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.

Furthermore, in mathematics, the letter alpha is used to denote the area underneath a normal curve in statistics to denote significance level when proving null and alternative hypotheses.

Bioinformatics also deals with algorithms, databases and information systems, web technologies, artificial intelligence and soft computing, information and computation theory, structural biology, software engineering, data mining, image processing, modeling and simulation, discrete mathematics, control and system theory, circuit theory, and statistics.

An innovator in mathematics, statistics, philosophy, research methodology, and various sciences, Peirce considered himself, first and foremost, a logician.

Econometrics is the unification of economics, mathematics, and statistics.

At the Cowles Commission, Simon ’ s main goal was to link economic theory to mathematics and statistics.

The field is at the intersection of mathematics, statistics, computer science, physics, neurobiology, and electrical engineering.

The use of matrices in quantum mechanics, special relativity, and statistics helped spread the subject of linear algebra beyond pure mathematics.

The concept has been given an axiomatic mathematical derivation in probability theory, which is used widely in such areas of study as mathematics, statistics, finance, gambling, science, artificial intelligence / machine learning and philosophy to, for example, draw inferences about the expected frequency of events.

* In mathematics and statistics:

Some consider statistics to be a mathematical body of science pertaining to the collection, analysis, interpretation or explanation, and presentation of data, while others consider it a branch of mathematics concerned with collecting and interpreting data.

Because of its empirical roots and its focus on applications, statistics is usually considered to be a distinct mathematical science rather than a branch of mathematics.

In the first half of the 20th century, statistics became a free-standing discipline of applied mathematics.

In specific disciplines, Stanford was ranked in English ( in the United States ), in modern languages ( 7 ), in history ( 8 ), in philosophy ( 4 ), in geography & area studies ( 4 ), in linguistics ( 3 ), in computer science ( 2 ), in civil & structural engineering ( 2 ), in chemical engineering ( 3 ), in electrical engineering ( 2 ), in mechanical, aeronautical, & manufacturing engineering, in medicine ( 3 ), in biological sciences ( 3 ), in chemistry ( 4 ), in physics and astronomy ( 4 ), in metallurgy ( 4 ), in mathematics ( 3 ), in environmental sciences ( 4 ), in earth and marine sciences ( 6 ), in psychology ( 2 ), in sociology ( 4 ), in statistics, in politics and international studies ( 4 ), in law ( 3 ), in economics ( 3 ), and in account and finance.

Additionally, the SOT advises aspiring toxicologists to take statistics and mathematics courses, as well as gain laboratory experience through lab courses, student research projects and internships.

The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics.

Though mathematics, statistics, and computer science are not considered natural sciences, for instance, they provide many tools and frameworks used within the natural sciences.

Remaining in academia, Dembski ultimately completed an undergraduate degree in psychology ( 1981, University of Illinois at Chicago ) and masters degrees in statistics, mathematics, and philosophy ( 1983, University of Illinois at Chicago ; 1985, University of Chicago ; 1993, University of Illinois at Chicago respectively ), two PhDs, one in mathematics and one in philosophy ( 1988, University of Chicago ; 1996, University of Illinois at Chicago respectively ), and a Master of Divinity in theology at the Princeton Theological Seminary ( 1996 ).

He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics.

In mathematics, probability, and statistics, a multivariate random variable or random vector is a list of mathematical variables each of whose values is unknown, either because the value has not yet occurred or because there is imperfect knowledge of its value.

In mathematics, statistics, empirical sciences, computer science, or management science, mathematical optimization ( alternatively, optimization or mathematical programming ) is the selection of a best element ( with regard to some criteria ) from some set of available alternatives.

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

Pythagoras believed that behind the appearance of things, there was the permanent principle of mathematics, and that the forms were based on a transcendental mathematical relation.

Blind students also complete mathematical assignments using a braille-writer and Nemeth code ( a type of braille code for mathematics ) but large multiplication and long division problems can be long and difficult.

In mathematics, an automorphism is an isomorphism from a mathematical object to itself.

In addition, Ampère used his access to the latest mathematical books to begin teaching himself advanced mathematics at age 12.

He used his time in Bourg to research mathematics, producing Considérations sur la théorie mathématique de jeu ( 1802 ; “ Considerations on the Mathematical Theory of Games ”), a treatise on mathematical probability that he sent to the Paris Academy of Sciences in 1803.

Realism in the philosophy of mathematics is the claim that mathematical entities such as number have a mind-independent existence.

In that case, a mathematician's knowledge of mathematics is one mathematical object making contact with another.

Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.

The informal content of this naive set theory supports both the aspects of mathematical sets familiar in discrete mathematics ( for example Venn diagrams and symbolic reasoning about their Boolean algebra ), and the everyday usage of set theory concepts in most contemporary mathematics.

Sets are of great importance in mathematics ; in fact, in modern formal treatments, most mathematical objects ( numbers, relations, functions, etc.

A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis.

Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows ( also called morphisms, although this term also has a specific, non category-theoretical meaning ), where these collections satisfy some basic conditions.

Many significant areas of mathematics can be formalised as categories, and the use of category theory allows many intricate and subtle mathematical results in these fields to be stated, and proved, in a much simpler way than without the use of categories.

Categories now appear in most branches of mathematics, some areas of theoretical computer science where they correspond to types, and mathematical physics where they can be used to describe vector spaces.

In mathematics, specifically general topology and metric topology, a compact space is a mathematical space in which any infinite collection of points sampled from the space must — as a set — be arbitrarily close to some point of the space.

It is also a tool used in branches of mathematics including combinatorics, abstract algebra, and mathematical analysis.

In mathematics, particularly theoretical computer science and mathematical logic, the computable numbers, also known as the recursive numbers or the computable reals, are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm.

The classification theorem has applications in many branches of mathematics, as questions about the structure of finite groups ( and their action on other mathematical objects ) can sometimes be reduced to questions about finite simple groups.

In mathematics and, in particular, functional analysis, convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions, giving the area overlap between the two functions as a function of the amount that one of the original functions is translated.

A famous example of his leadership in mathematics is his 1900 presentation of a collection of problems that set the course for much of the mathematical research of the 20th century.

Hilbert is known as one of the founders of proof theory and mathematical logic, as well as for being among the first to distinguish between mathematics and metamathematics.

The mathematical community as a whole could enlist in problems, which he had identified as crucial aspects of the areas of mathematics he took to be key.

As he began to understand physics and how physicists were using mathematics, he developed a coherent mathematical theory for what he found, most importantly in the area of integral equations.