In mathematics, Archimedes used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of pi.

The notation e < sub > i </ sub > is compatible with the index notation and the summation convention commonly used in higher level mathematics, physics, and engineering.

* The product operator in mathematics, indicated with capital pi notation ∏ ( in analogy to the use of the capital Sigma Σ as summation symbol ).

In mathematics, especially in applications of linear algebra to physics, the Einstein notation or Einstein summation convention is a notational convention that implies summation over a set of indexed terms in a formula, thus achieving notational brevity.

In mathematics, an empty sum, or nullary sum, is a summation involving no terms at all.

* In mathematics, summation notation

In mathematics, the Poisson summation formula is an equation that relates the Fourier series coefficients of the periodic summation of a function to values of the function's continuous Fourier transform.

In mathematics, the Fejér kernel is used to express the effect of Cesàro summation on Fourier series.

In mathematics, σ-approximation adjusts a Fourier summation to eliminate the Gibbs phenomenon which would otherwise occur at discontinuities.

In mathematics, Borel summation is a summation method for divergent series, introduced by.

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.

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.

Ethics cannot be based on the authoritative certainty given by mathematics and logic, or prescribed directly from the empirical findings of science.

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

Another possibility, raised in an essay by the Swedish fantasy writer and editor Rickard Berghorn, is that the name Alhazred was influenced by references to two historical authors whose names were Latinized as Alhazen: Alhazen ben Josef, who translated Ptolemy into Arabic ; and Abu ' Ali al-Hasan ibn al-Haytham, who wrote about optics, mathematics and physics.

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 ).

Two aspects of this attitude deserve to be mentioned: 1 ) he did not only study science from books, as other academics did in his day, but actually observed and experimented with nature ( the rumours starting by those who did not understand this are probably at the source of Albert's supposed connections with alchemy and witchcraft ), 2 ) he took from Aristotle the view that scientific method had to be appropriate to the objects of the scientific discipline at hand ( in discussions with Roger Bacon, who, like many 20th century academics, thought that all science should be based on mathematics ).

From the ages of 6 to 9, Alexei was educated by his tutor Vyazemsky, but after the removal of his mother by Peter the Great to the Suzdal Intercession Convent, Alexei was confined to the care of educated foreigners, who taught him history, geography, mathematics and French.

This program culminated in the proofs of the Weil conjectures, the last of which was settled by Grothendieck's student Pierre Deligne in the early 1970s after Grothendieck had largely withdrawn from mathematics.

In mathematics, an associative algebra A is an associative ring that has a compatible structure of a vector space over a certain field K or, more generally, of a module over a commutative ring R. Thus A is endowed with binary operations of addition and multiplication satisfying a number of axioms, including associativity of multiplication and distributivity, as well as compatible multiplication by the elements of the field K or the ring R.

In mathematics, the axiom of regularity ( also known as the axiom of foundation ) is one of the axioms of Zermelo – Fraenkel set theory and was introduced by.

Though respected for their contributions to various academic disciplines ( respectively mathematics, linguistics, and literature ), the three men became known to the general public only by making often-controversial and disputed pronouncements on politics and public policy that would not be regarded as noteworthy if offered by a medical doctor or skilled tradesman.

This is reinforced by his theoretical treatises, which involve principles of mathematics, perspective and ideal proportions.

" The Four Books on Measurement " were published at Nuremberg in 1525 and was the first book for adults on mathematics in German, as well as being cited later by Galileo and Kepler.

By focusing consciously on an idea, feeling or intention the meditant seeks to arrive at pure thinking, a state exemplified by but not confined to pure mathematics.

It ranks amongst the most prestigious mathematics journals in the world by criteria such as impact factor.

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.

Arithmetic or arithmetics ( from the Greek word ἀριθμός, arithmos " number ") is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations.

This is philosophically unsatisfying to some and has motivated additional work in set theory and other methods of formalizing the foundations of mathematics such as New Foundations by Willard Van Orman Quine.

In mathematics terminology, the vector space of bras is the dual space to the vector space of kets, and corresponding bras and kets are related by the Riesz representation theorem.

In mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions y ( x ) of Bessel's differential equation:

His Foundations of Arithmetic, published 1884, expressed ( parts of ) mathematics in formal logic.

These connections shed the boundaries between combinatorics and parts of mathematics and theoretical computer science, but at the same time led to a partial fragmentation of the field.

The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to business accounts.

In mathematics, graphs are useful in geometry and certain parts of topology, e. g. Knot Theory.

Lie groups represent the best-developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics.

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.

# proof theory and constructive mathematics ( considered as parts of a single area ).

The notion that philosophy, especially ontology and the philosophy of mathematics should abstain from set theory owes much to the writings of Nelson Goodman ( see especially Goodman 1977 ), who argued that concrete and abstract entities having no parts, called individuals exist.

* Order of operations, in mathematics, rules for which parts of an expression are evaluated first

In mathematics, a self-similar object is exactly or approximately similar to a part of itself ( i. e. the whole has the same shape as one or more of the parts ).

Groups recur throughout mathematics, and the methods of group theory have strongly influenced many parts of algebra.

In mathematics, a Dedekind cut, named after Richard Dedekind, is a partition of the rational numbers into two non-empty parts A and B, such that all elements of A are less than all elements of B, and A contains no greatest element.

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.

" Although he admitted that what he called " real " mathematics may someday become useful, he asserted that, at the time in which the Apology was written, only the " dull and elementary parts " of either pure or applied mathematics could " work for good or ill ."

In mathematics, the theory of linear systems is the basis and a fundamental part of linear algebra, a subject which is used in most parts of modern mathematics.

The book is divided into four parts: logic, natural sciences, mathematics ( a quadrivium of arithmetic, geometry, astronomy, and music ), and metaphysics.

This is particularly true for the less applied parts of mathematics.

Certain parts of mathematics that initially arose from the development of physics are not, in fact, considered parts of mathematical physics, while other closely related fields are.