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Walter Lewis Baily Jr.
Walter Lewis Baily Jr. (born July 5, 1930, in Waynesburg, Pennsylvania, Waynesburg, Pennsylvania; d. January 15, 2013 in Northbrook, Illinois, Northbrook, Illinois) was an American mathematician. Walter Baily's research focused on areas of algebraic groups, modular forms and Number theory, number-theoretical applications of automorphic forms. One of his significant works was with Armand Borel, now known as the Baily–Borel compactification, which is a Compactification (mathematics), compactification of a quotient of a Hermitian symmetric space by an arithmetic group (that is, a linear algebraic group over the rational numbers). Baily and Borel built on the work of Ichirō Satake and others. Baily became a William Lowell Putnam Mathematical Competition, Putnam Fellow in 1952. He studied at the Massachusetts Institute of Technology (MIT), receiving a Bachelor's degree, Bachelor of Science in Mathematics in 1952, after which he attended Princeton University, receiving a Master's de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Waynesburg, Pennsylvania
Waynesburg is a borough in and the county seat of Greene County, Pennsylvania, United States, located about south of Pittsburgh. Its population was 3,987 at the 2020 census. The region around Waynesburg is underlaid with several layers of coking coal, including the Pittsburgh No. 8 seam, the Waynesburg seam, and the Sewickley (Mapletown) seam. The area is also rich with coalbed methane, which is being developed from the underlying Marcellus Shale, the largest domestic natural gas reserve. Early in the 20th century, four large gas compressing stations and a steam shovel factory were located in Waynesburg. Waynesburg is named for General "Mad" Anthony Wayne, one of the top lieutenants of George Washington during the Revolutionary War (1776–81). The borough is the location of Waynesburg University, and it is served by the Greene County Airport. History In 1796, the Pennsylvania General Assembly passed legislation to create Greene County, dividing Washington County into two ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."German original: "Die Mathematik ist die Königin der Wissenschaften, und die Arithmetik ist die Königin der Mathematik." Number theorists study prime numbers as well as the properties of mathematical objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory are often best understood through the study of Complex analysis, analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Assistant Professor
Assistant Professor is an academic rank just below the rank of an associate professor used in universities or colleges, mainly in the United States and Canada. Overview This position is generally taken after earning a doctoral degree and generally after several years of holding one or more Postdoctoral Researcher positions. It is below the position of Associate Professor at most universities and is equivalent to the rank of Lecturer at most Commonwealth universities. In the United States, Assistant Professor is often the first position held in a tenure track, although it can also be a non-tenure track position. A typical professorship sequence is Assistant Professor, Associate Professor, and Full Professor in order. After 7 years, if successful, Assistant Professors can get tenure and also get promotion to Associate Professor. There is high demand for vacant tenure-track Assistant Professor positions, often with hundreds of applicants. Less than 20% of doctoral graduates move ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bell Labs
Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984), then AT&T Bell Laboratories (1984–1996) and Bell Labs Innovations (1996–2007), is an American industrial research and scientific development company owned by multinational company Nokia. With headquarters located in Murray Hill, New Jersey, the company operates several laboratories in the United States and around the world. Researchers working at Bell Laboratories are credited with the development of radio astronomy, the transistor, the laser, the photovoltaic cell, the charge-coupled device (CCD), information theory, the Unix operating system, and the programming languages B, C, C++, S, SNOBOL, AWK, AMPL, and others. Nine Nobel Prizes have been awarded for work completed at Bell Laboratories. Bell Labs had its origin in the complex corporate organization of the Bell System telephone conglomerate. In the late 19th century, the laboratory began as the Western Electric Engineering Department, l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Master's Degree
A master's degree (from Latin ) is an academic degree awarded by universities or colleges upon completion of a course of study demonstrating mastery or a high-order overview of a specific field of study or area of professional practice. A master's degree normally requires previous study at the bachelor's degree, bachelor's level, either as a separate degree or as part of an integrated course. Within the area studied, master's graduates are expected to possess advanced knowledge of a specialized body of and applied topics; high order skills in |
Bachelor's Degree
A bachelor's degree (from Middle Latin ''baccalaureus'') or baccalaureate (from Modern Latin ''baccalaureatus'') is an undergraduate academic degree awarded by colleges and universities upon completion of a course of study lasting three to six years (depending on institution and academic discipline). The two most common bachelor's degrees are the Bachelor of Arts (BA) and the Bachelor of Science (BS or BSc). In some institutions and educational systems, certain bachelor's degrees can only be taken as graduate or postgraduate educations after a first degree has been completed, although more commonly the successful completion of a bachelor's degree is a prerequisite for further courses such as a master's or a doctorate. In countries with qualifications frameworks, bachelor's degrees are normally one of the major levels in the framework (sometimes two levels where non-honours and honours bachelor's degrees are considered separately). However, some qualifications titled bachelor's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Association Of America
