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Counterexamples In Probability And Statistics
''Counterexamples in Probability and Statistics'' is a mathematics book by Joseph P. Romano and Andrew F. Siegel. It began as Romano's senior thesis at Princeton University under Siegel's supervision, and was intended for use as a supplemental work to augment standard textbooks on statistics and probability theory. Reception R. D. Lee gave the book a strong recommendation despite certain reservations, particularly that the organization of the book was intimidating to a large fraction of its potential audience: "There are plenty of good teachers of A-level statistics who know little or nothing about σ-fields or Borel subsets, the subjects of the first 3 or 4 pages." Reviewing new books for ''Mathematics Magazine,'' Paul J. Campbell called Romano and Siegel's work "long overdue" and quipped, "it's too bad we can't count on more senior professionals to compile such useful handbooks." Eric R. Ziegel's review in ''Technometrics'' was unenthusiastic, saying that the book was "only for ... [...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] |
A-level
The A-level (Advanced Level) is a subject-based qualification conferred as part of the General Certificate of Education, as well as a school leaving qualification offered by the educational bodies in the United Kingdom and the educational authorities of British Crown dependencies to students completing secondary or pre-university education. They were introduced in England and Wales in 1951 to replace the Higher School Certificate. The A-level permits students to have potential access to a chosen university they applied to with UCAS points. They could be accepted into it should they meet the requirements of the university. A number of Commonwealth countries have developed qualifications with the same name as and a similar format to the British A-levels. Obtaining an A-level, or equivalent qualifications, is generally required across the board for university entrance, with universities granting offers based on grades achieved. Particularly in Singapore, its A-level examin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
σ-algebra
In mathematical analysis and in probability theory, a σ-algebra ("sigma algebra") is part of the formalism for defining sets that can be measured. In calculus and analysis, for example, σ-algebras are used to define the concept of sets with area or volume. In probability theory, they are used to define events with a well-defined probability. In this way, σ-algebras help to formalize the notion of ''size''. In formal terms, a σ-algebra (also σ-field, where the σ comes from the German "Summe", meaning "sum") on a set ''X'' is a nonempty collection Σ of subsets of ''X'' closed under complement, countable unions, and countable intersections. The ordered pair (X, \Sigma) is called a measurable space. The set ''X'' is understood to be an ambient space (such as the 2D plane or the set of outcomes when rolling a six-sided die ), and the collection Σ is a choice of subsets declared to have a well-defined size. The closure requirements for σ-algebras are designed to cap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Borel Subset
In mathematics, a Borel set is any subset of a topological space that can be formed from its open sets (or, equivalently, from closed sets) through the operations of countable union, countable intersection, and relative complement. Borel sets are named after Émile Borel. For a topological space ''X'', the collection of all Borel sets on ''X'' forms a σ-algebra, known as the Borel algebra or Borel σ-algebra. The Borel algebra on ''X'' is the smallest σ-algebra containing all open sets (or, equivalently, all closed sets). Borel sets are important in measure theory, since any measure defined on the open sets of a space, or on the closed sets of a space, must also be defined on all Borel sets of that space. Any measure defined on the Borel sets is called a Borel measure. Borel sets and the associated Borel hierarchy also play a fundamental role in descriptive set theory. In some contexts, Borel sets are defined to be generated by the compact sets of the topological ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Mathematical Gazette
''The Mathematical Gazette'' is a triannual peer-reviewed academic journal published by Cambridge University Press on behalf of the Mathematical Association. It covers mathematics education with a focus on the 15–20 years age range. The journal was established in 1894 by Edward Mann Langley as the successor to the ''Reports of the Association for the Improvement of Geometrical Teaching''. William John Greenstreet was its editor-in-chief for more than thirty years (1897–1930). Since 2000, the editor is Gerry Leversha. Editors-in-chief The following persons are or have been editor-in-chief: Abstracting and indexing The journal is abstracted and indexed in EBSCO databases, Emerging Sources Citation Index, Scopus Scopus is a scientific abstract and citation database, launched by the academic publisher Elsevier as a competitor to older Web of Science in 2004. The ensuing competition between the two databases has been characterized as "intense" and is c ..., and zbMA ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Magazine
''Mathematics Magazine'' is a refereed bimonthly publication of the Mathematical Association of America. Its intended audience is teachers of collegiate mathematics, especially at the junior/senior level, and their students. It is explicitly a journal of mathematics rather than pedagogy. Rather than articles in the terse "theorem-proof" style of research journals, it seeks articles which provide a context for the mathematics they deliver, with examples, applications, illustrations, and historical background. Paid circulation in 2008 was 9,500 and total circulation was 10,000. ''Mathematics Magazine'' is a continuation of ''Mathematics News Letter'' (1926–1934) and ''National Mathematics Magazine'' (1934–1945). Doris Schattschneider became the first female editor of ''Mathematics Magazine'' in 1981. .. The MAA gives the Carl B. Allendoerfer Awards annually "for articles of expository excellence" published in ''Mathematics Magazine''. See also *''American Mathematical Mon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Technometrics
