Related Research Articles
Discrete mathematics is the study of mathematical structures that can be considered "discrete" rather than "continuous". Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers; more formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets. However, there is no exact definition of the term "discrete mathematics".
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members. The number of elements is called the length of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers to the elements at each position. The notion of a sequence can be generalized to an indexed family, defined as a function from an index set that may not be numbers to another set of elements.
In mathematics, a recurrence relation is an equation according to which the th term of a sequence of numbers is equal to some combination of the previous terms. Often, only previous terms of the sequence appear in the equation, for a parameter that is independent of ; this number is called the order of the relation. If the values of the first numbers in the sequence have been given, the rest of the sequence can be calculated by repeatedly applying the equation.
The On-Line Encyclopedia of Integer Sequences (OEIS) is an online database of integer sequences. It was created and maintained by Neil Sloane while researching at AT&T Labs. He transferred the intellectual property and hosting of the OEIS to the OEIS Foundation in 2009. Sloane is chairman of the OEIS Foundation.
David Stifler Johnson was an American computer scientist specializing in algorithms and optimization. He was the head of the Algorithms and Optimization Department of AT&T Labs Research from 1988 to 2013, and was a visiting professor at Columbia University from 2014 to 2016. He was awarded the 2010 Knuth Prize.
John Frank Adams was a British mathematician, one of the major contributors to homotopy theory.
In number theory, the Padovan sequence is the sequence of integers P(n) defined by the initial values
In mathematics, Somos' quadratic recurrence constant, named after Michael Somos, is the number
In number theory, Sylvester's sequence is an integer sequence in which each term of the sequence is the product of the previous terms, plus one. The first few terms of the sequence are
Hillel (Harry) Furstenberg is a German-born American-Israeli mathematician and professor emeritus at the Hebrew University of Jerusalem. He is a member of the Israel Academy of Sciences and Humanities and U.S. National Academy of Sciences and a laureate of the Abel Prize and the Wolf Prize in Mathematics. He is known for his application of probability theory and ergodic theory methods to other areas of mathematics, including number theory and Lie groups.
In number theory and enumerative combinatorics, the ordered Bell numbers or Fubini numbers count the number of weak orderings on a set of n elements. Starting from n = 0, these numbers are
The Fibonacci Quarterly is a scientific journal on mathematical topics related to the Fibonacci numbers, published four times per year. It is the primary publication of The Fibonacci Association, which has published it since 1963. Its founding editors were Verner Emil Hoggatt Jr. and Alfred Brousseau; the present editor is Professor Curtis Cooper of the Mathematics Department of the University of Central Missouri.
Edward Burger Burger is a mathematician and President Emeritus of Southwestern University in Georgetown, Texas. Previously, he was the Francis Christopher Oakley Third Century Professor of Mathematics at Williams College, and the Robert Foster Cherry Professor for Great Teaching at Baylor University. He also had been named to a single-year-appointment as vice provost of strategic educational initiatives at Baylor University in February 2011. He currently serves as the president and CEO of St. David's Foundation.
In mathematics, a Somos sequence is a sequence of numbers defined by a certain recurrence relation, described below. They were discovered by mathematician Michael Somos. From the form of their defining recurrence, one would expect the terms of the sequence to be fractions, but nevertheless many Somos sequences have the property that all of their members are integers.
In combinatorics, the Schröder–Hipparchus numbers form an integer sequence that can be used to count the number of plane trees with a given set of leaves, the number of ways of inserting parentheses into a sequence, and the number of ways of dissecting a convex polygon into smaller polygons by inserting diagonals. These numbers begin
In mathematics, the telephone numbers or the involution numbers form a sequence of integers that count the ways n telephone lines can be connected to each other, where each line can be connected to at most one other line. These numbers also describe the number of matchings of a complete graph on n vertices, the number of permutations on n elements that are involutions, the sum of absolute values of coefficients of the Hermite polynomials, the number of standard Young tableaux with n cells, and the sum of the degrees of the irreducible representations of the symmetric group. Involution numbers were first studied in 1800 by Heinrich August Rothe, who gave a recurrence equation by which they may be calculated, giving the values
Péter Kiss was a Hungarian mathematician, Doctor of Mathematics, and professor of mathematics at Eszterházy Károly College, who specialized in number theory. In 1992 he won the Albert Szent-Györgyi Prize for his achievements.
Henry Wadsworth Gould is a Professor Emeritus of Mathematics at West Virginia University.
Francis Edward Su is an American mathematician. He joined the Harvey Mudd College faculty in 1996, and is currently Benediktsson-Karwa Professor of Mathematics. Su served as President of the Mathematical Association of America from 2015–2017 and is serving as a Vice President of the American Mathematical Society from 2020-2023. Su has received multiple awards from the MAA, including the Henry L. Alder Award and the Haimo Award, both for distinguished teaching. He was also a Phi Beta Kappa Visiting Scholar during the 2019-2020 term.
In mathematics and computer science, the sorting numbers are a sequence of numbers introduced in 1950 by Hugo Steinhaus for the analysis of comparison sort algorithms. These numbers give the worst-case number of comparisons used by both binary insertion sort and merge sort. However there are other algorithms that use fewer comparisons.
References
- Michael Somos and Robert Haas, "A Linked Pair of Sequences Implies the Primes Are Infinite", The American Mathematical Monthly , volume 110, number 6 (June – July, 2003), pp. 539–540
