* Édouard Lucas, ( 1842 – 1891 ) Famous French mathematician, inventor of the Tower of Hanoi puzzle, discovered that 2 < sup > 127 </ sup > − 1 was prime and published 4 large volumes on recreational mathematics.

John Lucas was educated at Winchester College and Balliol College, Oxford, where he studied first mathematics, then Greats ( Philosophy and Ancient History ), obtaining first class honours, and proceeding to an MA in Philosophy in 1954.

A prolific author with unusually diverse teaching and research interests, Lucas has written on the philosophy of mathematics, especially the implications of Gödel's incompleteness theorem, the philosophy of mind, free will and determinism, the philosophy of science including two books on physics coauthored with Peter E. Hodgson, causality, political philosophy, ethics and business ethics, and the philosophy of religion.

In mathematics, the Lucas – Lehmer test ( LLT ) is a primality test for Mersenne numbers.

Lehmer received a Master's degree and a Ph. D., both from Brown University, in 1929 and 1930, respectively ; his wife obtained a Master's degree in 1930 as well, coaching mathematics to supplement the family income, while also helping her husband type his Ph. D. thesis, An Extended Theory of Lucas ' Functions, which he wrote under Jacob Tamarkin.

That the latter theorems have much to say about all of mathematics and more controversially, about a range of philosophical issues ( e. g., Lucas 1961 ) is less than evident.

In mathematics, a Lucas chain is a restricted type of addition chain, named for the French mathematician Édouard Lucas.

In mathematics, a Lucas – Carmichael number is a positive composite integer n such that if p is a prime factor of n, then p + 1 is a factor of n + 1.

In mathematics, in particular number theory, an odd composite number N is a Somer – Lucas d-pseudoprime ( with given d ≥ 1 ) if there exists a nondegenerate Lucas sequence with the discriminant such that and the rank appearance of N in the sequence U ( P, Q ) is

In mathematics, a Lehmer number is a generalization of a Lucas sequence.

In mathematics, the Hofstadter Female and Male sequences are an example of a pair of integer sequences defined in a mutually recursive manner.

There are various and quite different notions of sequences in mathematics, some of which ( e. g., exact sequence ) are not covered by the notations introduced below.

Numbering sequences starting at 0 is quite common in mathematics, in particular in combinatorics.

In mathematics, several specific infinite sequences of bits have been studied for their mathematical properties ; these include the Baum – Sweet sequence, Ehrenfeucht – Mycielski sequence, Fibonacci word, Kolakoski sequence, regular paperfolding sequence, Rudin – Shapiro sequence, and Thue – Morse sequence.

In the context of classical mathematics, this is impossible, and the diagonal argument establishes that, although both sets are infinite, there are actually more infinite sequences of ones and zeros than there are natural numbers.

* Elliptic divisibility sequence, a class of integer sequences in mathematics

The snake lemma is a tool used in mathematics, particularly homological algebra, to construct long exact sequences.

In mathematics, the dot product, or scalar product ( or sometimes inner product in the context of Euclidean space ), is an algebraic operation that takes two equal-length sequences of numbers ( usually coordinate vectors ) and returns a single number obtained by multiplying corresponding entries and then summing those products.

Polynomial sequences are a topic of interest in enumerative combinatorics and algebraic combinatorics, as well as applied mathematics.

In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or ( especially ) estimation of certain types of sums.

Different levels of mathematics are taught at different ages and in somewhat different sequences in different countries.

* Convergence ( mathematics ), refers to the notion that some functions and sequences approach a limit under certain conditions

Hurewicz is best remembered for two remarkable contributions to mathematics, his discovery of the higher homotopy groups in 1935-36, and his discovery of exact sequences in 1941.

In mathematics, lexicographical order is a means of ordering sequences in a manner analogous to that used to produce alphabetical order.

In mathematics, the random Fibonacci sequence is a stochastic analogue of the Fibonacci sequence defined by the recurrence relation f < sub > n </ sub > = f < sub > n − 1 </ sub > ± f < sub > n − 2 </ sub >, where the signs + or − are chosen at random with equal probability 1 / 2, independently for different n. By a theorem of Harry Kesten and Hillel Fürstenberg, random recurrent sequences of this kind grow at a certain exponential rate, but it is difficult to compute the rate explicitly.

