The notion of abstract data types is related to the concept of data abstraction, important in object-oriented programming and design by contract methodologies for software development.

Its development is likely to have been closely connected with the development of human language, which ( whether spoken or written ) appears to both involve and facilitate abstract thinking.

Dialectics as represented in dialectical materialism is a theory of the general and abstract factors that govern the development of nature, society, and thought.

* Scientific modelling, the process of generating abstract models for the iterative development of hypotheses as part of the scientific method

With the later development of abstract groups, this result of Lagrange on polynomials was recognized to extend to the general theorem about finite groups which now bears his name.

Kandinsky's creation of purely abstract work followed a long period of development and maturation of intense thought based on his artistic experiences.

* The art world experienced the development of new styles and explorations such as expressionism, Dadaism, cubism, de stijl, abstract expressionism and surrealism.

The last stage of moral development is the post-conventional level where people move beyond society's norms and consider abstract ethical principles.

The Boston figurative Expressionists post World War II were increasingly marginalized by the development of abstract expressionism centered in New York City.

They paved the way for the early 20th century development of abstract and non-representational art.

During the development of Christian art in the Byzantine empire ( see Byzantine art ), a more abstract aesthetic replaced the naturalism previously established in Hellenistic art.

Early visits to New York art galleries influenced his artist development, and his work was influenced by the abstract expressionism of Jackson Pollock and Franz Kline.

Nevertheless, some critically acclaimed science fiction movies have followed in the path of science fiction literature, using story development to explore abstract concepts.

Besides these abstract ten Sefirot, which are conceived only ideally, the twenty-two letters of the alphabet produced the material world, for they are real, and are the formative powers of all existence and development.

Cobra was a milestone in the development of Tachisme and European abstract expressionism.

Because of his development of the concept of a " one god greatest among gods and men " that is abstract, universal, unchanging, immobile and always present, Xenophanes is often seen as one of the first monotheists, in the Western philosophy of religion, although the quotation that seems to point to Xenophanes's monotheism also refers to multiple " gods " who the supreme God is greater than.

During the development of Christian art in the Byzantine empire ( see Byzantine art ), a more abstract aesthetic replaced the naturalism previously established in Hellenistic art.

Speech, a critical tool to scaffold thinking and responding, plays a crucial role in the development of higher psychological processes ( Luria, 1979 ) because it enables thinking to be more abstract, flexible, and independent ( Bodrova & Leong, 1996 ).

His experiences with object technology through the Simula language, as well as early work on abstract data types and formal specification ( including the Z notation ), provided some of the background for the development of Eiffel.

As contrasted to theories of ethics that derive from dispute resolution, or the meta-ethics as defined in Western moral philosophy, ethical traditions emphasizing abstract moral codes expressed in some language with some judgmental hierarchy, ethical relationship theories tend to emphasize human development.

This result was proven by Israel Gelfand and Mark Naimark in 1943 and was a significant point in the development of the theory of C *- algebras since it established the possibility of considering a C *- algebra as an abstract algebraic entity without reference to particular realizations as an algebra of operators.

Although short-lived, Rayonism was a crucial step in the development of Russian abstract art.

Abstraction is an ongoing process in mathematics and the historical development of many mathematical topics exhibits a progression from the concrete to the abstract.

The complexity of this law served as an impetus behind the development of algebra ( Arabic: al-jabr ) by the Persian mathematician Muhammad ibn Mūsā al-Khwārizmī and other medieval Islamic mathematicians.

Schelter is credited with the development of the GNU Common Lisp ( gcl ) implementation of Common Lisp and the GPL'd version of the computer algebra system Macsyma called GNU Maxima.

The subsequent development of category theory was powered first by the computational needs of homological algebra, and later by the axiomatic needs of algebraic geometry, the field most resistant to being grounded in either axiomatic set theory or the Russell-Whitehead view of united foundations.

Editions of Arithmetica exerted a profound influence on the development of algebra in Europe in the late sixteenth and through the seventeenth and eighteenth centuries.

Another important factor of common development of graph theory and topology came from the use of the techniques of modern algebra.

The development of computers led to increased research in efficient algorithms for Gaussian elimination and matrix decompositions, and linear algebra became an essential tool for modelling and simulations.

One of Descartes ' most enduring legacies was his development of Cartesian or analytic geometry, which uses algebra to describe geometry.

Historically, with the nineteenth century development of Boolean algebra mathematical models of logic began to treat " truth ", also represented as " T " or " 1 ", as an arbitrary constant.

Although not recognized as such by Dirac at the time the equation was formulated, in hindsight the introduction of this geometric algebra represents an enormous stride forward in the development of quantum theory.

A more recent development in category theory that generalizes operations is operad theory – an operad is a set of operations, similar to a universal algebra.

Although the development of mathematical logic had made applications to algebra possible, they came about slowly ; results published by Anatoly Maltsev in the 1940s went unnoticed because of the war.

Maclisp was used to implement the Macsyma symbolic algebra program ; Macsyma's development also drove a number of features in Maclisp.

In combination with a Greek intellectual attitude unconcerned with practical problems, there followed a significant retreat from the development of techniques in arithmetic and algebra.

One recent significant development here is the introduction of a quantum group, a certain kind of Hopf algebra.

However, Fred Richman proved a reformulated version of the theorem that does work .< ref > See Fred Richman ; 1998 ; < cite > The fundamental theorem of algebra: a constructive development without choice </ cite >; available from .</ ref >

While earlier Greek proofs were largely geometric demonstrations, the development of arithmetic and algebra by Islamic mathematicians allowed more general proofs that no longer depended on geometry.

This led to the development of a specific IS information algebra.

* The 1990 Harold Pender Award for his application of concepts from logic and algebra to the development of mathematical semantics of programming languages ;

In 1830 he published a Treatise on Algebra which had for its object the placing of algebra on a true scientific basis, adequate for the development which it had received at the hands of the Continental mathematicians.

In 1957, Artin wrote a book on geometric algebra an insightful development of the classical groups in a Kleinian context.

The historical development of commutative algebra, which was initially called ideal theory, is closely linked to concepts in elimination theory: ideas of Kronecker, who wrote a major paper on the subject, were adapted by Hilbert and effectively ' linearised ' while dropping the explicit constructive content.

Much of the modern development of commutative algebra emphasizes modules.

Algebraic geometry and algebraic number theory, which provide many natural examples of commutative rings, have driven much of the development of commutative ring theory, which is now, under the name of commutative algebra, a major area of modern mathematics.

After the rise of Boolean algebra and the development of positional notation, it became possible to mechanize simple circuits for counting, first by mechanical means, such as gears and rods, using rotation and translation to represent changes of state, then by electrical means, using changes in voltage and current to represent the analogs of quantity.