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J. L. Doob
Joseph Leo Doob (February 27, 1910 – June 7, 2004) was an American mathematician, specializing in Mathematical analysis, analysis and probability theory. The theory of Martingale (probability theory), martingales was developed by Doob. Early life and education Doob was born in Cincinnati, Ohio, February 27, 1910, the son of a Jewish couple, Leo Doob and Mollie Doerfler Doob. The family moved to New York City before he was three years old. The parents felt that he was underachieving in grade school and placed him in the Ethical Culture School, from which he graduated in 1926. He then went on to Harvard University, Harvard where he received a BA in 1930, an MA in 1931, and a PhD (''Boundary Values of Analytic Functions'', advisor Joseph L. Walsh) in 1932. After postdoctoral research at Columbia University, Columbia and Princeton University, Princeton, he joined the department of mathematics of the University of Illinois at Urbana-Champaign, University of Illinois in 1935 and ser ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cincinnati
Cincinnati ( ; colloquially nicknamed Cincy) is a city in Hamilton County, Ohio, United States, and its county seat. Settled in 1788, the city is located on the northern side of the confluence of the Licking River (Kentucky), Licking and Ohio River, Ohio rivers, the latter of which marks the state line with Kentucky. It is the List of cities in Ohio, third-most populous city in Ohio and List of united states cities by population, 66th-most populous in the U.S., with a population of 309,317 at the 2020 census. The city is the economic and cultural hub of the Cincinnati metropolitan area, Ohio's most populous metro area and the Metropolitan statistical area, nation's 30th-largest, with over 2.3 million residents. Throughout much of the 19th century, Cincinnati was among the Largest cities in the United States by population by decade, top 10 U.S. cities by population. The city developed as a port, river town for cargo shipping by steamboats, located at the crossroads of the Nor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th ed., (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', vol. 1, 3rd ed., (1968), Wiley, . This number is often expressed as a percentage (%), ranging from 0% to 100%. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These concepts have been given an axiomatic mathematical formaliza ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Measure Theory
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude (mathematics), magnitude, mass, and probability of events. These seemingly distinct concepts have many similarities and can often be treated together in a single mathematical context. Measures are foundational in probability theory, integral, integration theory, and can be generalized to assume signed measure, negative values, as with electrical charge. Far-reaching generalizations (such as spectral measures and projection-valued measures) of measure are widely used in quantum physics and physics in general. The intuition behind this concept dates back to Ancient Greece, when Archimedes tried to calculate the area of a circle. But it was not until the late 19th and early 20th centuries that measure theory became a branch of mathematics. The foundations of modern measure theory were laid in the works of Émile B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrey Kolmogorov
Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Soviet mathematician who played a central role in the creation of modern probability theory. He also contributed to the mathematics of topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and Analysis of algorithms, computational complexity. Biography Early life Andrey Kolmogorov was born in Tambov, about 500 kilometers southeast of Moscow, in 1903. His unmarried mother, Maria Yakovlevna Kolmogorova, died giving birth to him. Andrey was raised by two of his aunts in Tunoshna (near Yaroslavl) at the estate of his grandfather, a well-to-do Russian nobility, nobleman. Little is known about Andrey's father. He was supposedly named Nikolai Matveyevich Katayev and had been an Agronomy, agronomist. Katayev ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harold Hotelling
Harold Hotelling (; September 29, 1895 – December 26, 1973) was an American mathematical statistician and an influential economic theorist, known for Hotelling's law, Hotelling's lemma, and Hotelling's rule in economics, as well as Hotelling's T-squared distribution in statistics. He also developed and named the principal component analysis method widely used in finance, statistics and computer science. He was associate professor of mathematics at Stanford University from 1927 until 1931, a member of the faculty of Columbia University from 1931 until 1946, and a professor of Mathematical Statistics at the University of North Carolina at Chapel Hill from 1946 until his death. A street in Chapel Hill bears his name. In 1972, he received the North Carolina Award for contributions to science. Statistics Hotelling is known to statisticians because of Hotelling's T-squared distribution which is a generalization of the Student's t-distribution in multivariate setting, and i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Great Depression
The Great Depression was a severe global economic downturn from 1929 to 1939. The period was characterized by high rates of unemployment and poverty, drastic reductions in industrial production and international trade, and widespread bank and business failures around the world. The economic contagion began in 1929 in the United States, the largest economy in the world, with the devastating Wall Street stock market crash of October 1929 often considered the beginning of the Depression. Among the countries with the most unemployed were the U.S., the United Kingdom, and Weimar Republic, Germany. The Depression was preceded by a period of industrial growth and social development known as the "Roaring Twenties". Much of the profit generated by the boom was invested in speculation, such as on the stock market, contributing to growing Wealth inequality in the United States, wealth inequality. Banks were subject to laissez-faire, minimal regulation, resulting in loose lending and wides ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre Fatou
