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Serial Exponentiation
In mathematics and computer programming, the order of operations (or operator precedence) is a collection of rules that reflect conventions about which procedures to perform first in order to evaluate a given mathematical expression. For example, in mathematics and most computer languages, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation. Thus, the expression is interpreted to have the value , and not . When exponents were introduced in the 16th and 17th centuries, they were given precedence over both addition and multiplication, and could be placed only as a superscript to the right of their base. Thus and . These conventions exist to eliminate notational ambiguity, while allowing notation to be as brief as possible. Where it is desired to override the precedence conventions, or even simply to emphasize them, parentheses ( ) can be used. For example, forces addition to precede multiplic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Operation
In mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two. More specifically, an internal binary operation ''on a set'' is a binary operation whose two domains and the codomain are the same set. Examples include the familiar arithmetic operations of addition, subtraction, and multiplication. Other examples are readily found in different areas of mathematics, such as vector addition, matrix multiplication, and conjugation in groups. An operation of arity two that involves several sets is sometimes also called a ''binary operation''. For example, scalar multiplication of vector spaces takes a scalar and a vector to produce a vector, and scalar product takes two vectors to produce a scalar. Such binary operations may be called simply binary functions. Binary operations are the keystone of most algebraic structures that are studie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mixed Division And Multiplication , a person who is of multiple races
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Mixed is the past tense of ''mix''. Mixed may refer to: * Mixed (United Kingdom ethnicity category), an ethnicity category that has been used by the United Kingdom's Office for National Statistics since the 1991 Census * ''Mixed'' (album), a compilation album of two avant-garde jazz sessions featuring performances by the Cecil Taylor Unit and the Roswell Rudd Sextet See also * Mix (other) * Mixed breed, an animal whose parents are from different breeds or species * Mixed ethnicity Mixed race people are people of more than one race or ethnicity. A variety of terms have been used both historically and presently for mixed race people in a variety of contexts, including ''multiethnic'', ''polyethnic'', occasionally ''bi-ethn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Slash (punctuation)
The slash is the oblique slanting line punctuation mark . Also known as a stroke, a solidus or several other historical or technical names including oblique and virgule. Once used to mark periods and commas, the slash is now used to represent division and fractions, exclusive 'or' and inclusive 'or', and as a date separator. A slash in the reverse direction is known as a backslash. History Slashes may be found in early writing as a variant form of dashes, vertical strokes, etc. The present use of a slash distinguished from such other marks derives from the medieval European virgule ( la, virgula, which was used as a period, scratch comma, and caesura mark. (The first sense was eventually lost to the low dot and the other two developed separately into the comma and caesura mark ) Its use as a comma became especially widespread in France, where it was also used to mark the continuation of a word onto the next line of a page, a sense later taken on by the hyphen .. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplication By Juxtaposition
Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a ''product''. The multiplication of whole numbers may be thought of as repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the ''multiplicand'', as the quantity of the other one, the ''multiplier''. Both numbers can be referred to as ''factors''. :a\times b = \underbrace_ For example, 4 multiplied by 3, often written as 3 \times 4 and spoken as "3 times 4", can be calculated by adding 3 copies of 4 together: :3 \times 4 = 4 + 4 + 4 = 12 Here, 3 (the ''multiplier'') and 4 (the ''multiplicand'') are the ''factors'', and 12 is the ''product''. One of the main properties of multiplication is th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Education In Australia
Mathematics education in Australia varies significantly between states, especially at the upper secondary level. Secondary New South Wales Higher School Certificate The Higher School Certificate (HSC) in NSW contains a number of mathematics courses catering for a range of abilities. There are four courses offered by the NSW Education Standards Authority (NESA) for HSC Study: *Mathematics Standard 1 or 2: A basic mathematics course containing precalculus concepts; the course is heavily based on practical mathematics used in everyday life. While the more advanced courses include statistical topics, this is the only course which introduces normal distributions, standard deviations and z-scores. These topics are alluded to in more advanced courses though not formally considered. *Mathematics Advanced: An advanced level calculus-based course with detailed study in probability and statistics, trigonometry, curve sketching, and applications of calculus. It is the highest level non-ext ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Education In The United Kingdom
