In mathematics, the Hausdorff maximal principle is an alternate and earlier formulation of Zorn's lemma proved by Felix Hausdorff in 1914 ( Moore 1982: 168 ).

In mathematics, a lemma ( plural lemmata or lemmas ) from the Greek λῆμμα ( lemma, “ anything which is received, such as a gift, profit, or a bribe ”) is a proven proposition which is used as a stepping stone to a larger result rather than as a statement of interest by itself.

A good stepping stone leads to many others, so some of the most powerful results in mathematics are known as lemmata, such as Bézout's lemma, Urysohn's lemma, Dehn's lemma, Euclid's lemma, Farkas ' lemma, Fatou's lemma, Gauss's lemma, Nakayama's lemma, Poincaré's lemma, Riesz's lemma, Schwarz's lemma, Itō's lemma and Zorn's lemma.

In mathematics, specifically in category theory, the Yoneda lemma is an abstract result on functors of the type morphisms into a fixed object.

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

In mathematics, especially homological algebra and other applications of abelian category theory, the short five lemma is a special case of the five lemma.

In mathematics, especially homological algebra and other applications of abelian category theory, the five lemma is an important and widely used lemma about commutative diagrams.

In mathematics, and more specifically in homological algebra, the splitting lemma states that in any abelian category, the following statements for short exact sequence are equivalent.

Facts about the computational aspects of the lemma suggest that no proof can be given that would be considered constructive by the main schools of constructive mathematics.

" He held that corollarial deduction matches Aristotle's conception of direct demonstration, which Aristotle regarded as the only thoroughly satisfactory demonstration, while theorematic deduction ( A ) is the kind more prized by mathematicians, ( B ) is peculiar to mathematics, and ( C ) involves in its course the introduction of a lemma or at least a definition uncontemplated in the thesis ( the proposition that is to be proved ); in remarkable cases that definition is of an abstraction that " ought to be supported by a proper postulate.

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.

He joined Bell Laboratories, then decided to continue his education and attended the University of Pennsylvania, and studied combinatorial mathematics.

Garfield studied under Herbert Wilf and earned a Ph. D. in combinatorial mathematics from Penn in 1993.

For example, Mancala is a mathematical game, because mathematicians can study it using combinatorial game theory, even though no mathematics is necessary in order to play it.

In combinatorial mathematics, a Steiner system ( named after Jakob Steiner ) is a type of block design, specifically a t-design with λ = 1 and t ≥ 2.

In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a finitely generated group G is the algorithmic problem of deciding whether two words in the generators represent the same element.

* Block design, a kind of set system in combinatorial mathematics

Magic squares were known to Chinese mathematicians, as early as 650 BCE and Arab mathematicians, possibly as early as the 7th century, when the Arabs conquered northwestern parts of the Indian subcontinent and learned Indian mathematics and astronomy, including other aspects of combinatorial mathematics.

Vladimir Batagelj is a Slovenian mathematician, born 1948 in Idrija, Slovenia, who works mainly in data analysis, discrete mathematics, combinatorial optimization and applications of IT in education.

* Incidence structure, a feature of combinatorial mathematics

The assignment problem is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research in mathematics.

In combinatorial mathematics, the theory of combinatorial species is an abstract, systematic method for analysing discrete structures in terms of generating functions.

In mathematics, the nimbers, also called Grundy numbers, are introduced in combinatorial game theory, where they are defined as the values of nim heaps.

In combinatorial mathematics, Hall's marriage theorem, or simply Hall's Theorem, gives a necessary and sufficient condition for being able to select a distinct element from each of a collection of finite sets.

In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects.

In mathematics, a building ( also Tits building, Bruhat – Tits building, named after François Bruhat and Jacques Tits ) is a combinatorial and geometric structure which simultaneously generalizes certain aspects of flag manifolds, finite projective planes, and Riemannian symmetric spaces.

During the twentieth century this was a fruitful area of combinatorial mathematics, with numerous connections to other fields.

In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces ( for example the Betti numbers ) were regarded as derived from combinatorial decompositions such as simplicial complexes.

In applied mathematics and theoretical computer science, combinatorial optimization

In combinatorial mathematics, the necklace polynomials, or ( Moreau's ) necklace-counting function are the polynomials in α such that

* WZ theory, a technique for simplifying certain combinatorial summations in mathematics

In combinatorial mathematics, an ordered partition O of a set S is a sequence