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Basic concepts of algebra
{b^{2}-4ac}}}{2a}}}}}} Elementary algebra, also known as high school algebra or college algebra, encompasses the basic concepts of algebra. It is often contrasted
Elementary_algebra
Branch of mathematics
variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication. Elementary algebra is the main form
Algebra
Algebraic manipulation of "true" and "false"
mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables
Boolean_algebra
Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until
History_of_algebra
Type of mathematical function
enumerated, all algebraic functions, and all functions obtained by roots of a polynomial whose coefficients are elementary. The elementary functions were
Elementary_function
Mathematical operation
mathematics, a basic algebraic operation is a mathematical operation similar to any one of the common operations of elementary algebra, which include addition
Algebraic_operation
Branch of mathematics
Linear algebra is the branch of mathematics concerning linear equations such as a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b
Linear_algebra
Number
The role of 0 as additive identity generalizes beyond elementary algebra. In abstract algebra, 0 is commonly used to denote a zero element, which is
0
Branch of mathematics
20th century to distinguish it from older parts of algebra, and more specifically from elementary algebra, the use of variables to represent numbers in computation
Abstract_algebra
Mathematical technique
variables, apart from the elementary symbolic algebra: Expectation algebra, Variance algebra, Covariance algebra, Moment algebra, etc. Considering two random
Algebra_of_random_variables
Boolean algebra
In mathematics and abstract algebra, the two-element Boolean algebra is the Boolean algebra whose underlying set (or universe or carrier) B is the Boolean
Two-element_Boolean_algebra
Algebraic expansion of powers of a binomial
21\quad 7\quad 1\end{array}}} In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial
Binomial_theorem
Finding values for variables that make an equation true
using the methods of elementary algebra. Smaller systems of linear equations can be solved likewise by methods of elementary algebra. For solving larger
Equation_solving
Property involving two mathematical operations
{\displaystyle x\cdot (y+z)=x\cdot y+x\cdot z} is always true in elementary algebra. For example, in elementary arithmetic, one has 2 ⋅ ( 1 + 3 ) = ( 2 ⋅ 1 ) + ( 2
Distributive_property
Overview of and topical guide to discrete mathematics
fixed integer Successor function – Elementary operation on a natural number Elementary algebra – Basic concepts of algebra Left-hand side and right-hand side
Outline of discrete mathematics
Outline_of_discrete_mathematics
Matrix which differs from the identity matrix by one elementary row operation
(2006), Linear Algebra: A Modern Introduction (2nd ed.), Brooks/Cole, ISBN 0-534-99845-3 Anton, Howard (2005), Elementary Linear Algebra (Applications
Elementary_matrix
Islamic mathematician (c. 780 – c. 850)
to be called "the father of algebra" than Diophantus because al-Khwarizmi is the first to teach algebra in an elementary form and for its own sake, Diophantus
Al-Khwarizmi
Class of mathematical expression
other number a {\displaystyle a} . Following the ordinary rules of elementary algebra while allowing division by zero can create a mathematical fallacy
Division_by_zero
Formula that provides the solutions to a quadratic equation
In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation. Other ways of solving quadratic
Quadratic_formula
Mnemonic for finding the product of two binomial functions
In elementary algebra, FOIL is a mnemonic for the standard method of multiplying two binomials—hence the method may be referred to as the FOIL method.
