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Serge Lang
Serge Lang (; May 19, 1927 – September 12, 2005) was a French-American mathematician and activist who taught at Yale University for most of his career. He is known for his work in number theory and for his mathematics textbooks, including the influential ''Algebra''. He received the Frank Nelson Cole Prize in 1960 and was a member of the Bourbaki group. As an activist, Lang campaigned against the Vietnam War, and also successfully fought against the nomination of the political scientist Samuel P. Huntington to the National Academies of Science. Later in his life, Lang was an HIV/AIDS denialist. He claimed that HIV had not been proven to cause AIDS and protested Yale's research into HIV/AIDS. Biography and mathematical work Lang was born in Saint-Germain-en-Laye, close to Paris, in 1927. He had a twin brother who became a basketball coach and a sister who became an actress. Lang moved with his family to California as a teenager, where he graduated in 1943 from Beverly Hills ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berkeley, California
Berkeley ( ) is a city on the eastern shore of San Francisco Bay in northern Alameda County, California, United States. It is named after the 18th-century Irish bishop and philosopher George Berkeley. It borders the cities of Oakland and Emeryville to the south and the city of Albany and the unincorporated community of Kensington to the north. Its eastern border with Contra Costa County generally follows the ridge of the Berkeley Hills. The 2020 census recorded a population of 124,321. Berkeley is home to the oldest campus in the University of California System, the University of California, Berkeley, and the Lawrence Berkeley National Laboratory, which is managed and operated by the university. It also has the Graduate Theological Union, one of the largest religious studies institutions in the world. Berkeley is considered one of the most socially progressive cities in the United States. History Indigenous history The site of today's City of Berkeley was the te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vietnam War
The Vietnam War (also known by other names) was a conflict in Vietnam, Laos, and Cambodia from 1 November 1955 to the fall of Saigon on 30 April 1975. It was the second of the Indochina Wars and was officially fought between North Vietnam and South Vietnam. The north was supported by the Soviet Union, China, and other communist states, while the south was supported by the United States and other anti-communist allies. The war is widely considered to be a Cold War-era proxy war. It lasted almost 20 years, with direct U.S. involvement ending in 1973. The conflict also spilled over into neighboring states, exacerbating the Laotian Civil War and the Cambodian Civil War, which ended with all three countries becoming communist states by 1975. After the French military withdrawal from Indochina in 1954 – following their defeat in the First Indochina War – the Viet Minh took control of North Vietnam, and the U.S. assumed financial and military support for the South Vietnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diophantine Geometry
In mathematics, Diophantine geometry is the study of Diophantine equations by means of powerful methods in algebraic geometry. By the 20th century it became clear for some mathematicians that methods of algebraic geometry are ideal tools to study these equations. Four theorems in Diophantine geometry which are of fundamental importance include: * Mordell–Weil Theorem * Roth's Theorem * Siegel's Theorem * Faltings's Theorem Background Serge Lang published a book ''Diophantine Geometry'' in the area in 1962, and by this book he coined the term "Diophantine Geometry". The traditional arrangement of material on Diophantine equations was by degree and number of variables, as in Mordell's ''Diophantine Equations'' (1969). Mordell's book starts with a remark on homogeneous equations ''f'' = 0 over the rational field, attributed to C. F. Gauss, that non-zero solutions in integers (even primitive lattice points) exist if non-zero rational solutions do, and notes a caveat of L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Class Field Theory
In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to the ground field. Hilbert is credited as one of pioneers of the notion of a class field. However, this notion was already familiar to Kronecker and it was actually Weber who coined the term before Hilbert's fundamental papers came out. The relevant ideas were developed in the period of several decades, giving rise to a set of conjectures by Hilbert that were subsequently proved by Takagi and Artin (with the help of Chebotarev's theorem). One of the major results is: given a number field ''F'', and writing ''K'' for the maximal abelian unramified extension of ''F'', the Galois group of ''K'' over ''F'' is canonically isomorphic to the ideal class group of ''F''. This statement was generalized to the so called Artin reciprocity law; in the idelic language, writing ''CF' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasi-algebraically Closed Field
In mathematics, a field ''F'' is called quasi-algebraically closed (or C1) if every non-constant homogeneous polynomial ''P'' over ''F'' has a non-trivial zero provided the number of its variables is more than its degree. The idea of quasi-algebraically closed fields was investigated by C. C. Tsen, a student of Emmy Noether, in a 1936 paper ; and later by Serge Lang in his 1951 Princeton University dissertation and in his 1952 paper . The idea itself is attributed to Lang's advisor Emil Artin. Formally, if ''P'' is a non-constant homogeneous polynomial in variables :''X''1, ..., ''X''''N'', and of degree ''d'' satisfying :''d'' < ''N'' then it has a non-trivial zero over ''F''; that is, for some ''x''''i'' in ''F'', not all 0, we have :''P''(''x''''1'', ..., ''x''''N'') = 0. In geometric language, the defined b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doctor Of Philosophy
