Structure is a fundamental, tangible or intangible notion referring to the recognition, observation, nature, and permanence of patterns and relationships of entities. This notion may itself be an object, such as a built structure, or an attribute, such as the structure of society. From a child's verbal description of a snowflake, to the detailed scientific analysis of the properties of magnetic fields, the concept of structure is now often an essential foundation of nearly every mode of inquiry and discovery in science, philosophy, and art. In early 20th-century and earlier thought, form often plays a role comparable to that of structure in contemporary thought. The neo-Kantianism of Ernst Cassirer (cf. his Philosophy of Symbolic Forms, completed in 1929 and published in English translation in the 1950s) is sometimes regarded as a precursor of the later shift to structuralism and poststructuralism.

The description of structure implicitly offers an account of what a system is made of: a configuration of items, a collection of inter-related components or services. A structure may be a hierarchy (a cascade of one-to-many relationships), a network featuring many-to-many links, or a lattice featuring connections between components that are neighbors in space.

A formalized interpretation of the structure is compiled as semiotics of the structure.

Types of structure

Physical structure

Built structures are a subset of physical structures resulting from construction. These are divided into buildings and nonbuilding structures, and make up the infrastructure of a human society. Built structures are composed of structural elements such as columns, beams and trusses. Built structures are broadly divided by their varying design approaches and standards, into categories including Building structures, Architectural structures, Civil engineering structures and Mechanical structures.

Biological structure

In biology, structures exist at all levels of organization, ranging hierarchically from the atomic and molecular to the cellular, tissue, organ, organismic, population and ecosystem level. Usually, a higher-level structure is composed of multiple copies of a lower-level structure.

Chemical structure

Chemistry is the science treating matter at the atomic to macromolecular scale, the reactions, transformations and aggregations of matter, as well as accompanying energy and entropy changes during these processes. The chemical structure refers to both molecular geometry and to electronic structure. The structural formula of a chemical compound is a graphical representation of the molecular structure showing how the atoms are arranged. A protein structure is the three dimensional coordinates of the atoms within (macro) molecules made of protein.

Musical composition

Social structure

A social structure is a pattern of relations. They are social organizations of individuals in various life situations. Structures are applicable to people in how a society is as a system organized by a characteristic pattern of relationships. This is known as the social organization of the group. Sociologists have studied the changing structure of these groups. Structure and agency are two confronted theories about human behaviour. The debate surrounding the influence of structure and agency on human thought is one of the central issues in sociology. In this context "agency" refers to the capacity of individual humans to act independently and to make their own free choices. "Structure" here refers to those factors such as social class, religion, gender, ethnicity, customs etc. which seem to limit or influence the opportunities that individuals have.

Data structure

In computer science, a data structure is a way of storing data in a computer so that it can be used efficiently. Often a carefully chosen data structure will allow the most efficient algorithm to be used. The choice of the data structure often begins from the choice of an abstract data type. A well-designed data structure allows a variety of critical operations to be performed, using as few resources, both execution time and memory space, as possible. Data structures are implemented in a programming language as data types and the references (e.g. relationships, links and pointers) and operations that are possible with them. For structure tables and structure functions, see data structure.

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References

Category:Systems

Terence Chi-Shen Tao FRS () (born 17 July 1975, Adelaide, South Australia) is an Australian mathematician working primarily on harmonic analysis, partial differential equations, combinatorics, analytic number theory and representation theory. Tao is a professor of mathematics at the University of California, Los Angeles.

His single most famous result is the proof that there exist arbitrarily long arithmetic progressions of prime numbers (the Green–Tao theorem).

Personal life

When he was 24, he was promoted to full professor at UCLA and remains the youngest person ever appointed to that rank by the institution. Tao's father was born and grew up in Shanghai, and Tao's mother is Cantonese by ethnicity. His parents are first generation immigrants from Hong Kong to Australia. His father, Billy Tao (Chinese name Xiangguo ) is a pediatrician, and his mother is a physics and mathematics graduate from the University of Hong Kong, formerly a secondary school teacher of mathematics in Hong Kong.