''Technometrics'' is a journal of statistics for the physical, chemical, and engineering sciences, published quarterly since 1959 by the American Society for Quality The American Society for Quality (ASQ), formerly the American Society for Quality Control (ASQC), is a society of quality professionals, with more than 30,000 members, in more than 140 countries. History ASQC was established on 16 February ... and the American Statistical Association. Statement of purpose The journal describes itself this way: "The purpose of ''Technometrics'' is to contribute to the development and use of statistical methods in physical, chemical, and engineering sciences as well as information sciences and technology. This vision includes developments on the interface of statistics and computer science such as data mining, machine learning, large databases, and so on. The journal places a premium on clear communication among statisticians and practitioners of these sciences and an emph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The American Statistical Association
The ''Journal of the American Statistical Association'' is a quarterly peer-reviewed scientific journal published by Taylor & Francis on behalf of the American Statistical Association. It covers work primarily focused on the application of statistics, statistical theory and methods in economic, social, physical, engineering, and health sciences. The journal also includes reviews of books which are relevant to the field. The journal was established in 1888 as the ''Publications of the American Statistical Association''. It was renamed ''Quarterly Publications of the American Statistical Association'' in 1912, obtaining its current title in 1922. Reception According to the ''Journal Citation Reports ''Journal Citation Reports'' (''JCR'') is an annual publication by Clarivate. It has been integrated with the Web of Science and is accessed from the Web of Science Core Collection. It provides information about academic journals in the natur ...'', the journal has a 2023 impac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Counterexamples In Probability
''Counterexamples in Probability'' is a mathematics book by Jordan M. Stoyanov. Intended to serve as a supplemental text for classes on probability theory and related topics, it covers cases where a mathematical proposition might seem to be true but actually turns out to be false. First published in 1987, the book received a second edition in 1997 and a third in 2013. Reception Robert W. Hayden, reviewing the book for the Mathematical Association of America, found it unsuitable for reading cover-to-cover, while recommending it as a reference for "graduate students and probabilists...the small audience whose needs match the title and level." Similarly, Geoffrey Grimmett called the book an "excellent browse" that, despite being a "serious work of scholarship" would not be suitable as a course textbook. R. W. Hammett wrote that it "should become a classic supplement" for those students who wish to go above and beyond their ordinary course requirements, and that "it should also becom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1986 Non-fiction Books
The year 1986 was designated as the International Year of Peace by the United Nations. Events January * January 1 ** Aruba gains increased autonomy from the Netherlands by separating from the Netherlands Antilles. ** Spain and Portugal enter the European Community, which becomes the European Union in 1993. * January 11 – The Sir Leo Hielscher Bridges, Gateway Bridge in Brisbane, Australia, at this time the world's longest prestressed concrete free-cantilever bridge, is opened. * January 13–January 24, 24 – South Yemen Civil War. * January 20 – The United Kingdom and France announce plans to construct the Channel Tunnel. * January 24 – The Voyager 2 space probe makes its first encounter with Uranus. * January 25 – Yoweri Museveni's National Resistance Army Rebel group takes over Uganda after leading a Ugandan Bush War, five-year guerrilla war in which up to half a million people are believed to have been killed. They will later use January 26 as the official date ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Books About Mathematical Counterexamples
A book is a structured presentation of recorded information, primarily verbal and graphical, through a medium. Originally physical, electronic books and audiobooks are now existent. Physical books are objects that contain printed material, mostly of writing and images. Modern books are typically composed of many pages bound together and protected by a cover, what is known as the ''codex'' format; older formats include the scroll and the tablet. As a conceptual object, a ''book'' often refers to a written work of substantial length by one or more authors, which may also be distributed digitally as an electronic book (ebook). These kinds of works can be broadly classified into fiction (containing invented content, often narratives) and non-fiction (containing content intended as factual truth). But a physical book may not contain a written work: for example, it may contain ''only'' drawings, engravings, photographs, sheet music, puzzles, or removable content like paper dolls. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Books
Probability is a branch of mathematics and statistics concerning Event (probability theory), 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 Probab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
