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Lillian Pierce
Lillian Beatrix Pierce is a mathematician whose research connects number theory with harmonic analysis. She is a professor of mathematics at Duke University. Early life and education Pierce was home-schooled in Fallbrook, California and began playing the violin at age four. By age 11 she began performing professionally as a violinist. As a teenager, she also started taking classes at a local community college, accumulating so many units that some of the universities she applied to refused to consider her for freshman admission. She entered Princeton University majoring in mathematics but intending to pursue an MD–PhD program; under the influence of faculty mentor and undergraduate thesis supervisor Elias M. Stein, her interests shifted towards pure mathematics. As an undergraduate, she also became an intern at the National Security Agency. She was Princeton's 2002 valedictorian and became a Rhodes Scholar, repeating two accomplishments of her brother Niles Pierce from nine ... [...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 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 analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes or other number-theoretic object ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Upper Bound
In mathematics, particularly in order theory, an upper bound or majorant of a subset of some preordered set is an element of that is greater than or equal to every element of . Dually, a lower bound or minorant of is defined to be an element of that is less than or equal to every element of . A set with an upper (respectively, lower) bound is said to be bounded from above or majorized (respectively bounded from below or minorized) by that bound. The terms bounded above (bounded below) are also used in the mathematical literature for sets that have upper (respectively lower) bounds. Examples For example, is a lower bound for the set (as a subset of the integers or of the real numbers, etc.), and so is . On the other hand, is not a lower bound for since it is not smaller than every element in . The set has as both an upper bound and a lower bound; all other numbers are either an upper bound or a lower bound for that . Every subset of the natural numbers has a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Whitehouse
Whitehouse may refer to: People * Charles S. Whitehouse (1921-2001), American diplomat * Cornelius Whitehouse (1796–1883), English engineer and inventor * E. Sheldon Whitehouse (1883-1965), American diplomat * Elliott Whitehouse (born 1993), English footballer * Eula Whitehouse (1892–1974), American botanist * Frederick William Whitehouse (1900–1973), Australian geologist * Jimmy Whitehouse (footballer, born 1924) (1924-2005), English footballer * Mary Whitehouse (1910–2001), British Christian morality campaigner * Morris H. Whitehouse (1878–1944), American architect * Paul Whitehouse (born 1958), Welsh comedian and actor * Paul Whitehouse (police officer) (born 1944) * Sheldon Whitehouse (born 1955), American politician from the state of Rhode Island * Wildman Whitehouse (1816–1890), English surgeon and chief electrician for the transatlantic telegraph cable Places ;in the United Kingdom * Whitehouse, Aberdeenshire, location of the Whitehouse railway st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NARA
The National Archives and Records Administration (NARA) is an " independent federal agency of the United States government within the executive branch", charged with the preservation and documentation of government and historical records. It is also tasked with increasing public access to those documents which make up the National Archive. NARA is officially responsible for maintaining and publishing the legally authentic and authoritative copies of acts of Congress, presidential directives, and federal regulations. NARA also transmits votes of the Electoral College to Congress. It also examines Electoral College and Constitutional amendment ratification documents for prima facie legal sufficiency and an authenticating signature. The National Archives, and its publicly exhibited Charters of Freedom, which include the original United States Declaration of Independence, United States Constitution, United States Bill of Rights, and many other historical documents, is head ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The New York Times
''The New York Times'' (''the Times'', ''NYT'', or the Gray Lady) is a daily newspaper based in New York City with a worldwide readership reported in 2020 to comprise a declining 840,000 paid print subscribers, and a growing 6 million paid digital subscribers. It also is a producer of popular podcasts such as '' The Daily''. Founded in 1851 by Henry Jarvis Raymond and George Jones, it was initially published by Raymond, Jones & Company. The ''Times'' has won 132 Pulitzer Prizes, the most of any newspaper, and has long been regarded as a national "newspaper of record". For print it is ranked 18th in the world by circulation and 3rd in the U.S. The paper is owned by the New York Times Company, which is publicly traded. It has been governed by the Sulzberger family since 1896, through a dual-class share structure after its shares became publicly traded. A. G. Sulzberger, the paper's publisher and the company's chairman, is the fifth generation of the family to head the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quanta Magazine
