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Chen Chung Chang
Chen Chung Chang (Chinese: 张晨钟) was a mathematician who worked in model theory. He obtained his PhD from Berkeley in 1955 on "Cardinal and Ordinal Factorization of Relation Types" under Alfred Tarski. He wrote the standard text on model theory. Chang's conjecture and Chang's model are named after him. He also proved the ordinal partition theorem (expressed in the arrow notation for Ramsey theory) ωω→(ωω,3)2, originally a problem of Erdős and Hajnal. He also introduced MV-algebras as models for Łukasiewicz logic. Chang was a professor at the mathematics department of the University of California, Los Angeles The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a teachers college then known as the southern branch of the California St .... Selected publications * * * C. C. Chang. Algebraic analysis of many-valued logics. Transactions of the Am ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
András Hajnal
András Hajnal (May 13, 1931 – July 30, 2016) was a professor of mathematics at Rutgers University and a member of the Hungarian Academy of Sciences known for his work in set theory and combinatorics. Biography Hajnal was born on 13 May 1931,Curriculum vitae in , . He received his university diploma (M.Sc. degree) in 1953 from the , his |
University Of California, Los Angeles Faculty
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the designation is reserved for colleges that have a graduate school. The word ''university'' is derived from the Latin ''universitas magistrorum et scholarium'', which roughly means "community of teachers and scholars". The first universities were created in Europe by Catholic Church monks. The University of Bologna (''Università di Bologna''), founded in 1088, is the first university in the sense of: *Being a high degree-awarding institute. *Having independence from the ecclesiastic schools, although conducted by both clergy and non-clergy. *Using the word ''universitas'' (which was coined at its foundation). *Issuing secular and non-secular degrees: grammar, rhetoric, logic, theology, canon law, notarial law.Hunt Janin: "The university ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of California, Berkeley Alumni
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the designation is reserved for colleges that have a graduate school. The word ''university'' is derived from the Latin ''universitas magistrorum et scholarium'', which roughly means "community of teachers and scholars". The first universities were created in Europe by Catholic Church monks. The University of Bologna (''Università di Bologna''), founded in 1088, is the first university in the sense of: *Being a high degree-awarding institute. *Having independence from the ecclesiastic schools, although conducted by both clergy and non-clergy. *Using the word ''universitas'' (which was coined at its foundation). *Issuing secular and non-secular degrees: grammar, rhetoric, logic, theology, canon law, notarial law.Hunt Janin: "The university ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Theorists
A model is an informative representation of an object, person or system. The term originally denoted the Plan_(drawing), plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. Models can be divided into physical models (e.g. a model plane) and abstract models (e.g. mathematical expressions describing behavioural patterns). Abstract or conceptual models are central to philosophy of science, as almost every scientific theory effectively embeds some kind of model of the universe, physical or human condition, human sphere. In commerce, "model" can refer to a specific design of a product as displayed in a catalogue or show room (e.g. Ford Model T), and by extension to the sold product itself. Types of models include: Physical model A physical model (most commonly referred to simply as a model but in this context distinguished from a conceptual model) is a smaller or larger physical copy of an physical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century American Mathematicians
The 1st century was the century spanning AD 1 ( I) through AD 100 ( C) according to the Julian calendar. It is often written as the or to distinguish it from the 1st century BC (or BCE) which preceded it. The 1st century is considered part of the Classical era, epoch, or historical period. The 1st century also saw the appearance of Christianity. During this period, Europe, North Africa and the Near East fell under increasing domination by the Roman Empire, which continued expanding, most notably conquering Britain under the emperor Claudius ( AD 43). The reforms introduced by Augustus during his long reign stabilized the empire after the turmoil of the previous century's civil wars. Later in the century the Julio-Claudian dynasty, which had been founded by Augustus, came to an end with the suicide of Nero in AD 68. There followed the famous Year of Four Emperors, a brief period of civil war and instability, which was finally brought to an end by Vespasian, ninth Roman empero ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elsevier