The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists; statisticians; and many others in academia, government, business, and industry. The MAA was founded in 1915 and is headquartered at 1529 18th Street, Northwest in the Dupont Circle neighborhood of Washington, D.C. The organization publishes mathematics journals and books, including the '' American Mathematical Monthly'' (established in 1894 by Benjamin Finkel), the most widely read mathematics journal in the world according to records on JSTOR. Mission and Vision The mission of the MAA is to advance the understanding of mathematics and its impact on our world. We envision a society that values the power and beauty of mathematics and fully realizes its potential to promote human flourishing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Lowell Putnam Mathematical Competition
The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual list of mathematics competitions, mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States and Canada (regardless of the students' nationalities). It awards a scholarship and cash prizes ranging from $250 to $2,500 for the top students and $5,000 to $25,000 for the top schools, plus one of the top five individual scorers (designated as ''#Putnam_Fellows, Putnam Fellows'') is awarded a scholarship of up to $12,000 plus tuition at Harvard University (Putnam Fellow Prize Fellowship), the top 100 individual scorers have their names mentioned in the American Mathematical Monthly (alphabetically ordered within rank), and the names and addresses of the top 500 contestants are mailed to all participating institutions. It is widely considered to be the most prestigious university-level mathematics competition in the world, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ichirō Satake
(25 December 1927 – 10 October 2014) was a Japanese mathematician working on algebraic groups who introduced the Satake isomorphism and Satake diagrams. He was considered an iconic figure in the theory of linear algebraic groups and symmetric spaces. Satake was born in Tokyo, Japan in 1927, and received his Ph.D. at the University of Tokyo in 1959 under the supervision of Shokichi Iyanaga. He was a professor at University of California, Berkeley from 1968 to 1983. After retirement he returned to Japan, where he spent time at Tohoku University and Chuo University. He died of respiratory failure on 10 October 2014. Although they are often attributed to William Thurston, Satake was the first to introduce orbifold, which he did in the 1950s under the name of ''V-manifold''. In , he gave the modern definition, along with the basic calculus of smooth functions and differential forms. He demonstrated that the de Rham theorem and Poincaré duality, along with their proofs, carry over ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Algebraic Group
In mathematics, a linear algebraic group is a subgroup of the group of invertible n\times n matrices (under matrix multiplication) that is defined by polynomial equations. An example is the orthogonal group, defined by the relation M^TM = I_n where M^T is the transpose of M. Many Lie groups can be viewed as linear algebraic groups over the field of real or complex numbers. (For example, every compact Lie group can be regarded as a linear algebraic group over R (necessarily R-anisotropic and reductive), as can many noncompact groups such as the simple Lie group SL(''n'',R).) The simple Lie groups were classified by Wilhelm Killing and Élie Cartan in the 1880s and 1890s. At that time, no special use was made of the fact that the group structure can be defined by polynomials, that is, that these are algebraic groups. The founders of the theory of algebraic groups include Maurer, Chevalley, and . In the 1950s, Armand Borel constructed much of the theory of algebraic groups as it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Group
In mathematics, an arithmetic group is a group obtained as the integer points of an algebraic group, for example \mathrm_2(\Z). They arise naturally in the study of arithmetic properties of quadratic forms and other classical topics in number theory. They also give rise to very interesting examples of Riemannian manifolds and hence are objects of interest in differential geometry and topology. Finally, these two topics join in the theory of automorphic forms which is fundamental in modern number theory. History One of the origins of the mathematical theory of arithmetic groups is algebraic number theory. The classical reduction theory of quadratic and Hermitian forms by Charles Hermite, Hermann Minkowski and others can be seen as computing fundamental domains for the action of certain arithmetic groups on the relevant symmetric spaces. The topic was related to Minkowski's geometry of numbers and the early development of the study of arithmetic invariant of number fields such as the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hermitian Symmetric Space
In mathematics, a Hermitian symmetric space is a Hermitian manifold which at every point has an inversion symmetry preserving the Hermitian structure. First studied by Élie Cartan, they form a natural generalization of the notion of Riemannian symmetric space from real manifolds to complex manifolds. Every Hermitian symmetric space is a homogeneous space for its isometry group and has a unique decomposition as a product of irreducible spaces and a Euclidean space. The irreducible spaces arise in pairs as a non-compact space that, as Borel showed, can be embedded as an open subspace of its compact dual space. Harish Chandra showed that each non-compact space can be realized as a bounded symmetric domain in a complex vector space. The simplest case involves the groups SU(2), SU(1,1) and their common complexification SL(2,C). In this case the non-compact space is the unit disk, a homogeneous space for SU(1,1). It is a bounded domain in the complex plane C. The one-point compactific ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
