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Mathbb
Blackboard bold is a style of writing Emphasis (typography), bold symbols on a blackboard by doubling certain strokes, commonly used in mathematical lectures, and the derived style of typeface used in printed mathematical texts. The style is most commonly used to represent the Set (mathematics)#Special sets of numbers in mathematics, number sets \N (natural numbers), \Z (integers), \Q (rational numbers), \R (real numbers), and \C (complex numbers). To imitate a bold typeface on a typewriter, a character can be typed over itself (called ''double-striking''); symbols thus produced are called double-struck, and this name is sometimes adopted for blackboard bold symbols, for instance in Unicode glyph names. In typography, a typeface with characters that are not solid is called ''inline'', ''handtooled'', or ''open face''. History Traditionally, various symbols were indicated by boldface in print but on blackboards and in manuscript (publishing), manuscripts "by wavy underscoring, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Number
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form a + bi, where and are real numbers. Because no real number satisfies the above equation, was called an imaginary number by René Descartes. For the complex number is called the , and is called the . The set of complex numbers is denoted by either of the symbols \mathbb C or . Despite the historical nomenclature, "imaginary" complex numbers have a mathematical existence as firm as that of the real numbers, and they are fundamental tools in the scientific description of the natural world. Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with real or complex coefficie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Number
In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion. The real numbers are fundamental in calculus (and in many other branches of mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives. The set of real numbers, sometimes called "the reals", is traditionally denoted by a bold , often using blackboard bold, . The adjective ''real'', used in the 17th century by René Descartes, distinguishes real numbers from imaginary numbers such as the square roots of . The real numbers include the rational numbers, such as the integer and the fraction . The rest of the real numbers are called irrational numbers. Some irrational numbers (as well as all the rationals) a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative integers. The set (mathematics), set of all integers is often denoted by the boldface or blackboard bold The set of natural numbers \mathbb is a subset of \mathbb, which in turn is a subset of the set of all rational numbers \mathbb, itself a subset of the real numbers \mathbb. Like the set of natural numbers, the set of integers \mathbb is Countable set, countably infinite. An integer may be regarded as a real number that can be written without a fraction, fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , 5/4, and Square root of 2, are not. The integers form the smallest Group (mathematics), group and the smallest ring (mathematics), ring containing the natural numbers. In algebraic number theory, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive integers Some authors acknowledge both definitions whenever convenient. Sometimes, the whole numbers are the natural numbers as well as zero. In other cases, the ''whole numbers'' refer to all of the integers, including negative integers. The counting numbers are another term for the natural numbers, particularly in primary education, and are ambiguous as well although typically start at 1. The natural numbers are used for counting things, like "there are ''six'' coins on the table", in which case they are called ''cardinal numbers''. They are also used to put things in order, like "this is the ''third'' largest city in the country", which are called ''ordinal numbers''. Natural numbers are also used as labels, like Number (sports), jersey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blackboard Bold On A Blackboard
A blackboard or a chalkboard is a reusable writing surface on which text or drawings are made with sticks of calcium sulphate or calcium carbonate, better known as chalk. Blackboards were originally made of smooth, thin sheets of black or dark grey slate stone. Design A blackboard can simply be a board painted with a dark matte (surface), matte paint (usually black, occasionally dark green). Matte black plastic sign material (known as closed-cell PVC foamboard) is also used to create custom chalkboard art. Blackboards on an A-frame are used by restaurants and bars to advertise daily specials. Adhesive chalkboard surface is also available in stores as rolls of textured black plastic shelf covering, which is applied to the desired wall, door or other surface. A more modern variation consists of a coiled sheet of plastic drawn across two parallel rollers, which can be scrolled to create additional writing space while saving what has been written. The highest grade blackboards ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Gunning (mathematician)
