American Mathematical Monthly
The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Francis for the Mathematical Association of America; the American Mathematical Monthly is an expository journal intended for a wide audience of mathematicians, from undergraduate students to research professionals. Articles are chosen on the basis of their broad interest and reviewed and edited for quality of exposition as well as content. In this the American Mathematical Monthly fulfills a different role from that of typical mathematical research journals; the American Mathematical Monthly is the most read mathematics journal in the world according to records on JSTOR. Tables of contents with article abstracts from 1997-2010 are available online; the MAA gives the Lester R. Ford Awards annually to "authors of articles of expository excellence" published in the American Mathematical Monthly. 2017-: Susan Colley 2012-2016: Scott T. Chapman 2007-2011: Daniel J. Velleman 2002-2006: Bruce Palka 1997-2001: Roger A.
Horn 1992-1996: John H. Ewing 1987-1991: Herbert S. Wilf 1982-1986: Paul Richard Halmos 1978-1981: Ralph Philip Boas, Jr. 1977-1978: Alex Rosenberg and Ralph Philip Boas Jr. 1974-1976: Alex Rosenberg 1969-1973: Harley Flanders 1967-1968: Robert Abraham Rosenbaum 1962-1966: Frederick Arthur Ficken 1957-1961: Ralph Duncan James 1952-1956: Carl Barnett Allendoerfer 1947-1951: Carroll Vincent Newsom 1942-1946: Lester Randolph Ford 1937-1941: Elton James Moulton 1932-1936: Walter Buckingham Carver 1927-1931: William Henry Bussey 1923-1926: Walter Burton Ford 1922: Albert Arnold Bennett 1919-1921: Raymond Clare Archibald 1918: Robert Daniel Carmichael 1916-1917: Herbert Ellsworth Slaught 1914-1915: Board of editors: C. H. Ashton, R. P. Baker, W. C. Brenke, W. H. Bussey, W. DeW. Cairns, Florian Cajori, R. D. Carmichael, D. R. Curtiss, I. M. DeLong, B. F. Finkel, E. R. Hedrick, L. C. Karpinski, G. A. Miller, W. H. Roever, H. E. Slaught 1913: Herbert Ellsworth Slaught 1909-1912: Benjamin Franklin Finkel, Herbert Ellsworth Slaught, George Abram Miller 1907-1908: Benjamin Franklin Finkel, Herbert Ellsworth Slaught 1905-1906: Benjamin Franklin Finkel, Leonard Eugene Dickson, Oliver Edmunds Glenn 1904: Benjamin Franklin Finkel, Leonard Eugene Dickson, Saul Epsteen 1903: Benjamin Franklin Finkel, Leonard Eugene Dickson 1894-1902: Benjamin Franklin Finkel, John Marvin Colaw Mathematics Magazine Notices of the American Mathematical Society, another "most read mathematics journal in the world" American Mathematical Monthly homepage Archive of tables of contents with article summaries Mathematical Association of America American Mathematical Monthly on JSTOR The American mathematical monthly, hathitrust
Friedrich Engel (mathematician)
Friedrich Engel was a German mathematician. Engel was born in Saxony, as the son of a Lutheran pastor, he attended the Universities of both Leipzig and Berlin, before receiving his doctorate from Leipzig in 1883. Engel studied under Felix Klein at Leipzig, collaborated with Sophus Lie for much of his life, he worked at Leipzig and Giessen. He died in Giessen. Engel was the co-author, with Sophus Lie, of the three volume work Theorie der Transformationsgruppen. Engel was the editor of the collected works of Sophus Lie with six volumes published between 1922 and 1937, he was the editor of the collected works of Hermann Grassmann. Engel translated the works of Nikolai Lobachevski from Russian into German, thus making these works more accessible. With Paul Stäckel he wrote a history of non-Euclidean geometry. With his former student Karl Faber, he wrote a book on the theory of partial differential equations of the first order using methods of Lie group theory. In 1910 Engel was the president of the Deutsche Mathematiker-Vereinigung.
