# what is algebra

Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians. The structural properties of these non-numerical objects were then abstracted into algebraic structures such as groups, rings, and fields.

It includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields.

The associativity requirement is met, because for any integers a, b and c, (a + b) + c = a + (b + c). Algebra gives methods for writing formulas and solving equations that are much clearer and easier than the older method of writing everything out in words. [34] George Peacock was the founder of axiomatic thinking in arithmetic and algebra.

Example: x + 3 = 7 "x" is used in place of a value we don't know yet and is called the "unknown" or the "variable". are variables, and the letter

What Type of Mathematical Function Is This? Babylonian mathematics dates from as early as 1800 bc, as indicated by cuneiform texts preserved in clay tablets. x

The notion of binary operation is meaningless without the set on which the operation is defined. Elementary algebra differs from arithmetic in the use of abstractions, such as using letters to stand for numbers that are either unknown or allowed to take on many values. His book Treatise on Demonstrations of Problems of Algebra (1070), which laid down the principles of algebra, is part of the body of Persian mathematics that was eventually transmitted to Europe.

Here are the listed fundamental concepts in abstract algebra.

Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Zero is the identity element for addition and one is the identity element for multiplication. [12], The Hellenistic mathematicians Hero of Alexandria and Diophantus[13] as well as Indian mathematicians such as Brahmagupta continued the traditions of Egypt and Babylon, though Diophantus' Arithmetica and Brahmagupta's Brāhmasphuṭasiddhānta are on a higher level. Full curriculum of exercises and videos. Under the first operator (+) it forms an abelian group. = Please select which sections you would like to print: Corrections? Well, in Algebra we don't use blank boxes, we use a letter (usually an x or y, but any letter is fine). The inverse of a is 1/a, since a × 1/a = 1. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. Algebra, branch of mathematics in which arithmetical operations and formal manipulations are applied to abstract symbols rather than specific numbers. Algebra is a branch of mathematics that substitutes letters for numbers, and an algebraic equation represents a scale where what is done on one side of the scale is also done to the other side of the scale and the numbers act as constants.

By the time of Plato, Greek mathematics had undergone a drastic change. One such practical use of algebra would be if you were trying to determine how many balloons you started the day with if you sold 37 but still had 13 remaining.

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A quasi-group satisfies a requirement that any element can be turned into any other by either a unique left-multiplication or right-multiplication; however, the binary operation might not be associative.

For example, 4 is an integer, but its multiplicative inverse is ¼, which is not an integer. Updates? In fact, it took until the late 16th century to consolidate the modern concept of an equation as a single mathematical entity. Omissions? For two elements a and b in a set S, a ∗ b is another element in the set; this condition is called closure.

A polynomial expression is an expression that may be rewritten as a polynomial, by using commutativity, associativity and distributivity of addition and multiplication. Ultimately, the more a person knows about math, the greater the opportunity for that individual to succeed in the engineering, actuary, physics, programming, or any other tech-related field, and algebra and other higher maths are typically required courses for entrance to most colleges and universities. What Is the Distributive Property Law in Mathematics? Shortened to just algeber or algebra in Latin, the word eventually entered the English language during the fifteenth century, from either Spanish, Italian, or Medieval Latin. In his work, the term al-jabr referred to the operation of moving a term from one side of an equation to the other, المقابلة al-muqābala "balancing" referred to adding equal terms to both sides.

which satisfy the equation. That is, the order of the numbers does not affect the result. He also computed ∑n2, ∑n3 and used the method of successive approximation to determine square roots.[33]. Get exclusive access to content from our 1768 First Edition with your subscription. A related class of problems is finding algebraic expressions for the roots of a polynomial in a single variable. [30] He also developed the concept of a function. Other examples of sets include the set of all two-by-two matrices, the set of all second-degree polynomials (ax2 + bx + c), the set of all two dimensional vectors in the plane, and the various finite groups such as the cyclic groups, which are the groups of integers modulo n. Set theory is a branch of logic and not technically a branch of algebra. As a single word with an article or in the plural, "an algebra" or "algebras" denotes a specific mathematical structure, whose precise definition depends on the context.

Geometry is the branch of mathematics that deals with the shape of objects, their spatial relations, and the properties of the space the objects are in.

Sets: Rather than just considering the different types of numbers, abstract algebra deals with the more general concept of sets: a collection of all objects (called elements) selected by property specific for the set. Computer scientist and author Mark Jason Dominus writes on his blog, The Universe of Discourse: \"In the first phase you translate the problem into algebra, and then in the second phase you manipulate the symbols, almost mechanically, until the answer pops out as if by magic.\" While these manipulation rules derive from mathematical principles… The most important of these are rings and fields. This is because, in general, the multiplicative inverse of an integer is not an integer. First you calculate the difference of this 10 to this 4. Let us know if you have suggestions to improve this article (requires login). is unknown, but applying additive inverses can reveal its value: cannot be A field is a ring with the additional property that all the elements excluding 0 form an abelian group under ×. x It and other texts attest to the ability of the ancient Egyptians to solve linear equations in one unknown. Usually, the structure has an addition, multiplication, and scalar multiplication (see.

This article presents that history, tracing the evolution over time of the concept of the equation, number systems, symbols for conveying and manipulating mathematical statements, and the modern abstract structural view of algebra. {\displaystyle E} However, throughout this period there was no use of symbols—problems were stated and solved verbally. The notion that there exists such a distinct subdiscipline of mathematics, as well as the term algebra to denote it, resulted from a slow historical development. a This subject is widely used in many fields including medicine and accounting, but can also be used for everyday problem solving when it comes to unknown variables in mathematical equations. It is taught to students who are presumed to have no knowledge of mathematics beyond the basic principles of arithmetic. In E = mc2, the letters Gabriel Cramer also did some work on matrices and determinants in the 18th century. are considered. For the integers (a + b) × c = a × c + b × c and c × (a + b) = c × a + c × b, and × is said to be distributive over +. A linear equation is a first-degree equation, or one in which all the variables are only to the first power. 3 Researchers have found in multiple studies that students who take more high-quality math in high school are more likely to declare science, technology, engineering, and mathematics (STEM) majors in college. b

Such problems explained a procedure to be followed for solving a specific problem, rather than proposing a general algorithm for solving similar problems. The non-zero rational numbers form a group under multiplication. is a constant, the speed of light in a vacuum. and For example, x + y = z or b - 2 = 5 are algebraic equations, but 2 + 3 = 5 and 73 * 46 = 3,358 are not.

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