reality behind appearances.

; Analysis of variance ( ANOVA ): A mathematical process for separating the variability of a group of observations into assignable causes and setting up various significance tests.

The Greek abacus was a table of wood or marble, pre-set with small counters in wood or metal for mathematical calculations.

The abacus teaches mathematical skills that can never be replaced with talking calculators and is an important learning tool for blind students.

Blind students also complete mathematical assignments using a braille-writer and Nemeth code ( a type of braille code for mathematics ) but large multiplication and long division problems can be long and difficult.

One motivation for this use is that a number of generally accepted mathematical results, such as Tychonoff's theorem, require the axiom of choice for their proofs.

( A formal proof for all finite sets would use the principle of mathematical induction to prove " for every natural number k, every family of k nonempty sets has a choice function.

Without the axiom of choice, these theorems may not hold for mathematical objects of large cardinality.

These axioms are sufficient for many proofs in elementary mathematical analysis, and are consistent with some principles, such as the Lebesgue measurability of all sets of reals, that are disprovable from the full axiom of choice.

Generalizations of the absolute value for real numbers occur in a wide variety of mathematical settings.

* three research-and-production enterprises — for mathematical machines, for the study of materials, and for automated control equipment — these being Soviet-era military-industrial plants