Engel group Engel expansion Engel's theorem Works by or about Friedrich Engel at Internet Archive O'Connor, John J.. Friedrich Engel at the Mathematics Genealogy Project Literature by and about Friedrich Engel in the German National Library catalogue
Jeffrey Outlaw Shallit is a computer scientist, number theorist, a noted critic of intelligent design. He is married to Anna Lubiw a computer scientist. Shallit was born in Philadelphia, Pennsylvania in 1957, his father was Joseph Shallit, a journalist and author, a son of Jewish immigrants from Vitebsk, Russia. His mother was a writer, he has Jonathan Shallit, a music professor. He earned a Bachelor's degree in mathematics from Princeton University in June 1979, he received a Ph. D. in mathematics, from the University of California, Berkeley in June 1983. His doctoral thesis was entitled Metric Theory of Pierce Expansions and his advisor was Manuel Blum. Since 1996, Shallit has held the position of Vice-President of Electronic Frontier Canada. In 1997, he gained attention for the publication on the Internet of Holocaust Revised: Lies of Our Times, a reprint of an article he had written for a Waterloo student publication in 1993, which detailed the backgrounds and past statements of various persons whom he accused of being Holocaust deniers, notably David Irving, Fred A. Leuchter, Eustace Mullins.
This triggered a public exchange of letters between Irving. Shallit has been a critic of the work of William Dembski promoting intelligent design, he has coauthored a paper with Wesley Elsberry demonstrating problems with Dembski's mathematical work, would have appeared as a witness opposing Dembski in the Kitzmiller v. Dover trial had Dembski not dropped out. Shallit is a Professor in the School of Computer Science at the University of Waterloo and the editor-in-chief of the Journal of Integer Sequences, his primary academic interests are combinatorics on words, formal languages, automata theory, algorithmic number theory. He has been recognized by the Association for Computing Machinery as a Distinguished Scientist, his publications include the books Algorithmic Number Theory, a noted text on algorithms, Automatic Sequences: Theory, Generalizations, A Second Course in Formal Languages and Automata Theory. Home page of Jeffrey O. Shallit Shallit's blog, Recursivity Electronic Frontier Canada Holocaust Revised: Lies of our Times
Journal of Number Theory
The Journal of Number Theory is a bimonthly peer-reviewed scientific journal covering all aspects of number theory. The journal was established in 1969 by R. P. Bambah, P. Roquette, A. Ross, A. Woods, H. Zassenhaus, it is published monthly by Elsevier and the editor-in-chief is Dorian Goldfeld. According to the Journal Citation Reports, the journal has a 2017 impact factor of 0.774. Official website
On-Line Encyclopedia of Integer Sequences
The On-Line Encyclopedia of Integer Sequences cited as Sloane's, is an online database of integer sequences. It was maintained by Neil Sloane while a researcher at AT&T Labs. Foreseeing his retirement from AT&T Labs in 2012 and the need for an independent foundation, Sloane agreed to transfer the intellectual property and hosting of the OEIS to the OEIS Foundation in October 2009. Sloane is president of the OEIS Foundation. OEIS records information on integer sequences of interest to both professional mathematicians and amateurs, is cited; as of September 2018 it contains over 300,000 sequences. Each entry contains the leading terms of the sequence, mathematical motivations, literature links, more, including the option to generate a graph or play a musical representation of the sequence; the database is searchable by subsequence. Neil Sloane started collecting integer sequences as a graduate student in 1965 to support his work in combinatorics; the database was at first stored on punched cards.
He published selections from the database in book form twice: A Handbook of Integer Sequences, containing 2,372 sequences in lexicographic order and assigned numbers from 1 to 2372. The Encyclopedia of Integer Sequences with Simon Plouffe, containing 5,488 sequences and assigned M-numbers from M0000 to M5487; the Encyclopedia includes the references to the corresponding sequences in A Handbook of Integer Sequences as N-numbers from N0001 to N2372 The Encyclopedia includes the A-numbers that are used in the OEIS, whereas the Handbook did not. These books were well received and after the second publication, mathematicians supplied Sloane with a steady flow of new sequences; the collection became unmanageable in book form, when the database had reached 16,000 entries Sloane decided to go online—first as an e-mail service, soon after as a web site. As a spin-off from the database work, Sloane founded the Journal of Integer Sequences in 1998; the database continues to grow at a rate of some 10,000 entries a year.
