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.

In 1926, Erwin Schrödinger used this idea to develop a mathematical model of the atom that described the electrons as three-dimensional waveforms rather than point particles.

In seeking to explain atomic spectra an entirely new mathematical model of matter was revealed.

In computer science, an abstract data type ( ADT ) is a mathematical model for a certain class of data structures that have similar behavior ; or for certain data types of one or more programming languages that have similar semantics.

An abstract data type is defined as a mathematical model of the data objects that make up a data type as well as the functions that operate on these objects.

Newton was the first to develop a mathematical model for calculating the speed of sound, but it was not correct until Pierre-Simon Laplace accounted for the molecular behavior of gases and introduced the heat capacity ratio.

In Thomson's mathematical model the " corpuscles " ( or modern electrons ) were arranged non-randomly, in rotating rings.

The term " Brownian motion " can also refer to the mathematical model used to describe such random movements, which is often called a particle theory.

The mathematical model of Brownian motion has several real-world applications.

For the mathematical formulation of the model, is also assumed to be twice continuously differentiable, so that differential equations describing the motion may be formulated.

In contrast to the frequency domain analysis of the classical control theory, modern control theory utilizes the time-domain state space representation, a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations.

In the mathematical model.

A mathematical model has been made of it by Sjors van der Stelt.

An alternative approach, which preceded the ERM, is using the Relational model and dependencies ( mathematical relationships ) among data to normalize the database, i. e., to define the (" optimal ") relations ( data record or tupple types ) in the database.

** Langevin dynamics, a mathematical model for stochastic dynamics ; used in modeling molecules, yet also the stock market and other systems

This is an idealized mathematical model: real physical Diesels do have an increase in pressure during this period, but it is less pronounced than in the Otto cycle.

Picture produced by Drawing Machine 2, an image generated from a mathematical model

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.

When a mathematician reasons from the statement " ABC is a triangle " to the statement " triangles exist ", she is not asserting that triangles are made up of atoms but rather that triangles exist within a particular mathematical model.

In the 20th century German chemist Walther Nernst proposed a mathematical model to determine the effect of reactant concentration on electrochemical cell potential.

The first stable mathematical model of an electronic oscillator, the Van der Pol oscillator, was derived by Balthasar van der Pol in 1927.

A finite-state machine ( FSM ) or finite-state automaton ( plural: automata ), or simply a state machine, is a mathematical model of computation used to design both computer programs and sequential logic circuits.

** Filtering problem ( stochastic processes ), a mathematical model for a number of filtering problems in signal processing and the like

Consequently, a common practice is to model " sampling " as a multiplication by the Dirac comb function, which of course is only " possible " in a purely mathematical sense .</ ref >

In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects from a certain collection.

Neoclassical economics is also often seen as relying too heavily on complex mathematical models, such as those used in general equilibrium theory, without enough regard to whether these actually describe the real economy.

Many see an attempt to model a system as complex as a modern economy by a mathematical model as unrealistic and doomed to failure.

Dickinson proposed a mathematical solution whereby the problems of a socialist economy could be solved by a central planning agency.

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.

One is the mathematical-physical-chemical subject group, which includes mathematics, computer science, actuarial science, mathematical economy, statistics, physics, astronomy, geophysics, meteorology, biophysics, chemistry, environmental chemistry, biochemistry and nano-science.

This is an argument which cannot be made through a conventional ( mathematical ) economic model, because it says that there are critical systemic-elements that will always be omitted from any top-down analysis of the economy.

In mathematical economics, the Arrow – Debreu model ( also referred to as the Arrow – Debreu – McKenzie model ) suggests that under certain economic assumptions ( convex preferences, perfect competition and demand independence ) there must be a set of prices such that aggregate supplies will equal aggregate demands for every commodity in the economy.

Laibman teaches economic theory, political economy, and mathematical economics, at the undergraduate, masters, and doctoral levels at CUNY.

Most critics have tried to refute Marx's theory with an elegant mathematical model, rather than actually looking at real data to see if the capitalist economy really behaves in the way Marx claims it does.