Mathematics education in the United Kingdom is largely carried out at ages 5–16 at primary school and secondary school (though basic numeracy is taught at an earlier age). However voluntary Mathematics education in the UK takes place from 16 to 18, in sixth forms and other forms of further education. Whilst adults can study the subject at universities and higher education more widely. Mathematics education is not taught uniformly as exams and the syllabus vary across the countries of the United Kingdom, notably Scotland. History The School Certificate was established in 1918, for education up to 16, with the Higher School Certificate for education up to 18; these were both established by the Secondary Schools Examinations Council (SSEC), which had been established in 1917. 1960s The Joint Mathematical Council was formed in 1963 to improve the teaching of mathematics in UK schools. The Ministry of Education had been created in 1944, which became the Department of Education and Sc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Education In The United States
From kindergarten through high school, mathematics education in public schools in the United States has historically varied widely from state to state, and often even varies considerably within individual states. With the adoption of the Common Core Standards by 45 states, mathematics content across the country is moving into closer agreement for each grade level. Furthermore, the SAT, a standardized university entrance exam, has been reformed to better reflect the contents of the Common Core. Curricular content Each state sets its own curricular standards and details are usually set by each local school district. Although there are no federal standards, since 2015 most states have based their curricula on the Common Core State Standards in mathematics. The National Council of Teachers of Mathematics published educational recommendations in mathematics education in 1991 and 2000 which have been highly influential, describing mathematical knowledge, skills and pedagogical emphases f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mnemonics
A mnemonic ( ) device, or memory device, is any learning technique that aids information retention or retrieval (remembering) in the human memory for better understanding. Mnemonics make use of elaborative encoding, retrieval cues, and imagery as specific tools to encode information in a way that allows for efficient storage and retrieval. Mnemonics aid original information in becoming associated with something more accessible or meaningful—which, in turn, provides better retention of the information. Commonly encountered mnemonics are often used for lists and in auditory form, such as short poems, acronyms, initialisms, or memorable phrases, but mnemonics can also be used for other types of information and in visual or kinesthetic forms. Their use is based on the observation that the human mind more easily remembers spatial, personal, surprising, physical, sexual, humorous, or otherwise "relatable" information, rather than more abstract or impersonal forms of information. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distributivity
In mathematics, the distributive property of binary operations generalizes the distributive law, which asserts that the equality x \cdot (y + z) = x \cdot y + x \cdot z is always true in elementary algebra. For example, in elementary arithmetic, one has 2 \cdot (1 + 3) = (2 \cdot 1) + (2 \cdot 3). One says that multiplication ''distributes'' over addition. This basic property of numbers is part of the definition of most algebraic structures that have two operations called addition and multiplication, such as complex numbers, polynomials, matrices, rings, and fields. It is also encountered in Boolean algebra and mathematical logic, where each of the logical and (denoted \,\land\,) and the logical or (denoted \,\lor\,) distributes over the other. Definition Given a set S and two binary operators \,*\, and \,+\, on S, *the operation \,*\, is over (or with respect to) \,+\, if, given any elements x, y, \text z of S, x * (y + z) = (x * y) + (x * z); *the operation \,*\, is over ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monomial
In mathematics, a monomial is, roughly speaking, a polynomial which has only one term. Two definitions of a monomial may be encountered: # A monomial, also called power product, is a product of powers of variables with nonnegative integer exponents, or, in other words, a product of variables, possibly with repetitions. For example, x^2yz^3=xxyzzz is a monomial. The constant 1 is a monomial, being equal to the empty product and to x^0 for any variable x. If only a single variable x is considered, this means that a monomial is either 1 or a power x^n of x, with n a positive integer. If several variables are considered, say, x, y, z, then each can be given an exponent, so that any monomial is of the form x^a y^b z^c with a,b,c non-negative integers (taking note that any exponent 0 makes the corresponding factor equal to 1). # A monomial is a monomial in the first sense multiplied by a nonzero constant, called the coefficient of the monomial. A monomial in the first sense is a special c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vinculum (symbol)
\overline = 0. Y = \overline \sqrt /math> a-\overline = a − (b + c) Vinculum usage A vinculum () is a horizontal line used in mathematical notation for various purposes. It may be placed as an overline (or underline) over (or under) a mathematical expression to indicate that the expression is to be considered grouped together. Historically, vincula were extensively used to group items together, especially in written mathematics, but in modern mathematics this function has almost entirely been replaced by the use of parentheses. It was also used to mark Roman numerals whose values are multiplied by 1,000. Today, however, the common usage of a vinculum to indicate the repetend of a repeating decimal is a significant exception and reflects the original usage. History The vinculum, in its general use, was introduced by Frans van Schooten in 1646 as he edited the works of François Viète (who had himself not used this notation). However, earlier versions, such as using a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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