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.

The anthropic principle is often criticized for lacking falsifiability and therefore critics of the anthropic principle may point out that the anthropic principle is a non-scientific concept, even though the weak anthropic principle, " conditions that are observed in the universe must allow the observer to exist ", is " easy " to support in mathematics and philosophy, i. e. it is a tautology or truism

It is very often convenient to consider the angular momentum of a collection of particles about their center of mass, since this simplifies the mathematics considerably.

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

Aside from these core elements, a civilization is often marked by any combination of a number of secondary elements, including a developed transportation system, writing, standardized measurement, currency, contractual and tort-based legal systems, characteristic art and architecture, mathematics, enhanced scientific understanding, metallurgy, political structures, and organized religion.

Although the main objects of study in discrete mathematics are discrete objects, analytic methods from continuous mathematics are often employed as well.

In mathematics, one can often define a direct product of objects

Instructors in primary and secondary institutions are often called teachers, and they direct the education of students and might draw on many subjects like reading, writing, mathematics, science and history.

In computer science and mathematics, which do not usually deal with natural languages, the adjective " formal " is often omitted as redundant.

In mathematics, the term Fourier analysis often refers to the study of both operations.

The beginning of set theory as a branch of mathematics is often marked by the publication of Cantor's 1874 article, " Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen " (" On a Property of the Collection of All Real Algebraic Numbers ").

In mathematics, especially in category theory and homotopy theory, a groupoid ( less often Brandt groupoid or virtual group ) generalises the notion of group in several equivalent ways.

Demonstrated ability in reading, mathematics, and writing, as typically measured in the United States by the SAT or similar tests such as the ACT, have often replaced colleges individual entrance exams, and is often required for admission to higher education.

The problem often arises in resource allocation where there are financial constraints and is studied in fields such as combinatorics, computer science, complexity theory, cryptography and applied mathematics.

This value is often calculated as the dominant eigenvalue of the age / size class matrix ( mathematics ).

Linear algebra is the branch of mathematics concerning vector spaces, often finite or countably infinite dimensional, as well as linear mappings between such spaces.

The term " applied mathematics " also describes the professional specialty in which mathematicians work on problems, often concrete but sometimes abstract.

Another aspect of mathematics, often referred to as " foundational mathematics ", consists of the fields of logic and set theory.

The development of algebraic geometry from its classical to modern forms is a particularly striking example of the way an area of mathematics can change radically in its viewpoint, without making what was correctly proved before in any way incorrect ; of course mathematical progress clarifies gaps in previous proofs, often by exposing hidden assumptions, which progress has revealed worth conceptualizing.

* Map ( mathematics ), often a synonym for function

Contemporary work in the foundations of mathematics often focuses on establishing which parts of mathematics can be formalized in particular formal systems ( as in reverse mathematics ) rather than trying to find theories in which all of mathematics can be developed.

Area plays an important role in modern mathematics.

It is considered an important milestone in the development of mathematics.

Overall, his contributions are considered the most important in advancing chemistry to the level reached in physics and mathematics during the 18th century.

Initially a study of systems of polynomial equations in several variables, the subject of algebraic geometry starts where equation solving leaves off, and it becomes even more important to understand the intrinsic properties of the totality of solutions of a system of equations, than to find a specific solution ; this leads into some of the deepest areas in all of mathematics, both conceptually and in terms of technique.

On the Infinite was Hilbert ’ s most important paper on the foundations of mathematics, serving as the heart of Hilbert's program to secure the foundation of transfinite numbers by basing them on finite methods.

Many important constructions in mathematics can be studied in this context.

This was a major discovery in an important field of mathematics ; construction problems had occupied mathematicians since the days of the Ancient Greeks, and the discovery ultimately led Gauss to choose mathematics instead of philology as a career.

Though Gauss had up to that point been financially supported by his stipend from the Duke, he doubted the security of this arrangement, and also did not believe pure mathematics to be important enough to deserve support.

This was particularly important because it shows that Cotton Mather had influence in mathematics during the time of Puritan New England.

C *- algebras ( pronounced " C-star ") are an important area of research in functional analysis, a branch of mathematics.

His work in this part of analysis provided the basis for important contributions to the mathematics of physics in the next two decades, though from an unanticipated direction.

Decision problems typically appear in mathematical questions of decidability, that is, the question of the existence of an effective method to determine the existence of some object or its membership in a set ; many of the important problems in mathematics are undecidable.

Several fields of discrete mathematics, particularly theoretical computer science, graph theory, and combinatorics, are important in addressing the challenging bioinformatics problems associated with understanding the tree of life.

The study of self-reference led to important developments in logic and mathematics in the twentieth century.

Unsurprisingly, Galois ' collected works amount to only some 60 pages, but within them are many important ideas that have had far-reaching consequences for nearly all branches of mathematics.

The field is largely focused on the modelling of derivatives, although other important subfields include insurance mathematics and quantitative portfolio problems.

Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus.

The theorems were proven by Kurt Gödel in 1931, and are important in the philosophy of mathematics.

" Its issues were considered no less important than the other main formal subjects of physical science, medicine, mathematics, poetics and music.

The set has a number of important mathematical properties that are foundational to various branches of mathematics.

When studying the mathematics of games, the mathematical analysis of the game is more important than actually playing the game.

They are important in many branches of mathematics and the sciences and are used in finance to solve problems involving compound interest.

To do this, he invented ( independently of Galois ) an extremely important branch of mathematics known as group theory, which is invaluable not only in many areas of mathematics, but for much of physics as well.