Tao has two brothers living in Australia, both of whom represented Australia at the International Mathematical Olympiad. Nigel Tao is part of the team at Google Australia that created Google Wave. Trevor Tao has a double degree in maths and music and will soon be featured in a book on autistic savants.

Tao currently lives with his wife and son in Los Angeles, California.

Tao exhibited extraordinary mathematical abilities from an early age, attending university level mathematics courses at the age of nine. He is one of only two children (besides Lenhard Ng) in the history of the Johns Hopkins' Study of Exceptional Talent program to have achieved a score of 700 or greater on the SAT math section while just 8 years old (he scored a 760). In 1986, 1987, and 1988, Tao was the youngest participant to date in the International Mathematical Olympiad, first competing at the age of ten, winning a bronze, silver, and gold medal respectively. He won the gold medal when he just turned thirteen and remains the youngest gold medallist in the Olympiad's history. At age 14, Tao attended the Research Science Institute. When he was 15 he published his first assistant paper. He received his bachelor's and master's degrees (at the age of 17) from Flinders University under Garth Gaudry. In 1992 he won a Fulbright Scholarship to undertake postgraduate study in the United States. From 1992 to 1996, Tao was a graduate student at Princeton University under the direction of Elias Stein, receiving his Ph.D. at the age of 20. He joined the faculty of the University of California, Los Angeles in 1996.

Research and awards

He received the Salem Prize in 2000, the Bôcher Prize in 2002, and the Clay Research Award in 2003, for his contributions to analysis including work on the Kakeya conjecture and wave maps. In 2005 he received the American Mathematical Society's Levi L. Conant Prize with Allen Knutson, and in 2006 he was awarded the SASTRA Ramanujan Prize.

In 2004, Ben Green and Tao released a preprint proving what is now known as the Green–Tao theorem. This theorem states that there are arbitrarily long arithmetic progressions of prime numbers. The New York Times described it this way: For this and other work, he was awarded the Australian Mathematical Society Medal in 2005.

In 2006, at the 25th International Congress of Mathematicians in Madrid, he became one of the youngest, the first Australian, and the first UCLA faculty member ever to be awarded a Fields Medal. An article by New Scientist writes of his ability:

Tao was a finalist to become Australian of the Year in 2007. He is a corresponding member of the Australian Academy of Science, and in 2007 was elected as a Fellow of the Royal Society. In the same year Tao also published Tao's inequality, an extension to The Sirivimedi Lemma in the field of information theory.

In April 2008, Tao received the Alan T. Waterman Award, which recognizes an early career scientist for outstanding contributions in their field. In addition to a medal, Waterman awardees also receive a $500,000 grant for advanced research.

In December 2008, he was named The Lars Onsager lecturer of 2008, for "his combination of mathematical depth, width and volume in a manner unprecedented in contemporary mathematics". He was presented the Onsager Medal, and held his Lars Onsager lecture entitled "Structure and randomness in the prime numbers" at NTNU, Norway.

In 2010, he received the King Faisal International Prize jointly with Enrico Bombieri. Also in 2010, he was awarded the Nemmers Prize in Mathematics along with the Polya Prize(SIAM). Tao and Van H. Vu solved the circular law conjecture.

As of 2010 Tao has published over 180 research papers and has won 13 different awards.

Publications

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References

External links

Category:Fields Medalists Category:Members of the United States National Academy of Sciences Category:Fellows of the Royal Society Category:MacArthur Fellows Category:Sloan Research Fellowships Category:Combinatorialists Category:Mathematical analysts Category:Number theorists Category:Australian mathematicians Category:20th-century mathematicians Category:21st-century mathematicians Category:Princeton University alumni Category:University of California, Los Angeles faculty Category:1975 births Category:People from Adelaide Category:People from Los Angeles, California Category:Australian people of Hong Kong descent Category:Australian people of Chinese descent Category:Australian expatriates in the United States Category:Living people Category:Flinders University alumni Category:Fellows of the American Academy of Arts and Sciences Category:Additive combinatorialists