Although no graduates of Morgan are known to have ever received a Ph. D. in mathematics, nine did so during his tenure there.

At the age of nine, Ruth gained an O-level in mathematics, setting a new age record, later surpassed in 2001 when Arran Fernandez successfully sat GCSE mathematics aged five.

Also at the age of nine she achieved a Grade A at A-level Pure Mathematics, an age record which stood until 2009 when Zohaib Ahmed passed A level mathematics with an A grade aged just turned nine years old.

After the war, he wrote or co-wrote a series of nine mathematics textbooks for kindergarten through high school which use an incremental teaching method often called " Saxon math ".

NTUA is divided into nine academic Schools, eight being for the engineering disciplines, including architecture, and one for applied sciences ( mathematics and physics ).

Tao exhibited extraordinary mathematical abilities from an early age, attending university level mathematics courses at the age of nine.

Before the course of study was regulated by the state, a Piarist establishment contained nine classes: reading, writing, elementary mathematics, schola parva or Rudimentorum, schola Principiorum, Grammatica, Syntaxis, Humanitas or Poesis and Rhetorica.

The Prussian defeats at the hand of Napoleon I led to the creation of the Allgemeine Kriegsschule ( General War Academy ) with a nine month programme covering mathematics, tactics, strategy, staff work, weapons science, military geography, languages, physics, chemistry and administration.

The disciplines involved are sub-divided into nine fields: the disciplines of physics and related disciplines ; astronomy ; chemistry ; the earth and environmental sciences ; the life sciences ( botany, agronomy, zoology, genetics, molecular biology, biochemistry, the neurosciences, surgery ); mathematics ; the applied sciences ; and the philosophy and history of sciences.

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.

A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: " Read Euler, read Euler, he is the master of us all.

One statement of this philosophy is the thesis that mathematics is not created but discovered.

A lucid statement of this is found in an essay written by the British mathematician G. H. Hardy in defense of pure mathematics.

In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms.

Some, on the other hand, may be called " deep ": their proofs may be long and difficult, involve areas of mathematics superficially distinct from the statement of the theorem itself, or show surprising connections between disparate areas of mathematics.

* Mathematical statement, a statement in logic and mathematics

Although most mathematicians and physicists ( and many philosophers ) would accept the statement " mathematics is a language ", linguists believe that the implications of such a statement must be considered.

In mathematics, Minkowski's theorem is the statement that any convex set in R < sup > n </ sup > which is symmetric with respect to the origin and with volume greater than 2 < sup > n </ sup > d ( L ) contains a non-zero lattice point.

This is the spectral theorem in mathematics, and in a finite state space it is just a statement of the completeness of the eigenvectors of a Hermitian matrix.

In mathematics, the Cauchy integral theorem ( also known as the Cauchy – Goursat theorem ) in complex analysis, named after Augustin-Louis Cauchy, is an important statement about line integrals for holomorphic functions in the complex plane.

In mathematics, Cauchy's integral formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis.

In mathematics, a proof is a demonstration that if some fundamental statements ( axioms ) are assumed to be true, then some mathematical statement is necessarily true.

In mathematics, an inequation is a statement that an inequality holds between two values.

In mathematics, the proof of a " some " statement may be achieved either by a constructive proof, which exhibits an object satisfying the " some " statement, or by a nonconstructive proof which shows that there must be such an object but without exhibiting one.

Famously, he stated that the point is to know one way or the other what the solution is, and he believed that we always can know this, that in mathematics there is not any " ignorabimus " ( statement that the truth can never be known ).

That is, if a professor of mathematics makes a statement about numbers, it will be assumed to be true in the absence of evidence to the contrary.

Assuming something to be true for all numbers when it has been shown for over 906 million cases would not generally be considered hasty, but in mathematics a statement remains a conjecture until it is shown to be universally true.

* Difference ( mathematics ), a statement about the relative size or order of two objects

In mathematics and logic, a direct proof is a way of showing the truth or falsehood of a given statement by a straightforward combination of established facts, usually existing lemmas and theorems, without making any further assumptions.