In mathematics, a Hurwitz polynomial, named after Adolf Hurwitz, is a polynomial whose coefficients are positive real numbers and whose zeros are located in the left half-plane of the complex plane, that is, the real part of every zero is negative.

In mathematics, the Bernoulli polynomials occur in the study of many special functions and in particular the Riemann zeta function and the Hurwitz zeta function.

In mathematics, the Hurwitz zeta function, named after Adolf Hurwitz, is one of the many zeta functions.

In mathematics, the Riemann – Hurwitz formula, named after Bernhard Riemann and Adolf Hurwitz, describes the relationship of the Euler characteristics of two surfaces when one is a ramified covering of the other.

In mathematics, the Lerch zeta-function, sometimes called the Hurwitz – Lerch zeta-function, is a special function that generalizes the Hurwitz zeta-function and the polylogarithm.

In mathematics, a Hurwitz matrix, or Routh-Hurwitz matrix, is a structured real square matrix constructed with coefficients

In mathematics, Routh – Hurwitz theorem gives a test to determine whether a given polynomial is Hurwitz-stable.

In mathematics, a rational zeta series is the representation of an arbitrary real number in terms of a series consisting of rational numbers and the Riemann zeta function or the Hurwitz zeta function.

In mathematics, a quaternion algebra over a field F is a central simple algebra A over F that has dimension 4 over F. Every quaternion algebra becomes the matrix algebra by extending scalars (= tensoring with a field extension ), i. e. for a suitable field extension K of F, is isomorphic to the 2 × 2 matrix algebra over K.

In mathematics, an algebraic number is a number that is a root of a non-zero polynomial in one variable with rational coefficients ( or equivalently — by clearing denominators — with integer coefficients ).

Methods for breaking modern cryptosystems often involve solving carefully constructed problems in pure mathematics, the best-known being integer factorization.

In number theory, a branch of mathematics, two integers a and b are said to be coprime ( also spelled co-prime ) or relatively prime if the only positive integer that evenly divides both of them is 1.

In mathematics, the Fibonacci numbers or Fibonacci series or Fibonacci sequence are the numbers in the following integer sequence:

An example of such a finite field is the ring Z / pZ, which is essentially the set of integers from 0 to p − 1 with integer addition and multiplication modulo p. It is also sometimes denoted Z < sub > p </ sub >, but within some areas of mathematics, particularly number theory, this may cause confusion because the same notation Z < sub > p </ sub > is used for the ring of p-adic integers.

In mathematics, the greatest common divisor ( gcd ), also known as the greatest common factor ( gcf ), or highest common factor ( hcf ), of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder.

In mathematics, a Mersenne number, named after Marin Mersenne ( a French monk who began the study of these numbers in the early 17th century ), is a positive integer that is one less than a power of two:

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

In constructive mathematics, one way to construct a real number is as a function ƒ that takes a positive integer and outputs a rational ƒ ( n ), together with a function g that takes a positive integer n and outputs a positive integer g ( n ) such that

In mathematics, a polynomial is an expression of finite length constructed from variables ( also called indeterminates ) and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

In mathematics, a square-free, or quadratfrei, integer is one divisible by no perfect square, except 1.

In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on.

In mathematics, a Golomb ruler is a set of marks at integer positions along an imaginary ruler such that no two pairs of marks are the same distance apart.

In mathematics, a divisor of an integer, also called a factor of, is an integer which divides without leaving a remainder.

In mathematics, an integer sequence is a sequence ( i. e., an ordered list ) of integers.

In mathematics and computer science, the floor and ceiling functions map a real number to the largest previous or the smallest following integer, respectively.

In mathematics, a dyadic fraction or dyadic rational is a rational number whose denominator is a power of two, i. e., a number of the form a / 2 < sup > b </ sup > where a is an integer and b is a natural number ; for example, 1 / 2 or 3 / 8, but not 1 / 3.

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

In mathematics, de Moivre's formula ( a. k. a. De Moivre's theorem and De Moivre's identity ), named after Abraham de Moivre, states that for any complex number ( and, in particular, for any real number ) x and integer n it holds that

In mathematics, the winding number of a closed curve in the plane around a given point is an integer representing the total number of times that curve travels counterclockwise around the point.

In mathematics, a ratio is a relationship between two numbers of the same kind ( e. g., objects, persons, students, spoonfuls, units of whatever identical dimension ), usually expressed as " a to b " or a: b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly indicates how many times the first number contains the second ( not necessarily an integer ).

This is an unsolved problem which probably has never been seriously investigated, although one frequently hears the comment that we have insufficient specialists of the kind who can compete with the Germans or Swiss, for example, in precision machinery and mathematics, or the Finns in geochemistry.

Next September, after receiving a degree from Yale's Master of Arts in Teaching Program, I will be teaching somewhere -- that much is guaranteed by the present shortage of mathematics teachers.

But because science is based on mathematics doesn't mean that a hot rodder must necessarily be a mathematician.

Like primitive numbers in mathematics, the entire axiological framework is taken to rest upon its operational worth.

In the new situation, philosophy is able to provide the social sciences with the same guidance that mathematics offers the physical sciences, a reservoir of logical relations that can be used in framing hypotheses having explanatory and predictive value.

So, too, is the mathematical competence of a college graduate who has majored in mathematics.

The principal of the school announced that -- despite the help of private tutors in Hollywood and Philadelphia -- Fabian is a 10-o'clock scholar in English and mathematics.

In mathematics and statistics, the arithmetic mean, or simply the mean or average when the context is clear, is the central tendency of a collection of numbers taken as the sum of the numbers divided by the size of the collection.

The term " arithmetic mean " is preferred in mathematics and statistics because it helps distinguish it from other means such as the geometric and harmonic mean.

In addition to mathematics and statistics, the arithmetic mean is used frequently in fields such as economics, sociology, and history, though it is used in almost every academic field to some extent.

The use of the soroban is still taught in Japanese primary schools as part of mathematics, primarily as an aid to faster mental calculation.

In mathematics and computer science, an algorithm ( originating from al-Khwārizmī, the famous Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī ) is a step-by-step procedure for calculations.

In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that " the product of a collection of non-empty sets is non-empty ".

The axiom of choice is avoided in some varieties of constructive mathematics, although there are varieties of constructive mathematics in which the axiom of choice is embraced.

The axiom of choice has also been thoroughly studied in the context of constructive mathematics, where non-classical logic is employed.

:" A choice function exists in constructive mathematics, because a choice is implied by the very meaning of existence.

Although the axiom of countable choice in particular is commonly used in constructive mathematics, its use has also been questioned.

One of the most interesting aspects of the axiom of choice is the large number of places in mathematics that it shows up.

There is no prize awarded for mathematics, but see Abel Prize.