A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common 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 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'' (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 universities or work in academic, edu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beverly Hills High School
Beverly Hills High School (usually abbreviated as Beverly or as BHHS) is the only major public high school in Beverly Hills, California. The other public high school in Beverly Hills, Moreno High School, is a small alternative school located on Beverly's campus. Beverly Hills High School is part of the Beverly Hills Unified School District and located on on the west side of Beverly Hills, at the border of the Century City area of Los Angeles. The land was previously part of the Beverly Hills Speedway board track, which was torn down in 1924. Beverly, which serves all of Beverly Hills, was founded in 1927. The original buildings were designed by Robert D. Farquhar in the French Normandy style. The school previously received income from its on-campus oil tower. History Beverly Hills High School was originally in the Los Angeles City High School District. On March 23, 1936, the Beverly Hills Elementary School District left the Los Angeles City High School District and formed th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
California
California is a state in the Western United States, located along the Pacific Coast. With nearly 39.2million residents across a total area of approximately , it is the most populous U.S. state and the 3rd largest by area. It is also the most populated subnational entity in North America and the 34th most populous in the world. The Greater Los Angeles area and the San Francisco Bay Area are the nation's second and fifth most populous urban regions respectively, with the former having more than 18.7million residents and the latter having over 9.6million. Sacramento is the state's capital, while Los Angeles is the most populous city in the state and the second most populous city in the country. San Francisco is the second most densely populated major city in the country. Los Angeles County is the country's most populous, while San Bernardino County is the largest county by area in the country. California borders Oregon to the north, Nevada and Arizona to the east, t ... [...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 visualization Mathematical phenomena can be understood and explored via visualization. Classically this consisted of two-dimensional drawings or building three-dimensional models (particularly plaster models in the 19th and early 20th century), while today it ...s. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paris
Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the List of cities proper by population density, 30th most densely populated city in the world in 2020. Since the 17th century, Paris has been one of the world's major centres of finance, diplomacy, commerce, Fashion capital, fashion, gastronomy, and science. For its leading role in the arts and sciences, as well as its very early system of street lighting, in the 19th century it became known as "the City of Light". Like London, prior to the Second World War, it was also sometimes called Caput Mundi#Paris, the capital of the world. The City of Paris is the centre of the Île-de-France Regions of France, region, or Paris Region, with an estimated population of 12,262,544 in 2019, or about 19% of the population of France, making the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Saint-Germain-en-Laye
Saint-Germain-en-Laye () is a commune in the Yvelines department in the Île-de-France in north-central France. It is located in the western suburbs of Paris, from the centre of Paris. Inhabitants are called ''Saint-Germanois'' or ''Saint-Germinois''. With its elegant tree-lined streets it is one of the more affluent suburbs of Paris, combining both high-end leisure spots and exclusive residential neighborhoods (see the Golden Triangle of the Yvelines). Saint-Germain-en-Laye is a sub-prefecture of the department. Because it includes the National Forest of Saint-Germain-en-Laye, it covers approximately , making it the largest commune in the Yvelines. It occupies a large loop of the Seine. Saint-Germain-en-Laye lies at one of the western termini of Line A of the RER. History Saint-Germain-en-Laye was founded in 1020 when King Robert the Pious (ruled 996–1031) founded a convent on the site of the present Church of Saint-Germain. In 1688, James II of England exiled h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AIDS
Human immunodeficiency virus infection and acquired immunodeficiency syndrome (HIV/AIDS) is a spectrum of conditions caused by infection with the human immunodeficiency virus (HIV), a retrovirus. Following initial infection an individual may not notice any symptoms, or may experience a brief period of influenza-like illness. Typically, this is followed by a prolonged incubation period with no symptoms. If the infection progresses, it interferes more with the immune system, increasing the risk of developing common infections such as tuberculosis, as well as other opportunistic infections, and tumors which are rare in people who have normal immune function. These late symptoms of infection are referred to as acquired immunodeficiency syndrome (AIDS). This stage is often also associated with Cachexia, unintended weight loss. HIV is #Transmission, spread primarily by unprotected sex (including anal sex, anal and vaginal sex), contaminated blood transfusions, hypodermic needles, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
