Algebra Encyclopedia

Algebra Encyclopedia

If you would like to prepare for school subjects or simply increase your general knowledge, then enjoy our algebra encyclopedia. We tried to focus only on very important terms and definitions. We also kept our terminology very brief so that you absorb the concept more quickly and easily.

Algebra Glossary (Page 1)

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ABSCISSA: The horizontal axis, or the first coordinate in an ordered pair.
ABSOLUTE MAXIMUM: The highest point on a graph, especially over a specified domain. It is the greatest value of f(x) over a defined interval of x, provided y=f(x).
ABSOLUTE MINIMUM: The lowest point on a graph, especially over a specified domain. It is the least value of f(x) over a defined interval of x, provided y=f(x).
ABSOLUTE VALUE: The absolute value of a number is the distance the number is from the zero point on the number line. The absolute value of a number or an expression is always greater than or equal to zero (i.e. Nonnegative).
ACCURACY: The quality of approaching an exact value. Distinct from precision, accuracy means to approach correctness, to tend toward an established value.
ADDING INTEGERS: To ADD integers with the same sign, add their absolute values. Give the result the same sign as the integers. To ADD integers with different signs, SUBTRACT the lesser absolute value from the greater absolute value. Give the result the same sign as the integer with the greater absolute value.
ADDITION: A mathematical process to combine numbers and/or variables into an equivalent quantity, number or algebraic expression.
ADDITIVE INVERSE FOR MATRICES: A matrix when added to another equals the Zero Matrix.
ALGEBRA: A language that helps translate real-life situations into mathematical form so that we can analyze change and answer the question "What if?".
ALGEBRAIC EXPRESSION: An expression consisting of one or more numbers and variables along with one or more arithmetic operations.
ALGORITHM: A sequence of steps to accomplish a familiar task; a recipe.
ALPHA: The first letter of the Greek alphabet.
ALTERNATING SERIES: A series in which successive terms have opposite signs. Every other term is positive; every other term is negative.
ARGUMENT OF A FUNCTION: The term or expression upon which a function operates. In y=f(x), the argument of the function is x.
ARGUMENT OF A VECTOR: The angle at which a vector is directed.
ARITHMETIC MEAN: What we generally consider to be the average. The sum of a set of values divided by the cardinal number of the set of values.
ARITHMETIC OPERATION: A mathematical process of addition, subtraction, multiplication or division.
ARITHMETIC PROGRESSION: A series of terms where successive terms are obtained by addition of a constant.
ARITHMETIC SEQUENCE: A series of terms where successive terms are obtained by addition of a constant.
ARITHMETIC SERIES: Akin to Arithmetic Progressions and Arithmetic Sequences, the series typically reflects an addition operator between terms, as a sum.
ASYMPTOTE: A line (or curve) that a function approaches without actually reaching the line as the domain either grows unbounded or approaches a limit.
AUGMENTED MATRIX: A matrix form for a linear system of equations where the number of columns is one greater than the number of rows, the final column typically coming from the constants in the linear equations.
AVERAGE: Most commonly, average means the arithmetic mean; we sum the values and divide that sum by the number of numbers. The average between two real values is the midpoint between those values.
AVERAGE RATE OF CHANGE: The change in value divided by elapsed time.
AXES: Two perpendicular number lines that are used to locate points in a coordinate plane. By convention, the x-axis is the horizontal line and the y-axis is the vertical line.
AXIOM: Accepted without proof (unlike a theorem), an axiom is readily understood and regarded as fact.
AXIS: In physics, a line about which a body rotates. In mathematics, a line that divides a plane or space into two equal halves, typically demarcated in units.
BASE, EXPONENTIAL: The value being raised by powers as exponents; the number being raised to the power.
BEST-FIT LINE: A line drawn so it is close to most or all of the data points in a graph.A best-fit line is described as strong or weak depending on how close the data points are on average.
BETA: Beta is the second letter of the Greek alphabet.
BICONDITIONAL: A biconditional statement has literally two conditions. The classic If-Then statement is the biconditional with a hypothesis and conclusion.
BINOMIAL: A binomial has two terms. Terms are usually separated by plus signs or minus signs.