Pierre Joseph Louis Fatou (28 February 1878 – 9 August 1929) was a French mathematician and astronomer. He is known for major contributions to several branches of mathematical analysis, analysis. The Fatou lemma and the Fatou set are named after him. Biography Pierre Fatou's parents were Prosper Ernest Fatou (1832-1891) and Louise Eulalie Courbet (1844-1911), both of whom were in the military. Pierre's family would have liked for him to enter the military as well, but his health was not sufficiently good for him to pursue a military career. Fatou entered the École Normale Supérieure in Paris in 1898 to study mathematics and graduated in 1901 when he was appointed an intern (''stagiaire'') in the Paris Observatory. Fatou was promoted to assistant astronomer in 1904 and to astronomer (''astronome titulaire'') in 1928. He worked in this observatory until his death. Fatou was awarded the Henri Becquerel, Becquerel prize in 1918; he was a knight of the Legion of Honour (1923). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oswald Veblen
Oswald Veblen (June 24, 1880 – August 10, 1960) was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905; while this was long considered the first rigorous proof of the theorem, many now also consider Camille Jordan's original proof rigorous. Early life Veblen was born in Decorah, Iowa. His parents were Andrew Anderson Veblen (1848–1932), Professor of Physics at the University of Iowa, and Kirsti (Hougen) Veblen (1851–1908). Veblen's uncle was Thorstein Veblen, noted economist and sociologist. Oswald went to school in Iowa City. He did his undergraduate studies at the University of Iowa, where he received an AB in 1898, and Harvard University, where he was awarded a second BA in 1900. For his graduate studies, he went to study mathematics at the University of Chicago, where he obtained a PhD in 1903. His dissertation, ''A System of Axioms for Geometr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Institute For Advanced Study
The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Einstein, J. Robert Oppenheimer, Emmy Noether, Hermann Weyl, John von Neumann, Michael Walzer, Clifford Geertz and Kurt Gödel, many of whom had emigrated from Europe to the United States. It was founded in 1930 by American educator Abraham Flexner, together with philanthropists Louis Bamberger and Caroline Bamberger Fuld. Despite collaborative ties and neighboring geographic location, the institute, being independent, has "no formal links" with Princeton University. The institute does not charge tuition or fees. Flexner's guiding principle in founding the institute was the pursuit of knowledge for its own sake.Jogalekar. The faculty have no classes to teach. There are no degree programs or experimental facilities at the institute. Research ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton University
Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest institution of higher education in the United States and one of the nine colonial colleges chartered before the American Revolution. The institution moved to Newark, New Jersey, Newark in 1747 and then to its Mercer County, New Jersey, Mercer County campus in Princeton nine years later. It officially became a university in 1896 and was subsequently renamed Princeton University. The university is governed by the Trustees of Princeton University and has an endowment of $37.7 billion, the largest List of colleges and universities in the United States by endowment, endowment per student in the United States. Princeton provides undergraduate education, undergraduate and graduate education, graduate instruction in the hu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Columbia University
Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church (Manhattan), Trinity Church in Manhattan, it is the oldest institution of higher education in New York (state), New York and the fifth-First university in the United States, oldest in the United States. Columbia was established as a Colonial colleges, colonial college by royal charter under George II of Great Britain. It was renamed Columbia College (New York), Columbia College in 1784 following the American Revolution, and in 1787 was placed under Trustees of Columbia University in the City of New York, a private board of trustees headed by former students Alexander Hamilton and John Jay. In 1896, the campus was moved to its current location in Morningside Heights and renamed Columbia University. Columbia is organized into twenty schoo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ethical Culture School
The Ethical Culture Fieldston School (ECFS), also known more simply as Fieldston or Ethical Culture, is a private pre-K through twelfth grade coeducational school in New York City with two campuses, in Manhattan and in the Bronx. The school is a member of the Ivy Preparatory School League. The school serves approximately 1,700 students with 480 faculty and staff. The school consists of four divisions: Ethical Culture (pre-K through fifth grade that is located on the Upper West Side of Manhattan) and located in the Riverdale section of the Bronx are, Fieldston Lower that also serves pre-K through fifth grade, Fieldston Middle that serves sixth–eighth grades, and Fieldston Upper that serves ninth–twelfth grades. Tuition and fees for the school were $60,595 for the 2022–2023 school year and $63,020 for the 2023–2024 school year. Fieldston awards more than $15 million in tuition-based financial aid to 22% of the student body. History The school opened in 1878 as a fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