''Quanta Magazine'' is an editorially independent online publication of the Simons Foundation covering developments in physics, mathematics, biology and computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (includin .... ''Undark Magazine'' described ''Quanta Magazine'' as "highly regarded for its masterful coverage of complex topics in science and math." The science news aggregator ''RealClearScience'' ranked ''Quanta Magazine'' first on its list of "The Top 10 Websites for Science in 2018." In 2020, the magazine received a National Magazine Award for General Excellence from the American Society of Magazine Editors for its "willingness to tackle some of the toughest and most difficult topics in science and math in a language that is accessible to the lay reader without condes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Notices Of The American Mathematical Society
''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue. The first volume appeared in 1953. Each issue of the magazine since January 1995 is available in its entirety on the journal web site. Articles are peer-reviewed by an editorial board of mathematical experts. Since 2019, the editor-in-chief is Erica Flapan. The cover regularly features mathematical visualizations. The ''Notices'' is self-described to be the world's most widely read mathematical journal. As the membership journal of the American Mathematical Society, the ''Notices'' is sent to the approximately 30,000 AMS members worldwide, one-third of whom reside outside the United States. By publishing high-level exposition, the ''Notices'' provides opportunities for mathematicians to find out what is going on in the field. Each issue contains one or two such expository articles that describe current d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fellow Of The American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential in in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Presidential Early Career Award For Scientists And Engineers
The Presidential Early Career Award for Scientists and Engineers (PECASE) is the highest honor bestowed by the United States government on outstanding scientists and engineers in the early stages of their independent research careers. The White House, following recommendations from participating agencies, confers the awards annually. To be eligible for a Presidential Award, an individual must be a US citizen, national or permanent resident. Some of the winning scientists and engineers receive up to a five-year research grant. History In February 1996, the National Science and Technology Council (NSTC), was commissioned by President Bill Clinton to create an award program that would honor and support the achievements of young professionals at the outset of their independent research careers in the fields of science and technology. The stated aim of the award is to help maintain the leadership position of the United States in science. Originally, 60 recipients received the PEC ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carleson's Theorem
Carleson's theorem is a fundamental result in mathematical analysis establishing the pointwise (Lebesgue measure, Lebesgue) almost everywhere convergence of Fourier series of Lp space, functions, proved by . The name is also often used to refer to the extension of the result by to functions for (also known as the ''Carleson–Hunt theorem'') and the analogous results for pointwise almost everywhere convergence of Fourier integrals, which can be shown to be equivalent by transference methods. Statement of the theorem The result, in the form of its extension by Hunt, can be formally stated as follows: The analogous result for Fourier integrals can be formally stated as follows: History A fundamental question about Fourier series, asked by Fourier himself at the beginning of the 19th century, is whether the Fourier series of a continuous function converges pointwise convergence, pointwise to the function. By strengthening the continuity assumption slightly one can easi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Singular Integral Operators
In mathematics, singular integrals are central to harmonic analysis and are intimately connected with the study of partial differential equations. Broadly speaking a singular integral is an integral operator : T(f)(x) = \int K(x,y)f(y) \, dy, whose kernel function ''K'' : R''n''×R''n'' → R is singular along the diagonal ''x'' = ''y''. Specifically, the singularity is such that , ''K''(''x'', ''y''), is of size , ''x'' − ''y'', −''n'' asymptotically as , ''x'' − ''y'', → 0. Since such integrals may not in general be absolutely integrable, a rigorous definition must define them as the limit of the integral over , ''y'' − ''x'', > ε as ε → 0, but in practice this is a technicality. Usually further assumptions are required to obtain results such as their boundedness on ''L''''p''(R''n''). The Hilbert transform The archetypal singular integral operator is t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Character Sum
In mathematics, a character sum is a sum \sum \chi(n) of values of a Dirichlet character χ '' modulo'' ''N'', taken over a given range of values of ''n''. Such sums are basic in a number of questions, for example in the distribution of quadratic residues, and in particular in the classical question of finding an upper bound for the least quadratic non-residue ''modulo'' ''N''. Character sums are often closely linked to exponential sums by the Gauss sums (this is like a finite Mellin transform). Assume χ is a nonprincipal Dirichlet character to the modulus ''N''. Sums over ranges The sum taken over all residue classes mod ''N'' is then zero. This means that the cases of interest will be sums \Sigma over relatively short ranges, of length ''R'' < ''N'' say, : A fundamental improvement on the trivial estimate is the |
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