Sloane has managed'his' sequences for 40 years, but starting in 2002, a board of associate editors and volunteers has helped maintain the database. In 2004, Sloane celebrated the addition of the 100,000th sequence to the database, A100000, which counts the marks on the Ishango bone. In 2006, the user interface was overhauled and more advanced search capabilities were added. In 2010 an OEIS wiki at OEIS.org was created to simplify the collaboration of the OEIS editors and contributors. The 200,000th sequence, A200000, was added to the database in November 2011. Besides integer sequences, the OEIS catalogs sequences of fractions, the digits of transcendental numbers, complex numbers and so on by transforming them into integer sequences. Sequences of rationals are represented by two sequences: the sequence of numerators and the sequence of denominators. For example, the fifth-order Farey sequence, 1 5, 1 4, 1 3, 2 5, 1 2, 3 5, 2 3, 3 4, 4 5, is catalogued as the numerator sequence 1, 1, 1, 2, 1, 3, 2, 3, 4 and the denominator sequence 5, 4, 3, 5, 2, 5, 3, 4, 5.
Important irrational numbers such as π = 3.1415926535897... are catalogued under representative integer sequences such as decimal expansions, binary expansions, or continued fraction expansions. The OEIS was limited to plain ASCII text until 2011, it still uses a linear form of conventional mathematical notation. Greek letters are represented by their full names, e.g. mu for μ, phi for φ. Every sequence is identified by the letter A followed by six digits always referred to with leading zeros, e.g. A000315 rather than A315. Individual terms of sequences are separated by commas. Digit groups are not separated by periods, or spaces. In comments, etc. A represents the nth term of the sequence. Zero is used to represent non-existent sequence elements. For example, A104157 enumerates the "smallest prime of n² consecutive primes to form an n×n magic square of least magic constant, or 0 if no such magic square exists." The value of a is 2. But there is no such 2×2 magic square, so a is 0; this special usage has a solid mathematical basis in certain counting functions.
For example, the totient valence function. There are 4 solutions for 4, but no solutions for 14, hence a of A014197 is 0—there are no solutions. −1 is used for this purpose instead, as in A094076. The OEIS ma
Janos Galambos is a mathematician affiliated with Temple University in Philadelphia, Pennsylvania, USA. Dr. Galambos works on probability theory, number theory and many other sub-specialties, has published hundreds of papers and many books. Galambos earned his Ph. D. in 1963 from Eötvös Loránd University, under the supervision of Alfréd Rényi. In 1993 he was elected external member of the Hungarian Academy of Sciences, in 2001 he became a corresponding member of the Spanish Royal Academy of Engineering; the Asymptotic Theory of Extreme Order Statistics, John Wiley, New York, 1978. Advanced Probability Theory, Marcel Dekker, New York, 1988. Bonferroni-type Inequalities with Applications, Springer-Verlag, New York, 1996. Janos Galambos in the Oberwolfach Photo Collection
Fibonacci was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages". The name he is called, "Fibonacci", was made up in 1838 by the Franco-Italian historian Guillaume Libri and is short for filius Bonacci, he is known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano. Fibonacci popularized the Hindu–Arabic numeral system in the Western World through his composition in 1202 of Liber Abaci, he introduced Europe to the sequence of Fibonacci numbers, which he used as an example in Liber Abaci. Fibonacci was born around 1170 to an Italian merchant and customs official. Guglielmo directed a trading post in Algeria. Fibonacci travelled with him as a young boy, it was in Bugia that he learned about the Hindu–Arabic numeral system. Fibonacci travelled around the Mediterranean coast, meeting with many merchants and learning about their systems of doing arithmetic, he soon realised the many advantages of the Hindu-Arabic system which, unlike the Roman numerals used at the time, allowed easy calculation using a place-value system.