Elsevier () is a Dutch academic publishing company specializing in scientific, technical, and medical content. Its products include journals such as ''The Lancet'', ''Cell'', the ScienceDirect collection of electronic journals, '' Trends'', the '' Current Opinion'' series, the online citation database Scopus, the SciVal tool for measuring research performance, the ClinicalKey search engine for clinicians, and the ClinicalPath evidence-based cancer care service. Elsevier's products and services also include digital tools for data management, instruction, research analytics and assessment. Elsevier is part of the RELX Group (known until 2015 as Reed Elsevier), a publicly traded company. According to RELX reports, in 2021 Elsevier published more than 600,000 articles annually in over 2,700 journals; as of 2018 its archives contained over 17 million documents and 40,000 e-books, with over one billion annual downloads. Researchers have criticized Elsevier for its high profit marg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Łukasiewicz Logic
In mathematics and philosophy, Łukasiewicz logic ( , ) is a non-classical, many-valued logic. It was originally defined in the early 20th century by Jan Łukasiewicz as a three-valued logic;Łukasiewicz J., 1920, O logice trójwartościowej (in Polish). Ruch filozoficzny 5:170–171. English translation: On three-valued logic, in L. Borkowski (ed.), ''Selected works by Jan Łukasiewicz'', North–Holland, Amsterdam, 1970, pp. 87–88. it was later generalized to ''n''-valued (for all finite ''n'') as well as infinitely-many-valued ( ℵ0-valued) variants, both propositional and first-order.Hay, L.S., 1963Axiomatization of the infinite-valued predicate calculus ''Journal of Symbolic Logic'' 28:77–86. The ℵ0-valued version was published in 1930 by Łukasiewicz and Alfred Tarski; consequently it is sometimes called the ŁukasiewiczTarski logic. citing Łukasiewicz, J., Tarski, A.Untersuchungen über den Aussagenkalkül Comp. Rend. Soc. Sci. et Lettres Varsovie Cl. III 23, 30–5 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MV-algebra
In abstract algebra, a branch of pure mathematics, an MV-algebra is an algebraic structure with a binary operation \oplus, a unary operation \neg, and the constant 0, satisfying certain axioms. MV-algebras are the algebraic semantics of Łukasiewicz logic; the letters MV refer to the ''many-valued'' logic of Łukasiewicz. MV-algebras coincide with the class of bounded commutative BCK algebras. Definitions An MV-algebra is an algebraic structure \langle A, \oplus, \lnot, 0\rangle, consisting of * a non-empty set A, * a binary operation \oplus on A, * a unary operation \lnot on A, and * a constant 0 denoting a fixed element of A, which satisfies the following identities: * (x \oplus y) \oplus z = x \oplus (y \oplus z), * x \oplus 0 = x, * x \oplus y = y \oplus x, * \lnot \lnot x = x, * x \oplus \lnot 0 = \lnot 0, and * \lnot ( \lnot x \oplus y)\oplus y = \lnot ( \lnot y \oplus x) \oplus x. By virtue of the first three axioms, \langle A, \oplus, 0 \rangle is a commutat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Erdős
Paul Erdős ( hu, Erdős Pál ; 26 March 1913 – 20 September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in discrete mathematics, graph theory, number theory, mathematical analysis, approximation theory, set theory, and probability theory. Much of his work centered around discrete mathematics, cracking many previously unsolved problems in the field. He championed and contributed to Ramsey theory, which studies the conditions in which order necessarily appears. Overall, his work leaned towards solving previously open problems, rather than developing or exploring new areas of mathematics. Erdős published around 1,500 mathematical papers during his lifetime, a figure that remains unsurpassed. He firmly believed mathematics to be a social activity, living an itinerant lifestyle with the sole purpose of writing mathematical papers with other mathem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of California, Los Angeles
The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a teachers college then known as the southern branch of the California State Normal School (now San José State University). This school was absorbed with the official founding of UCLA as the Southern Branch of the University of California in 1919, making it the second-oldest of the 10-campus University of California system (after UC Berkeley). UCLA offers 337 undergraduate and graduate degree programs in a wide range of disciplines, enrolling about 31,600 undergraduate and 14,300 graduate and professional students. UCLA received 174,914 undergraduate applications for Fall 2022, including transfers, making the school the most applied-to university in the United States. The university is organized into the College of Letters and Science and 12 professional schools. Six of the schools offer undergraduate degre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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