FOIL_method
dimensions (using techniques from algebraic geometry). It is named after Suren Arakelov. Arithmetic 1. Also known as elementary arithmetic, the methods and
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Symbolic description of a mathematical object
"semantic equality", that is, both expressions "mean the same thing." In elementary algebra, a variable in an expression is a letter that represents a number
Expression_(mathematics)
these solutions. Pre-algebra Elementary algebra Boolean algebra Abstract algebra Linear algebra Universal algebra An algebraic equation is an equation
Outline_of_algebra
Practical mathematics used in business
analysis. Mathematics typically used in commerce includes elementary arithmetic, elementary algebra, statistics and probability. For some management problems
Business_mathematics
Mathematical expression using basic operations
mathematics, an algebraic expression is an expression built up from constants (usually, algebraic numbers), variables, and the basic algebraic operations:
Algebraic_expression
Property of a mathematical operation
non-associative algebras, which have also an addition and a scalar multiplication. Examples are the octonions and Lie algebras. In Lie algebras, the multiplication
Associative_property
Relating coefficients and roots of a polynomial
distinct) complex roots r1, r2, ..., rn by the fundamental theorem of algebra. Vieta's formulas relate the polynomial coefficients to signed sums of
Vieta's_formulas
Functional equation
additive function. Over the rational numbers, it can be shown using elementary algebra that there is a single family of solutions, namely f : x ↦ c x {\displaystyle
Cauchy's_functional_equation
Branch of mathematics that studies algebraic structures
algebra in Wiktionary, the free dictionary. In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures
List of abstract algebra topics
List_of_abstract_algebra_topics
Mathematical software
as number theory, group theory, or teaching of elementary mathematics. General-purpose computer algebra systems aim to be useful to a user working in any
Computer_algebra_system
Algebraic structure used in analysis
quantum mechanics and particle physics. An elementary example (not directly coming from an associative algebra) is the 3-dimensional space g = R 3 {\displaystyle
Lie_algebra
First letter of the Latin alphabet
and c", and this convention is still often followed, especially in elementary algebra. In geometry, capital Latin letters are used to denote objects including
A
Equation that is satisfied for all values of the variables
a+0=a} and a + ( − a ) = 0 {\displaystyle a+(-a)=0} , form the basis of algebra, while other identities, such as ( a + b ) 2 = a 2 + 2 a b + b 2 {\displaystyle
Identity_(mathematics)
Removal of square roots from denominators
In elementary algebra, root rationalisation (or rationalization) is a process by which radicals in the denominator of an algebraic fraction are eliminated
Rationalisation_(mathematics)
Topics referred to by the same term
Look up algebra in Wiktionary, the free dictionary. Algebra may refer to: Elementary algebra Universal algebra Abstract algebra Linear algebra Relational
Algebra_(disambiguation)
Dimension of the column space of a matrix
In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns. This corresponds to the maximal
Rank_(linear_algebra)
Mathematical polynomial formula
a b + b 2 ) {\displaystyle a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})} in elementary algebra. Binomial numbers generalize this factorization to higher odd powers
Sum_of_two_cubes
Symbol connecting formulas in logic
comes from Boole's interpretation of logic as an elementary algebra over the two-element Boolean algebra; other notations include V {\displaystyle \mathrm
Logical_connective
Number that, when added to the original number, yields the additive identity
negation is closely related to subtraction and is important in solving algebraic equations. Not all sets where addition is defined have an additive inverse
Additive_inverse
Topics referred to by the same term
property of binary operations that generalises the distributive law from elementary algebra Distribution problems, a common type of problems in combinatorics
Distribution
Polynomial that has three terms
In elementary algebra, a trinomial is a polynomial consisting of three terms or monomials. 3 x + 5 y + 8 z {\displaystyle 3x+5y+8z} with x , y , z {\displaystyle
Trinomial
Topics referred to by the same term
Libraries Elementary abelian group, an abelian group in which every nontrivial element is of prime order Elementary algebra Elementary arithmetic Elementary charge
Elementary
Mathematical technique
In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can
Cross-multiplication