From 1895 to 1900 he held a lawyers office in The Hague until 1900, after which he studied mathematical economy in Vienna and Berlin.

The origin of the goes back to Gottfried Leibniz, who in the seventeenth century, after having constructed a successful mechanical calculating machine, dreamt of building a machine that could manipulate symbols in order to determine the truth values of mathematical statements.

One of Dijkstra's sidelines was serving as Chairman of the Board of the fictional Mathematics Inc., a company that he imagined having commercialized the production of mathematical theorems in the same way that software companies had commercialized the production of computer programs.

The general consensus is that theoretical fractals are infinitely self-similar, iterated, and detailed mathematical constructs having fractal dimensions, of which many examples have been formulated and studied in great depth.

The wide array of traditional mathematical astronomy methods having failed him, Kepler set about trying to fit an ovoid orbit to the data.

that, being closed loops, imply the presence of diverging integrals having no mathematical meaning.

Tree structures are used to depict all kinds of taxonomic knowledge, such as family trees, the biological evolutionary tree, the evolutionary tree of a language family, the grammatical structure of a language ( a key example being S → NP VP, meaning a sentence is a noun phrase and a verb phrase, with each in turn having other components which have other components ), the way web pages are logically ordered in a web site, mathematical trees of integer sets, et cetera.

Structuralism is a position holding that mathematical theories describe structures, and that mathematical objects are exhaustively defined by their places in such structures, consequently having no intrinsic properties.

Kripke was labelled a prodigy, having taught himself Ancient Hebrew by the age of six, read the complete works of Shakespeare by nine, and mastered the works of Descartes and complex mathematical problems before graduating elementary school.

In fact, the wave aspect of matter was formalized by a wavefunction defined by the Schrödinger equation, which is a pure mathematical entity having a probabilistic interpretation, without the support of real physical elements.

A sigmoid curve is produced by a mathematical function having an " S " shape.

Paul Erdős is legendary for having posed hundreds, if not thousands, of mathematical problems, many of them profound.

Assessment practice overlaps with teaching practice in a sense ( it is difficult to teach individuals to a certain level of mathematical competence without first having fore-knowledge of their current mathematical abilities ).

Having the same shape is an equivalence relation, and accordingly a precise mathematical definition of the notion of shape can be given as being an equivalence class of subsets of a Euclidean space having the same shape.

In 1920 Hilbert succeeded in having Brouwer, whom he considered a threat to mathematics, removed from the editorial board of Mathematische Annalen, the leading mathematical journal of the time.

Other important mathematical physicists of the seventeenth century included the Dutchman Christiaan Huygens ( famous for having suggested the wave theory of light ), and the German Johannes Kepler ( Tycho Brahe's assistant who discovered the equations for planetary motion ).

Based on the philosophical assumption of the Strong Church-Turing Universe Thesis, a mathematical criterion for evaluation of evidence has been proven, with the criterion having a resemblance to the idea of Occam's Razor that the simplest comprehensive description of the evidence is most likely correct.

The QED manifesto was a proposal for a computer-based database of all mathematical knowledge, strictly formalized and with all proofs having been checked automatically.

In mathematical analysis, a function of bounded variation, also known as a BV function, is a real-valued function whose total variation is bounded ( finite ): the graph of a function having this property is well behaved in a precise sense.

PSO optimizes a problem by having a population of candidate solutions, here dubbed particles, and moving these particles around in the search-space according to simple mathematical formulae over the particle's position and velocity.

However this doesn't apply to mathematics, which is not subject to such retractions of established results, notwithstanding nineteenth and early twentieth century discoveries in mathematical logic which may be popularly misunderstood as having overthrown prior mathematics.

In Roald Dahl's novel, " Matilda ", the lead character is portrayed having exceptional mathematical skills as she computes her dad's profit without the need for paper computations.

He also is known for having once recited 11, 944 successive digits of the mathematical quantity of pi from memory.