In 1202, he completed the Liber Abaci. Fibonacci became a guest of Emperor Frederick II. In 1240, the Republic of Pisa honored Fibonacci by granting him a salary in a decree that recognized him for the services that he had given to the city as an advisor on matters of accounting and instruction to citizens; the date of Fibonacci's death is not known, but it has been estimated to be between 1240 and 1250, most in Pisa. In the Liber Abaci, Fibonacci introduced the so-called modus Indorum, today known as the Hindu–Arabic numeral system; the book advocated numeration with the digits place value. The book showed the practical use and value of the new Hindu-Arabic numeral system by applying the numerals to commercial bookkeeping, converting weights and measures, calculation of interest, money-changing, other applications; the book had a profound impact on European thought. No copies of the 1202 edition are known to exist; the 1228 edition, first section introduces the Hindu-Arabic numeral system and compares the system with other systems, such as Roman numerals, methods to convert the other numeral systems into Hindu-Arabic numerals.
Replacing the Roman numeral system, its ancient Egyptian multiplication method, using an abacus for calculations, with a Hindu-Arabic numeral system was an advance in making business calculations easier and faster, which led to the growth of banking and accounting in Europe. The second section explains the uses of Hindu-Arabic numerals in business, for example converting different currencies, calculating profit and interest, which were important to the growing banking industry; the book discusses irrational numbers and prime numbers. Liber Abaci posed and solved a problem involving the growth of a population of rabbits based on idealized assumptions; the solution, generation by generation, was a sequence of numbers known as Fibonacci numbers. Although Fibonacci's Liber Abaci contains the earliest known description of the sequence outside of India, the sequence had been described by Indian mathematicians as early as the sixth century. In the Fibonacci sequence, each number is the sum of the previous two numbers.
Fibonacci omitted the "0" included today and began the sequence with 1, 1, 2.... He carried the calculation up to the thirteenth place, the value 233, though another manuscript carries it to the next place, the value 377. Fibonacci did not speak about the golden ratio as the limit of the ratio of consecutive numbers in this sequence. In the 19th century, a statue of Fibonacci was raised in Pisa. Today it is located in the western gallery of the Camposanto, historical cemetery on the Piazza dei Miracoli. There are many mathematical concepts named after Fibonacci because of a connection to the Fibonacci numbers. Examples include the Brahmagupta–Fibonacci identity, the Fibonacci search technique, the Pisano period. Beyond mathematics, namesakes of Fibonacci include the asteroid 6765 Fibonacci and the art rock band The Fibonaccis. Liber Abaci, a book on calculations Practica Geometriae, a compendium of techniques in surveying, the measurement and partition of areas and volumes, other topics in practical geometry.
Flos, solutions to problems posed by Johannes of Palermo Liber quadratorum on Diophantine equations, dedicated to Emperor Frederick II. See in particular congruum and the Brahmagupta–Fibonacci identity. Di minor guisa Commentary on Book X of Euclid's Elements Fibonacci numbers in popular culture Republic of Pisa Adelard of Bath Footnotes Citations Devlin, Keith; the Man of Numbers: Fibonacci's Arithmetic Revolution. Walker Books. ISBN 978-0802779083. Goetzmann, William N. and Rouwenhorst, K. Geert, The Origins of Value: The Financial Innovations That Created Modern Capital Markets, ISBN 0-19-517571-9. Goetzmann, William N. Fibonacci and the Financial Revolution, Yale School of Management International Center for Finance Working Paper No. 03–28 Grimm, R. E. "The Autobiography of Leonardo Pisano", Fibonacci Quarterly, Vol. 11, No. 1, February 1973, pp. 99–104. Horadam, A. F. "Eight hundred years young," The Australian Mathematics Teacher 31 (1975