Branch of mathematics
calculus. Calculus provides a generalization of concepts from elementary geometry and algebra. For example, instead of describing the slope of a straight
Calculus
Collection of mathematical objects
ISBN 978-1-285-60843-3. Bracken, Laura; Miller, Ed (15 February 2013). Elementary Algebra. Cengage. p. 36. ISBN 978-0-618-95134-5. Frank Ruda (6 October 2011)
Set_(mathematics)
American standardized test used for college admissions
approximately 14 covering pre-algebra, 10 elementary algebra, 9 intermediate algebra, 14 plane geometry, 9 coordinate geometry, and 4 elementary trigonometry questions
ACT_(test)
Mathematical process used for removing subexpressions from a mathematical expression
execution time of numerical algorithms. Al-Jabr Elementary algebra Equation "How to Cancel out in basic algebra". WonderHowTo. 22 April 2010. Retrieved 2022-08-12
Cancelling_out
Method of problem-solving
science, the method is called generate and test (brute force). In elementary algebra, when solving equations, it is called guess and check. This approach
Trial_and_error
9th-century Arabic work on algebra
the second degree. It was the first text to teach elementary algebra, and the first to teach algebra for its own sake. It also introduced the fundamental
Al-Jabr
Study of systems of inequalitites
mathematics, real algebraic geometry is the sub-branch of algebraic geometry studying real algebraic sets, i.e. real-number solutions to algebraic equations with
Real_algebraic_geometry
Algebra theorem about convex functions
Karamata, also known as the majorization inequality, is a theorem in elementary algebra for convex and concave real-valued functions, defined on an interval
Karamata's_inequality
Field in mathematics similar to the real numbers
p. 177 McNaughton, Robert (1953). "Review: A decision method for elementary algebra and geometry by A. Tarski" (PDF). Bull. Amer. Math. Soc. 59 (1): 91–93
Real_closed_field
Polynomial equation of degree 4
the solution to the quartic in 1540, but since this solution, like all algebraic solutions of the quartic, requires the solution of a cubic to be found
Quartic_equation
Circle associated with a quadratic equation
contains an analogous circle construction, it was presented solely in elementary geometric terms without the notion of a Cartesian coordinate system or
Carlyle_circle
Algebra associated to any vector space
In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle
Exterior_algebra
Mathematical formula expressing equality
polynomial equations. Modern algebraic geometry is based on more abstract techniques of abstract algebra, especially commutative algebra, with the language and
Equation
Sort of mathematical expression
In algebra, an algebraic fraction is a fraction whose numerator and denominator are algebraic expressions. Two examples of algebraic fractions are 3 x
Algebraic_fraction
Polish–American mathematician (1901–1983)
his work on model theory, metamathematics, and algebraic logic, he also contributed to abstract algebra, topology, geometry, measure theory, mathematical
Alfred_Tarski
The product of two nonzero elements is nonzero
In algebra, the zero-product property states that the product of two nonzero elements is nonzero. In other words, if a b = 0 , then a = 0 or b =
Zero-product_property
Method for solving quadratic equations
In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form a x 2 + b x + c {\displaystyle \textstyle
Completing_the_square
Mathematical operation with only one operand
In mathematics, a unary operation is an operation with only one operand, i.e. a single input. This is in contrast to binary operations, which use two operands
Unary_operation
Property of some mathematical operations
assumed. Thus, this property was not named until the 19th century, when new algebraic structures started to be studied. A binary operation ∗ {\displaystyle
Commutative_property
Number in {..., –2, –1, 0, 1, 2, ...}
numbers. In algebraic number theory, integers are sometimes called rational integers to distinguish them from the more general algebraic integers. In
Integer
Teaching, learning, and scholarly research in mathematics
to all students The teaching of practical mathematics (arithmetic, elementary algebra, plane and solid geometry, trigonometry, probability, statistics)
Mathematics_education
Brackets as used in mathematical notation
thickness, a lot of angle quotation marks and deprecated characters. In elementary algebra, parentheses ( ) are used to specify the order of operations. Terms
Bracket_(mathematics)
Polynomial equation of degree 3
In algebra, a cubic equation in one variable is an equation of the form a x 3 + b x 2 + c x + d = 0 {\displaystyle ax^{3}+bx^{2}+cx+d=0} in which a is
Cubic_equation
