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Lynn Loomis
__NOTOC__ Lynn Harold Loomis (25 April 1915 – 9 June 1994) was an American mathematician working on analysis. Together with Hassler Whitney, he discovered the Loomis–Whitney inequality. Loomis received his PhD in 1942 from Harvard University under Salomon Bochner with thesis ''Some Studies on Simply-Connected Riemann Surfaces: I. The Problem of Imbedding II. Mapping on the Boundary for Two Classes of Surfaces''. After completing his PhD, Loomis was a professor at Radcliffe College and from 1949 at Harvard. From 1956, he was a member of the American Academy of Arts and Sciences. Selected works Articles * * * * * *with Hassler Whitney: Books *''Introduction to Abstract Harmonic Analysis'', Van Nostrand 1953 *with Shlomo Sternberg Shlomo Zvi Sternberg (born 1936), is an American mathematician known for his work in geometry, particularly symplectic geometry and Lie theory. Education and career Sternberg earned his PhD in 1955 from Johns Hopkins University, with a thesis e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hassler Whitney
Hassler Whitney (March 23, 1907 – May 10, 1989) was an American mathematician. He was one of the founders of singularity theory, and did foundational work in manifolds, embeddings, immersions, characteristic classes, and geometric integration theory. Biography Life Hassler Whitney was born on March 23, 1907, in New York City, where his father Edward Baldwin Whitney was the First District New York Supreme Court judge. His mother, A. Josepha Newcomb Whitney, was an artist and active in politics. He was the paternal nephew of Connecticut Governor and Chief Justice Simeon Eben Baldwin, his paternal grandfather was William Dwight Whitney, professor of Ancient Languages at Yale University, linguist and Sanskrit scholar. Whitney was the great-grandson of Connecticut Governor and US Senator Roger Sherman Baldwin, and the great-great-grandson of American founding father Roger Sherman. His maternal grandparents were astronomer and mathematician Simon Newcomb (1835-1909), a Steeves desce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Loomis–Whitney Inequality
In mathematics, the Loomis–Whitney inequality is a result in geometry, which in its simplest form, allows one to estimate the "size" of a d-dimensional set by the sizes of its (d-1)-dimensional projections. The inequality has applications in incidence geometry, the study of so-called "lattice animals", and other areas. The result is named after the American mathematicians Lynn Harold Loomis and Hassler Whitney, and was published in 1949. Statement of the inequality Fix a dimension d\ge 2 and consider the projections :\pi_ : \mathbb^ \to \mathbb^, :\pi_ : x = (x_, \dots, x_) \mapsto \hat_ = (x_, \dots, x_, x_, \dots, x_). For each 1 ≤ ''j'' ≤ ''d'', let :g_ : \mathbb^ \to [0, + \infty), :g_ \in L^ (\mathbb^). Then the Loomis–Whitney inequality holds: :\int_ \prod_^ g_ ( \pi_ (x) ) \, \mathrm x \leq \prod_^ \, g_ \, _. Equivalently, taking :f_ (x) = g_ (x)^, :\int_ \prod_^ f_ ( \pi_ (x) )^ \, \mathrm x \leq \prod_^ \left( \int_ f_ (\hat_) \, \mathrm \hat_ \right)^. A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard University
Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher learning in the United States and one of the most prestigious and highly ranked universities in the world. The university is composed of ten academic faculties plus Harvard Radcliffe Institute. The Faculty of Arts and Sciences offers study in a wide range of undergraduate and graduate academic disciplines, and other faculties offer only graduate degrees, including professional degrees. Harvard has three main campuses: the Cambridge campus centered on Harvard Yard; an adjoining campus immediately across Charles River in the Allston neighborhood of Boston; and the medical campus in Boston's Longwood Medical Area. Harvard's endowment is valued at $50.9 billion, making it the wealthiest academic institution in the world. Endowment inco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Salomon Bochner
Salomon Bochner (20 August 1899 – 2 May 1982) was an Austrian mathematician, known for work in mathematical analysis, probability theory and differential geometry. Life He was born into a Jewish family in Podgórze (near Kraków), then Austria-Hungary, now Poland. Fearful of a Russian invasion in Galicia at the beginning of World War I in 1914, his family moved to Germany, seeking greater security. Bochner was educated at a Berlin gymnasium (secondary school), and then at the University of Berlin. There, he was a student of Erhard Schmidt, writing a dissertation involving what would later be called the Bergman kernel. Shortly after this, he left the academy to help his family during the escalating inflation. After returning to mathematical research, he lectured at the University of Munich from 1924 to 1933. His academic career in Germany ended after the Nazis came to power in 1933, and he left for a position at Princeton University. He was a visiting scholar at the Institu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radcliffe College
Radcliffe College was a women's liberal arts college in Cambridge, Massachusetts, and functioned as the female coordinate institution for the all-male Harvard College. Considered founded in 1879, it was one of the Seven Sisters colleges and held the popular reputation of having a particularly intellectual, literary, and independent-minded female student body. Radcliffe conferred Radcliffe College diplomas on undergraduates and graduate students for approximately the first 70 years of its history. Beginning in 1963, it awarded joint Harvard-Radcliffe diplomas to undergraduates. In 1977 Radcliffe signed a formal "non-merger merger" agreement with Harvard and completed full integration with Harvard in 1999. Today, within Harvard University, Radcliffe's former administrative campus (Radcliffe Yard) is home to the Radcliffe Institute for Advanced Study. Former Radcliffe housing at the Radcliffe Quadrangle (Pforzheimer House, Cabot House, and Currier House) has been incorporated ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Academy Of Arts And Sciences
