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Sequences (book)
''Sequences'' is a mathematical monograph on integer sequences. It was written by Heini Halberstam and Klaus Roth, published in 1966 by the Clarendon Press, and republished in 1983 with minor corrections by Springer-Verlag. Although planned to be part of a two-volume set, the second volume was never published. Topics The book has five chapters, each largely self-contained and loosely organized around different techniques used to solve problems in this area, with an appendix on the background material in number theory needed for reading the book. Rather than being concerned with specific sequences such as the prime numbers or square numbers, its topic is the mathematical theory of sequences in general. The first chapter considers the natural density of sequences, and related concepts such as the Schnirelmann density. It proves theorems on the density of sumsets of sequences, including Mann's theorem that the Schnirelmann density of a sumset is at least the sum of the Schnirelmann d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monograph
A monograph is a specialist work of writing (in contrast to reference works) or exhibition on a single subject or an aspect of a subject, often by a single author or artist, and usually on a scholarly subject. In library cataloging, ''monograph'' has a broader meaning—that of a nonserial publication complete in one volume (book) or a definite number of volumes. Thus it differs from a serial or periodical publication such as a magazine, academic journal, or newspaper. In this context only, books such as novels are considered monographs.__FORCETOC__ Academia The English term "monograph" is derived from modern Latin "monographia", which has its root in Greek. In the English word, "mono-" means "single" and "-graph" means "something written". Unlike a textbook, which surveys the state of knowledge in a field, the main purpose of a monograph is to present primary research and original scholarship ascertaining reliable credibility to the required recipient. This research is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erdős–Tetali Theorem
In additive number theory, an area of mathematics, the Erdős–Tetali theorem is an existence theorem concerning economical additive bases of every order. More specifically, it states that for every fixed integer h \geq 2, there exists a subset of the natural numbers \mathcal \subseteq \mathbb satisfying r_(n) \asymp \log n, where r_(n) denotes the number of ways that a natural number ''n'' can be expressed as the sum of ''h'' elements of ''B''. The theorem is named after Paul Erdős and Prasad V. Tetali, who published it in 1990. Motivation The original motivation for this result is attributed to a problem posed by S. Sidon in 1932 on ''economical bases''. An additive basis \mathcal\subseteq\mathbb is called ''economical'' (or sometimes ''thin'') when it is an additive basis of order ''h'' and :r_(n) \ll_ n^\varepsilon for every \varepsilon > 0. In other words, these are additive bases that use as few numbers as possible to represent a given ''n'', and yet represent every na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bulletin Of The American Mathematical Society
The ''Bulletin of the American Mathematical Society'' is a quarterly mathematical journal published by the American Mathematical Society. Scope It publishes surveys on contemporary research topics, written at a level accessible to non-experts. It also publishes, by invitation only, book reviews and short ''Mathematical Perspectives'' articles. History It began as the ''Bulletin of the New York Mathematical Society'' and underwent a name change when the society became national. The Bulletin's function has changed over the years; its original function was to serve as a research journal for its members. Indexing The Bulletin is indexed in Mathematical Reviews, Science Citation Index, ISI Alerting Services, CompuMath Citation Index, and Current Contents ''Current Contents'' is a rapid alerting service database from Clarivate Analytics, formerly the Institute for Scientific Information and Thomson Reuters. It is published online and in several different printed subject sectio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Mathematical Gazette
''The Mathematical Gazette'' is an academic journal of mathematics education, published three times yearly, that publishes "articles about the teaching and learning of mathematics with a focus on the 15–20 age range and expositions of attractive areas of mathematics." It was established in 1894 by Edward Mann Langley as the successor to the Reports of the Association for the Improvement of Geometrical Teaching. Its publisher is the Mathematical Association. William John Greenstreet was its editor for more than thirty years (1897–1930). Since 2000, the editor is Gerry Leversha. Editors * Edward Mann Langley: 1894-1896 * Francis Sowerby Macaulay: 1896-1897 * William John Greenstreet: 1897-1930 * Alan Broadbent: 1930-1955 * Reuben Goodstein: 1956-1962 * Edwin A. Maxwell Edwin Arthur Maxwell (12 January 1907 – 27 August 1987) was a Scottish mathematician, who worked at Cambridge University for most of his career. Although his contributions to original research were li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The London Mathematical Society
The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical Society and the Operational Research Society (ORS). History The Society was established on 16 January 1865, the first president being Augustus De Morgan. The earliest meetings were held in University College, but the Society soon moved into Burlington House, Piccadilly. The initial activities of the Society included talks and publication of a journal. The LMS was used as a model for the establishment of the American Mathematical Society in 1888. Mary Cartwright was the first woman to be President of the LMS (in 1961–62). The Society was granted a royal charter in 1965, a century after its foundation. In 1998 the Society moved from rooms in Burlington House into De Morgan House (named after the society's first president), at 57 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ZbMATH
zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH. Editors are the European Mathematical Society, FIZ Karlsruhe, and the Heidelberg Academy of Sciences. zbMATH is distributed by Springer Science+Business Media. It uses the Mathematics Subject Classification codes for organising reviews by topic. History Mathematicians Richard Courant, Otto Neugebauer, and Harald Bohr, together with the publisher Ferdinand Springer, took the initiative for a new mathematical reviewing journal. Harald Bohr worked in Copenhagen. Courant and Neugebauer were professors at the University of Göttingen. At that time, Göttingen was considered one of the central places for mathematical research, having appointed mathematicians like David Hilbert, Hermann Minkowski, Carl Runge, and Felix Klein, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Science (journal)
''Science'', also widely referred to as ''Science Magazine'', is the peer-reviewed academic journal of the American Association for the Advancement of Science (AAAS) and one of the world's top academic journals. It was first published in 1880, is currently circulated weekly and has a subscriber base of around 130,000. Because institutional subscriptions and online access serve a larger audience, its estimated readership is over 400,000 people. ''Science'' is based in Washington, D.C., United States, with a second office in Cambridge, UK. Contents The major focus of the journal is publishing important original scientific research and research reviews, but ''Science'' also publishes science-related news, opinions on science policy and other matters of interest to scientists and others who are concerned with the wide implications of science and technology. Unlike most scientific journals, which focus on a specific field, ''Science'' and its rival ''Nature'' cover the full r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Reviews
''Mathematical Reviews'' is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science. The AMS also publishes an associated online bibliographic database called MathSciNet which contains an electronic version of ''Mathematical Reviews'' and additionally contains citation information for over 3.5 million items as of 2018. Reviews Mathematical Reviews was founded by Otto E. Neugebauer in 1940 as an alternative to the German journal ''Zentralblatt für Mathematik'', which Neugebauer had also founded a decade earlier, but which under the Nazis had begun censoring reviews by and of Jewish mathematicians. The goal of the new journal was to give reviews of every mathematical research publication. As of November 2007, the ''Mathematical Reviews'' database contained information on over 2.2 million articles. The authors of reviews are volunteer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harold Stark
Harold Mead Stark (born August 6, 1939 in Los Angeles, California) is an American mathematician, specializing in number theory. He is best known for his solution of the Gauss class number 1 problem, in effect correcting and completing the earlier work of Kurt Heegner, and for Stark's conjecture. More recently, he collaborated with Audrey Terras to study zeta functions in graph theory. He is currently on the faculty of the University of California, San Diego. Stark received his bachelor's degree from California Institute of Technology in 1961 and his PhD from the University of California, Berkeley in 1964. He was on the faculty at the University of Michigan from 1964 to 1968, at the Massachusetts Institute of Technology from 1968 to 1980, and at the University of California, San Diego from 1980 to the present. Stark was elected to the American Academy of Arts and Sciences in 1983 and to the United States National Academy of Sciences in 2007. In 2012, he became a fellow of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marvin Knopp
Marvin Isadore Knopp (January 4, 1933 – December 24, 2011) was an American mathematician who worked primarily in number theory. He made notable contributions to the theory of modular forms. Life and education Knopp was born on January 4, 1933, in Chicago, Illinois. He received his PhD under Paul T. Bateman from the University of Illinois in 1958 where he became friends with fellow student Gene Golub., Video of Knopp's Talk at Gene Golub Memorial (Talk #3), retrieved 2011-12-29. Over the course of his career, he advised twenty Ph.D. students. Knopp's Math Genealogy Entry, retrieved 2011-12-29. He is the father of pianist Seth Knopp, and of Yehudah, Abby, and Elana. Marvin Knopp Tribute Blog, retrieved 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Davenport–Erdős Theorem
In number theory, the Davenport–Erdős theorem states that, for sets of multiples of integers, several different notions of density are equivalent. Let A=a_1,a_2,\dots be a sequence of positive integers. Then the multiples of A are another set M(A) that can be defined as the set M(A)=\ of numbers formed by multiplying members of A by arbitrary positive integers. According to the Davenport–Erdős theorem, for a set M(A), the following notions of density are equivalent, in the sense that they all produce the same number as each other for the density of M(A): *The lower natural density, the inferior limit as n goes to infinity of the proportion of members of M(A) in the interval ,n/math>. *The logarithmic density or multiplicative density, the weighted proportion of members of M(A) in the interval ,n/math>, again in the limit, where the weight of an element a is 1/a. *The sequential density, defined as the limit (as i goes to infinity) of the densities of the sets M(\) of multi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abram Samoilovitch Besicovitch
Abram Samoilovitch Besicovitch (or Besikovitch) (russian: link=no, Абра́м Само́йлович Безико́вич; 23 January 1891 – 2 November 1970) was a Russian mathematician, who worked mainly in England. He was born in Berdyansk on the Sea of Azov (now in Ukraine) to a Karaite Jewish family. Life and career Abram Besicovitch studied under the supervision of Andrey Markov at the St. Petersburg University, graduating with a PhD in 1912. He then began research in probability theory. He converted to Eastern Orthodoxy, joining the Russian Orthodox Church, on marrying in 1916. He was appointed professor at the University of Perm in 1917, and was caught up in the Russian Civil War over the next two years. In 1920 he took a position at the Petrograd University. In 1924 he went to Copenhagen on a Rockefeller Fellowship, where he worked on almost periodic functions under Harald Bohr. A type of function space in that field now bears his name. After a visit to G.H. Har ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