relativity, and mathematical tools, spanning from elementary algebra and hyperbolic functions, to linear algebra and group theory. This article provides a few
Derivations of the Lorentz transformations
Derivations_of_the_Lorentz_transformations
Certain type of mistaken proof
Mathematical fallacies exist in many branches of mathematics. In elementary algebra, typical examples may involve a step where division by zero is performed
Mathematical_fallacy
Value that makes no change when added
x. One of the most familiar additive identities is the number 0 from elementary mathematics, but additive identities occur in other mathematical structures
Additive_identity
Type of binary relation
Transitive relation Type Binary relation Field Elementary algebra Statement A relation R {\displaystyle R} on a set X {\displaystyle X} is transitive if
Transitive_relation
Puzzle of reconstructing equations that have been enciphered into words
useful as a motivation and source of exercises in the teaching of elementary algebra. Verbal arithmetic puzzles are quite old and their inventor is unknown
Verbal_arithmetic
Term in an algebraic expression which does not contain any variables
constant term (sometimes referred to as a free term) is a term in an algebraic expression that does not contain any variables and therefore is constant
Constant_term
High school curriculum in the Philippines
Educations' Engineering and Science Education Program, the Special Science Elementary School was established, to serve as feeder school for science high schools
Engineering and Science Education Program (Philippines)
Engineering_and_Science_Education_Program_(Philippines)
Mathematical statement that two values are not equal
In mathematics, an inequation is a statement that either an inequality (relations "greater than" and "less than", < and >) or a relation "not equal to"
Inequation
true and false, usually denoted 1 and 0, respectively. Contrary to elementary algebra, where the values of the variables are numbers and the prime operations
Glossary_of_computer_science
Branch of elementary mathematics
number theory include elementary number theory, analytic number theory, algebraic number theory, and geometric number theory. Elementary number theory studies
Arithmetic
Problem-solving technique
In elementary algebra, the unitary method is a problem-solving technique taught to students as a method for solving word problems involving proportionality
Unitary_method
American author
(1979). Elementary Algebra. ISBN 9780716710479. Teacher's Guide: Harold R. Jacobs. Teacher's Guide to Elementary Algebra. ISBN 9780716710752. Elementary Algebra
Harold_R._Jacobs
In mathematics, the method of equating the coefficients is a way of solving a functional equation of two expressions such as polynomials for a number of
Equating_coefficients
Mathematical proofs of basic properties of addition of the natural numbers
This article contains mathematical proofs for some properties of addition of the natural numbers: the additive identity, commutativity, and associativity
Proofs involving the addition of natural numbers
Proofs_involving_the_addition_of_natural_numbers
Polynomial function of degree 4
In algebra, a quartic function is a function of the form f ( x ) = a x 4 + b x 3 + c x 2 + d x + e , {\displaystyle f(x)=ax^{4}+bx^{3}+cx^{2}+dx+e,} where
Quartic_function
Middle-school math class in the U.S.
for the study of algebra. Usually, Algebra I is taught in the 8th or 9th grade. As an intermediate stage after arithmetic, pre-algebra helps students pass
Pre-algebra
Expression of symbolic information
formula. However, in some areas mathematics, and in particular in computer algebra, formulas are viewed as expressions that can be evaluated to true or false
Formula
Type of mathematical expression
used to construct polynomial rings and algebraic varieties, which are central concepts in algebra and algebraic geometry. The word polynomial joins two
Polynomial
Polynomial equation of degree two
Schmidt, Philip (2004), Schaum's Outline of Theory and Problems of Elementary Algebra, The McGraw-Hill Companies, ISBN 978-0-07-141083-0, Chapter 13 §4
Quadratic_equation
Mathematical technique for simplification
Variable changes for differentiation and integration are taught in elementary calculus and the steps are rarely carried out in full. The very broad
Change_of_variables
Method for simplifying equations
solutions were introduced. Richard N. Aufmann; Joanne Lockwood (2012). Algebra: Beginning and Intermediate (3 ed.). Cengage Learning. p. 88. ISBN 978-1-133-70939-8
Clearing_denominators
Mathematical polynomial factorization
)}\\&=(x^{2}+2xy+2y^{2})\cdot (x^{2}-2xy+2y^{2}).\end{aligned}}} Beyond its use in elementary algebra, it can also be used in number theory to factorize integers of the
Sophie_Germain's_identity