Robert Clifford Gunning (born 27 November 1931) is an American mathematician. He is a professor of mathematics at Princeton University, specializing in complex analysis, who introduced indigenous bundles. Education and career Gunning was born in Longmont, Colorado, and attended to high school in his hometown. In 1947 he was admitted into the University of Colorado, graduating with a bachelor's degree in 1952. For his graduate studies he went to Princeton University, where he earned his Ph.D. in 1955 under Salomon Bochner with thesis ''A classification of factors of automorphy''. He then taught at the University of Chicago and in 1956 as Higgins-Lecturer at Princeton University. At Princeton, Gunning became in 1957 assistant professor, in 1962 associate professor, and in 1966 professor. He was a visiting professor in São Paulo in 1958, Cambridge in 1959/60, Munich in 1967, Oxford in 1968, Boulder in 1970, and Los Angeles in 1972. Gunning is known as the author of important boo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hugo Rossi
Hugo E. Rossi (born 1935) is an American mathematician working in complex analysis. Rossi graduated from the City College of New York with bachelor's degree in 1956, and graduated from Massachusetts Institute of Technology with the master's degree in 1957, and received a Ph.D. under the supervision of Isadore Singer in 1960 (''Maximality of algebras of holomorphic functions''). In 1960 he became an assistant professor at the University of California, Berkeley, and in the same year at Princeton University. In 1963 he became an associate professor and a professor at Brandeis University in 1966. After 11 years at Brandeis and two years as the department chair, he moved to the University of Utah in 1975, and he served as dean of the College of Science from 1987 to 1993. In 1989 Rossi went on temporary leave from his post as dean to serve as director of the National Cold Fusion Institute. Amid increasing concerns about the lack of conclusive results regarding cold fusion, Rossi resign ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lynn Harold Loomis
__NOTOC__ Lynn Harold Loomis (April 25, 1915 – June 9, 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 (January 20, 1936 – August 23, 2024) was an American mathematician known for his work in geometry, particularly symplectic geometry and Lie theory. He also wrote some well-known textbooks. Education and career Ste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shlomo Sternberg
Shlomo Zvi Sternberg (January 20, 1936 – August 23, 2024) was an American mathematician known for his work in geometry, particularly symplectic geometry and Lie theory. He also wrote some well-known textbooks. 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 was Emeritus Professor at the Harvard Mathematics Department. Sternberg was awarded a Guggenheim fellowship in 1974 and an honorary doctorate by the University of Mannheim in 1991. He delivered the AMS Colloquium Lecture in 1990 and the Hebrew University's Alb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wiley (publisher)
John Wiley & Sons, Inc., commonly known as Wiley (), is an American multinational publishing company that focuses on academic publishing and instructional materials. The company was founded in 1807 and produces books, journals, and encyclopedias, in print and electronically, as well as online products and services, training materials, and educational materials for undergraduate, graduate, and continuing education students. History The company was established in 1807 when Charles Wiley opened a print shop in Manhattan. The company was the publisher of 19th century American literary figures like James Fenimore Cooper, Washington Irving, Herman Melville, and Edgar Allan Poe, as well as of legal, religious, and other non-fiction titles. The firm took its current name in 1865. Wiley later shifted its focus to scientific, technical, and engineering subject areas, abandoning its literary interests. Wiley's son John (born in Flatbush, New York, October 4, 1808; died in East ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Donald Knuth
Donald Ervin Knuth ( ; born January 10, 1938) is an American computer scientist and mathematician. He is a professor emeritus at Stanford University. He is the 1974 recipient of the ACM Turing Award, informally considered the Nobel Prize of computer science. Knuth has been called the "father of the analysis of algorithms". Knuth is the author of the multi-volume work '' The Art of Computer Programming''. He contributed to the development of the rigorous analysis of the computational complexity of algorithms and systematized formal mathematical techniques for it. In the process, he also popularized the asymptotic notation. In addition to fundamental contributions in several branches of theoretical computer science, Knuth is the creator of the TeX computer typesetting system, the related METAFONT font definition language and rendering system, and the Computer Modern family of typefaces. As a writer and scholar, Knuth created the WEB and CWEB computer programming systems des ... [...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] |
