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George Mackey
George Whitelaw Mackey (February 1, 1916 – March 15, 2006) was an American mathematician known for his contributions to quantum logic, representation theory, and noncommutative geometry. Career Mackey earned his bachelor of arts at Rice University (then the Rice Institute) in 1938 and obtained his Ph.D. at Harvard University in 1942 under the direction of Marshall H. Stone. He joined the Harvard University Mathematics Department in 1943, was appointed Landon T. Clay Professor of Mathematics and Theoretical Science in 1969 and remained there until he retired in 1985. Work Earlier in his career Mackey did significant work in the duality theory of locally convex spaces, which provided tools for subsequent work in this area, including Alexander Grothendieck's work on topological tensor products. Mackey was one of the pioneer workers in the intersection of quantum logic, the theory of infinite-dimensional unitary representations of groups, the theory of operator algebras and nonc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Missouri
Missouri is a U.S. state, state in the Midwestern United States, Midwestern region of the United States. Ranking List of U.S. states and territories by area, 21st in land area, it is bordered by eight states (tied for the most with Tennessee): Iowa to the north, Illinois, Kentucky and Tennessee to the east, Arkansas to the south and Oklahoma, Kansas and Nebraska to the west. In the south are the Ozarks, a forested highland, providing timber, minerals, and recreation. The Missouri River, after which the state is named, flows through the center into the Mississippi River, which makes up the eastern border. With more than six million residents, it is the List of U.S. states and territories by population, 19th-most populous state of the country. The largest urban areas are St. Louis, Kansas City, Missouri, Kansas City, Springfield, Missouri, Springfield and Columbia, Missouri, Columbia; the Capital city, capital is Jefferson City, Missouri, Jefferson City. Humans have inhabited w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calvin C
Calvin may refer to: Names * Calvin (given name) ** Particularly Calvin Coolidge, 30th President of the United States * Calvin (surname) ** Particularly John Calvin, theologian Places In the United States * Calvin, Arkansas, a hamlet * Calvin Township, Jewell County, Kansas * Calvin, Louisiana, a village * Calvin Township, Michigan ** Calvin crater, an impact crater * Calvin, North Dakota, a city * Calvin, Oklahoma, a town * Calvin, Virginia * Calvin, West Virginia, an unincorporated community Elsewhere * Calvin, Ontario, Canada, a township * Mount Calvin, Victoria Land, Antarctica Schools * Calvin University (South Korea), a Presbyterian-affiliated university in South Korea * Calvin University, Grand Rapids, Michigan * Calvin Theological Seminary, Grand Rapids, Michigan * Calvin High School (other), various American schools * Calvin Christian School (Escondido, California) * Calvin Christian School (Kingston, Tasmania) * Collège Calvin, the oldest public secondary s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Locally Convex Space
In functional analysis and related areas of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces. They can be defined as topological vector spaces whose topology is generated by translations of balanced, absorbent, convex sets. Alternatively they can be defined as a vector space with a family of seminorms, and a topology can be defined in terms of that family. Although in general such spaces are not necessarily normable, the existence of a convex local base for the zero vector is strong enough for the Hahn–Banach theorem to hold, yielding a sufficiently rich theory of continuous linear functionals. Fréchet spaces are locally convex spaces that are completely metrizable (with a choice of complete metric). They are generalizations of Banach spaces, which are complete vector spaces with respect to a metric generated by a norm. History Metrizable topologies on vecto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Landon T
Landon is a personal name of English origin that means "long hill". It is a variant of Langdon. Landon became popular in the United States in the 1990s, and by 2010 had become the 32nd most popular name for boys. BehindtheName.com. Notable people with the given name "Landon" include A * (born 1984), American actorB * (born 1995), Canadian ice hockey player * |
Doctor Of Philosophy
A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common Academic degree, degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is an earned research degree, those studying for a PhD are required to produce original research that expands the boundaries of knowledge, normally in the form of a Thesis, dissertation, and defend their work before a panel of other experts in the field. The completion of a PhD is often a requirement for employment as a university professor, researcher, or scientist in many fields. Individuals who have earned a Doctor of Philosophy degree may, in many jurisdictions, use the title ''Doctor (title), Doctor'' (often abbreviated "Dr" or "Dr.") with their name, although the proper etiquette associated with this usage may also be subject to the professional ethics of their own scholarly field, culture, or society. Those who teach at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noncommutative Geometry
Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of ''spaces'' that are locally presented by noncommutative algebras of functions (possibly in some generalized sense). A noncommutative algebra is an associative algebra in which the multiplication is not commutative, that is, for which xy does not always equal yx; or more generally an algebraic structure in which one of the principal binary operations is not commutative; one also allows additional structures, e.g. topology or norm, to be possibly carried by the noncommutative algebra of functions. An approach giving deep insight about noncommutative spaces is through operator algebras (i.e. algebras of bounded linear operators on a Hilbert space). Perhaps one of the typical examples of a noncommutative space is the " noncommutative tori", which played a key role in the early development of this field in 1980s and lead to noncommutativ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Representation Theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication). The theory of matrices and linear operators is well-understood, so representations of more abstract objects in terms of familiar linear algebra objects helps glean properties and sometimes simplify calculations on more abstract theories. The algebraic objects amenable to such a description include groups, associative algebras and Lie algebras. The most prominent of these (and historically the first) is the representation theory of groups, in which elements of a group are represented by invertible matrices in such a way that the group operation i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Logic
In the mathematical study of logic and the physical analysis of quantum foundations, quantum logic is a set of rules for manipulation of propositions inspired by the structure of quantum theory. The field takes as its starting point an observation of Garrett Birkhoff and John von Neumann, that the structure of experimental tests in classical mechanics forms a Boolean algebra, but the structure of experimental tests in quantum mechanics forms a much more complicated structure. Quantum logic has been proposed as the correct logic for propositional inference generally, most notably by the philosopher Hilary Putnam, at least at one point in his career. This thesis was an important ingredient in Putnam's 1968 paper " Is Logic Empirical?" in which he analysed the epistemological status of the rules of propositional logic. Modern philosophers reject quantum logic as a basis for reasoning, because it lacks a material conditional; a common alternative is the system of linear logi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leroy P
Leroy or Le Roy may refer to: People * Leroy (name), a given name and surname * Leroy (musician), American musician * Leroy (sailor), French sailor Places United States * Leroy, Alabama * Le Roy, Illinois * Le Roy, Iowa * Le Roy, Kansas * Le Roy, Michigan * Le Roy, Minnesota * Le Roy (town), New York ** Le Roy (village), New York * Leroy, Indiana * Leroy, Texas * LeRoy, Wisconsin, a town * LeRoy (community), Wisconsin, an unincorporated community * Leroy Township, Calhoun County, Michigan * Leroy Township, Ingham County, Michigan * LeRoy Township, Lake County, Ohio * Leroy Township, Pennsylvania * LeRoy, West Virginia Elsewhere * Leroy, Saskatchewan, Canada * Rural Municipality of Leroy No. 339, Saskatchewan, Canada * 93102 Leroy, an asteroid Arts and entertainment * ''Leroy'' (film), a 2007 German comedy film * Leroy (''Lilo & Stitch''), a character in ''Leroy & Stitch'' * Leroy (''South Park''), a ''South Park'' character * "Leroy", a 1958 song by Jack Scott Other us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrew M
Andrew is the English form of a given name common in many countries. In the 1990s, it was among the top ten most popular names given to boys in English-speaking countries. "Andrew" is frequently shortened to "Andy" or "Drew". The word is derived from the el, Ἀνδρέας, ''Andreas'', itself related to grc, ἀνήρ/ἀνδρός ''aner/andros'', "man" (as opposed to "woman"), thus meaning "manly" and, as consequence, "brave", "strong", "courageous", and "warrior". In the King James Bible, the Greek "Ἀνδρέας" is translated as Andrew. Popularity Australia In 2000, the name Andrew was the second most popular name in Australia. In 1999, it was the 19th most common name, while in 1940, it was the 31st most common name. Andrew was the first most popular name given to boys in the Northern Territory in 2003 to 2015 and continuing. In Victoria, Andrew was the first most popular name for a boy in the 1970s. Canada Andrew was the 20th most popular name chosen for male ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Zimmer
Robert Jeffrey Zimmer (born November 5, 1947) is an American mathematician and academic administrator. From 2006 until 2021, he served as the 13th president of the University of Chicago and as the Chair of the Board for Argonne National Lab, Fermi National Accelerator Laboratory, and the Marine Biological Laboratory. He then served as chancellor of the University of Chicago until July 2022. As a mathematician, Zimmer specializes in geometry, particularly ergodic theory, Lie groups, and differential geometry. Education and work experience Zimmer graduated from New York's Stuyvesant High School in 1964. He matriculated to Brandeis University as an undergraduate, earning his B.A., summa cum laude, in 1968. He conducted his mathematics graduate study at Harvard University, receiving his master's degree in 1971 and his Ph.D. in 1975 under the supervision of George Mackey. Zimmer taught at the United States Naval Academy from 1975 to 1977, and moved to the mathematics department of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