Furthermore, where musical set theory refers to ordered sets, mathematics would normally refer to tuples or sequences ( though mathematics does speak of ordered sets, and these can be seen to include the musical kind in some sense, they are far more involved ).

* The space ℓ < sup > 2 </ sup > of square-summable sequences, in mathematics

In mathematics, the nine lemma is a statement about commutative diagrams and exact sequences valid in any abelian category, as well as in the category of groups.

In mathematics, the Cauchy product, named after Augustin Louis Cauchy, of two sequences,, is the discrete convolution of the two sequences, the sequence whose general term is given by

In mathematics, and in particular in combinatorics, the combinatorial number system of degree k ( for some positive integer k ), also referred to as combinadics, is a correspondence between natural numbers ( taken to include 0 ) N and k-combinations, represented as strictly decreasing sequences c < sub > k </ sub > > ... > c < sub > 2 </ sub > > c < sub > 1 </ sub > ≥ 0.

In mathematics, Horner's method ( also known as Horner scheme in the UK or Horner's rule in the U. S .) is either of two things: ( i ) an algorithm for calculating polynomials, which consists in transforming the monomial form into a computationally efficient form ; or ( ii ) a method for approximating the roots of a polynomial.

He started studying mathematics in 1941 in the U. S., but his studies were interrupted by the war, during which he served in the military.

Enrollment in computer-related degrees in U. S. has dropped recently due to lack of general interests in science and mathematics and also out of an apparent fear that programming will be subject to the same pressures as manufacturing and agriculture careers.

Albert first considered becoming a minister but instead he turned to the study of mathematics and physics, where he later became a co-inventor of the x-ray microscope and author of one of the most widely used physics textbooks in the U. S. The Baez family converted to Quakerism during Joan's early childhood, and she has continued to identify with the tradition, particularly in her commitment to pacifism and social issues.

In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f: U → R ( where U is an open subset of R < sup > n </ sup >) which satisfies Laplace's equation, i. e.

Unicode discourages their use for mathematics and in Western texts because they are canonically equivalent to the CJK code points U + 300x and thus likely to render as double-width symbols.

Some mathematics books use U and E to represent the Identity Matrix ( meaning " Unit Matrix " and " Elementary Matrix ", or from the German " Einheitsmatrix ", respectively ), although I is considered more universal.

In what is, in the U. S., called traditional mathematics, a specific process is taught to students at the end of the 1st year or during the 2nd year for use with multi-digit whole numbers, and is extended in either the fourth or fifth grade to include decimal representations of fractional numbers.

Although Fuller was not the original inventor, he developed the intrinsic mathematics of the dome, thereby allowing popularization of the idea — for which he received U. S. patent 2, 682, 235 29 June 1954.

* Miner Knowlton ( 1804 – 70 ), graduated from West Point in 1829, He served with the French Army as aid to Marshall Beaugand in Algeria in 1845 and with the U. S. Army in the Mexican War, an instructor of mathematics, French, artillery and cavalry tactics at West Point for 14 years, instructing many of the noted Civil War generals, including U. S. Grant.

In mathematics, a complex square matrix U is unitary if

Mathematically, a scalar field on a region U is a real or complex-valued function or distribution on U. The region U may be a set in some Euclidean space, Minkowski space, or more generally a subset of a manifold, and it is typical in mathematics to impose further conditions on the field, such that it be continuous or often continuously differentiable to some order.

In mathematics, the unitary group of degree n, denoted U ( n ), is the group of n × n unitary matrices, with the group operation that of matrix multiplication.

In functional analysis, a branch of mathematics, a unitary operator ( not to be confused with a unity operator ) is a bounded linear operator U: H → H on a Hilbert space H satisfying

They are resolved by applying the science of logic and psychology together with mathematics, the supreme solution finder being Dr. Susan Calvin, Chief Robopsychologist of U. S. Robots.

In mathematics, more specifically algebraic topology, a covering map is a continuous surjective function p from a topological space, C, to a topological space, X, such that each point in X has a neighbourhood evenly covered by p. This means that for each point x in X, there is associated an ordered pair, ( K, U ), where U is a neighborhood of x and where K is a collection of disjoint open sets in C, each of which gets mapped homeomorphically, via p, to U ( as shown in the image ).

In mathematics, a function f from a topological space A to a set B is called locally constant, if for every a in A there exists a neighborhood U of a, such that f is constant on U.

During World War II, he served in the U. S. Army, where he became interested in mathematics.