The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other Founding Fathers of the United States. It is headquartered in Cambridge, Massachusetts. Membership in the academy is achieved through a thorough petition, review, and election process. The academy's quarterly journal, ''Dædalus'', is published by MIT Press on behalf of the academy. The academy also conducts multidisciplinary public policy research. History The Academy was established by the Massachusetts legislature on May 4, 1780, charted in order "to cultivate every art and science which may tend to advance the interest, honor, dignity, and happiness of a free, independent, and virtuous people." The sixty-two incorporating fellows represented varying interests and high standing in the political, professional, and commercial secto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shlomo Sternberg
Shlomo Zvi Sternberg (born 1936), is an American mathematician known for his work in geometry, particularly symplectic geometry and Lie theory. Education and career Sternberg earned his PhD in 1955 from Johns Hopkins University, with a thesis entitled "''Some Problems in Discrete Nonlinear Transformations in One and Two Dimensions''", supervised by Aurel Wintner. After postdoctoral work at New York University (1956–1957) and an instructorship at University of Chicago (1957–1959), Sternberg joined the Mathematics Department at Harvard University in 1959, where he was George Putnam Professor of Pure and Applied Mathematics until 2017. Since 2017, he is Emeritus Professor at the Harvard Mathematics Department. Among other honors, Sternberg was awarded a List of Guggenheim Fellowships awarded in 1974, Guggenheim fellowship in 1974 and a honorary doctorate by the University of Mannheim in 1991. He delivered the American Mathematical Society, AMS in 1990 and the Hebrew University ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Math 55
Math 55 is a two-semester long freshman undergraduate mathematics course at Harvard University founded by Lynn Loomis and Shlomo Sternberg. The official titles of the course are Honors Abstract Algebra (Math 55a) and Honors Real and Complex Analysis (Math 55b). Previously, the official title was Honors Advanced Calculus and Linear Algebra. Description In the past, Harvard University's Department of Mathematics had described Math 55 as "probably the most difficult undergraduate math class in the country." But Math 55 lecturer for 2022 Professor Denis Auroux clarified that "if you’re reasonably good at math, you love it, and you have lots of time to devote to it, then Math 55 is completely fine for you." Formerly, students would begin the year in Math 25 (which was created in 1983 as a lower-level Math 55) and, after three weeks of point-set topology and special topics (for instance, in 1994, ''p''-adic analysis was taught by Wilfried Schmid), students would take a quiz. As of 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard University Alumni
The list of Harvard University people includes notable graduates, professors, and administrators affiliated with Harvard University. For a list of notable non-graduates of Harvard, see notable non-graduate alumni of Harvard. For a list of Harvard's presidents, see President of Harvard University. Eight President of the United States, Presidents of the United States have graduated from Harvard University: John Adams, John Quincy Adams, Rutherford B. Hayes, John F. Kennedy, Franklin Delano Roosevelt, Theodore Roosevelt, George W. Bush, and Barack Obama. Bush graduated from Harvard Business School, Hayes and Obama from Harvard Law School, and the others from Harvard College. Over 150 Nobel Prize winners have been associated with the university as alumni, researchers or faculty. Nobel laureates Pulitzer Prize winners ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1915 Births
Events Below, the events of World War I have the "WWI" prefix. January * January – British physicist Sir Joseph Larmor publishes his observations on "The Influence of Local Atmospheric Cooling on Astronomical Refraction". *January 1 ** WWI: British Royal Navy battleship HMS ''Formidable'' is sunk off Lyme Regis, Dorset, England, by an Imperial German Navy U-boat, with the loss of 547 crew. ** Battle of Broken Hill: A train ambush near Broken Hill, New South Wales, Australia, is carried out by two men (claiming to be in support of the Ottoman Empire) who are killed, together with 4 civilians. * January 5 – Joseph E. Carberry sets an altitude record of , carrying Capt. Benjamin Delahauf Foulois as a passenger, in a fixed-wing aircraft. * January 12 ** The United States House of Representatives rejects a proposal to give women the right to vote. ** '' A Fool There Was'' premières in the United States, starring Theda Bara as a '' femme fatale''; she quickly become ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1994 Deaths
File:1994 Events Collage.png, From left, clockwise: The 1994 Winter Olympics are held in Lillehammer, Norway; The Kaiser Permanente building after the 1994 Northridge earthquake; A model of the MS Estonia, which sank in the Baltic Sea; Nelson Mandela casts his vote in the 1994 South African general election, in which he was elected South Africa's first president, and which effectively brought Apartheid to an end; NAFTA, which was signed in 1992, comes into effect in Canada, the United States, and Mexico; The first passenger rail service to utilize the newly-opened Channel tunnel; The 1994 FIFA World Cup is held in the United States; Skulls from the Rwandan genocide, in which over half a million Tutsi people were massacred by Hutus., 300x300px, thumb rect 0 0 200 200 1994 Winter Olympics rect 200 0 400 200 Northridge earthquake rect 400 0 600 200 Sinking of the MS Estonia rect 0 200 300 400 Rwandan genocide rect 300 200 600 400 Nelson Mandela rect 0 400 200 600 1994 FIFA ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