Mathematical function
In mathematics, specifically in commutative algebra, the elementary symmetric polynomials are one type of basic building block for symmetric polynomials
Elementary symmetric polynomial
Elementary_symmetric_polynomial
Mathematical identity of polynomials
In elementary algebra, a difference of two squares is one squared number (the number multiplied by itself) subtracted from another squared number. Every
Difference_of_two_squares
Principle in geometry and linear algebra
generalization of the method of completing the square from elementary algebra. In linear algebra and functional analysis, the principal axis theorem is a
Principal_axis_theorem
Types of solutions in mathematics
implications from being bidirectional. One of the basic principles of algebra is that one can multiply both sides of an equation by the same expression
Extraneous and missing solutions
Extraneous_and_missing_solutions
Procedure of abstract algebra
Clifford, Alfred Hoblitzelle; Preston, Gordon Bamford (1961). The algebraic theory of semigroups. Vol. I. Mathematical Surveys, No. 7. Providence
Light's_associativity_test
Change of the sign of a square root
In mathematics, the conjugate of an expression of the form a + b d {\displaystyle a+b{\sqrt {d}}} is a − b d , {\displaystyle a-b{\sqrt {d}},} provided
Conjugate_(square_roots)
Algebraic structure with addition, multiplication, and division
rational numbers do. A field is thus a fundamental algebraic structure that is widely used in algebra, number theory, and many other areas of mathematics
Field_(mathematics)
Curve generated by rolling a circle inside another circle with 4x or (4/3)x the radius
therefore, a real algebraic curve of degree six. The polynomial equation may be derived from Leibniz's equation by elementary algebra: x 2 / 3 + y 2 /
Astroid
Multiplicative factor in a mathematical expression
coefficient. Though coefficients are frequently viewed as constants in elementary algebra, they can also be viewed as variables as the context broadens. For
Coefficient
Subfield of mathematics
publisher location (link) Tarski, Alfred (1948). A decision method for elementary algebra and geometry. Santa Monica CA: RAND Corporation. Turing, Alan M. (1939)
Mathematical_logic
Sanskrit word for "rule of three"
pre-modern era to denote what is known as the "rule of three" in elementary mathematics and algebra. In the contemporary mathematical literature, the term "rule
Trairāśika
Rational fractions as sums of simple terms
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the
Partial fraction decomposition
Partial_fraction_decomposition
ELEMENTARY ALGEBRA
ELEMENTARY ALGEBRA
ELEMENTARY ALGEBRA
ELEMENTARY ALGEBRA
Boy/Male
Tamil
Mountain
Boy/Male
American, Australian, British, Christian, English
From the Brook; Place Name
Boy/Male
Hindu, Indian
Lord Shiva; King
Girl/Female
Arabic
One of the Lovers
Boy/Male
Australian, German, Italian, Latin, Spanish
Lucky; Fortunate; Enjoying Good Luck
Boy/Male
Hindu
Place of farms
Girl/Female
Muslim
Praised
Female
English
English name, derived from the name of the gemstone, from Greek opallios, from Sanskrit utpala, OPAL means "gem, precious stone." This is the birthstone for the month of October.
Girl/Female
Yiddish
Bitter.
Female
Hebrew
(עַלִּיזָה) Hebrew name ALEEZA means "joy."
ELEMENTARY ALGEBRA
ELEMENTARY ALGEBRA
ELEMENTARY ALGEBRA
ELEMENTARY ALGEBRA
ELEMENTARY ALGEBRA
n.
An elementary piece of the mechanism of a lock.
a.
Pertaining to one of the four elements, air, water, earth, fire.
a.
Relating to hypostasis, or substance; hence, constitutive, or elementary.
a.
Having only one principle or constituent part; consisting of a single element; simple; uncompounded; as, an elementary substance.
n.
Unorganized material; elementary matter.
n.
The doctrine of the elementary requisites of mere thought.
a.
Pertaining to aliment or food, or to the function of nutrition; nutritious; alimental; as, alimentary substances.
a.
Elementary.
a.
Capable of being leased; held by tenants.
adv.
According to elements; literally; as, the words, "Take, eat; this is my body," elementally understood.
n.
The whole alimentary, or enteric, canal.
a.
Pertaining to the elements, first principles, and primary ingredients, or to the four supposed elements of the material world; as, elemental air.
a.
Pertaining to rudiments or first principles; rudimentary; elementary.
a.
Regulative.
a.
Combined with arsenic; -- said some elementary substances or radicals; as, arseniureted hydrogen.
a.
Elementary; rudimental.
a.
Elementary.
n.
The state of being elementary; original simplicity; uncompounded state.
a.
Pertaining to, or treating of, the elements, rudiments, or first principles of anything; initial; rudimental; introductory; as, an elementary treatise.
n.
Elementariness.