BINOMIAL COEFFICIENTS: Binomial coefficients are found in Pascal's Triangle. We use these coefficients to raise binomials to successive powers as well as to determine the number of combinations or ways we can take a number of objects from a set of objects. Statistics and probability calculations make significant use of binomial coefficients.
BINOMIAL PROBABILITY: When outcomes are of a binary nature, the logic of two states (high or low, true or false, or the ones and zeroes of computer data streams) we can employ techniques of binomial probability, with coefficients from Pascal's Triangle, to determine the likelihood of potential events or outcomes.
BINOMIAL THEOREM: The Binomial Theorem affords the use of coefficients to calculate probabilities that are determined with the logic of two states. In situations where outcomes are either true or false, high or low, or the 1 or 0 of binary data streams, the Binomial Theorem gives us efficient calculations for likelihoods of events.
BOUNDARY: Some functions are bounded, some are not. Some regions are bounded, some are not. To be bounded means to have a limit; its extent only goes so far, and then it stops or ends.
BOUNDED FUNCTION: A bounded function approaches or reaches a limit. If a function goes toward infinity it is generally considered unbounded.
BOX-AND-WHISKER PLOT: In statistical data, a box-and-whisker plot is sometimes used to graphically represent quartiles. Quartiles are the extremes of the body of data, as well as the 25th, 50th and 75 percentiles.
BRACES: Braces act just like parentheses. Always (almost) used in pairs, braces look like this: { }.
BRACKETS: Brackets act just like parentheses, coming in pairs to group data or terms.
CARDINAL NUMBER: The number of objects or elements within a set is the Cardinal Number of the set.
CARTESIAN COORDINATES: The familiar x-y coordinate plane is called the plane of Cartesian Coordinates; it is named for Rene Descartes.
CARTESIAN PLANE: The Cartesian Plane contains the familiar x-axis and y-axis in which we plot ordered pairs. It is the familiar Rectangular Coordinate system.
CHANGE-OF-BASE FORMULA: There is an easy way to change the bases between logarithms. A simple formula, the Change-of-Base formula is an acquired taste.
CHI: The twenty-second letter of the Greek alphabet.
CLOSED INTERVAL: A segment of the real number line including the endpoints.
COEFFICIENT: The numerical factor in a term. In the term 4x, 4 is the coefficient. In the term 4x/5 ; 4/5 is the coefficient. Note that 4x/5 can also be written as ( 4/5 )x.
COEFFICIENT MATRIX: A matrix comprised of coefficients which can be used to solve a system of equations.
COFACTOR: Typically the result of taking a determinant, it is a number associated with an element in a matrix.
COLUMN, MATRIX: Strictly speaking, a Column Matrix is often a single column. More generally, a column is a vertical array of elements within a matrix.
COMBINATIONS: Combinations are calculated to be the number of ways that a number of objects may be selected from a group of objects.
COMBINATORICS: The branch of math that provides calculations for the selection of a number of elements from a set is called Combinatorics.
COMMON LOGARITHM: The base-ten logarithm is often called the Common Logarithm.
COMMON RATIO: In a geometric progression, subsequent terms are obtained by multiplication of terms by a constant called the Common Ratio.
COMPLEMENT OF AN EVENT: The complement of an event pertains to probability. If the probability of an event is x, then the probability of the complement of that event is 100 percent minus x.
COMPLEX CONJUGATE: The Complex Conjugate of (a + bi) is (a - bi). The Complex Conjugate of (c - di) is (c + di).
COMPLEX FRACTION: A fraction that has one or more fractions in the numerator or denominator.
COMPLEX NUMBER: All numbers, as it turns out, are complex. When the "imaginary part" has a zero coefficient, the number is purely real.
COMPLEX PLANE: The complex number plane is required to map or plot complex numbers because the complex numbers themselves have two components.
COMPOSITE NUMBER: Composite Numbers relate to positive integers that are not prime. If a positive integer has factors other than itself and one, it is a Composite Number.
COMPOUND EVENT: A compound event consists of two or more simple events (i.e. The tossing of two or more coins).
COMPOUND INEQUALITY: Two inequalities connected by AND or OR.
COMPOUND INTEREST: When the Time Value of Money generates interest and that interest is added to the principal to increase the amount of money to which subsequent interest is added, this is Compound Interest.
COMPUTATION: Computation is the act of taking values and logical mathematical steps to make a calculation.
CONCLUSION: When mathematical conclusions are valid the laws of math and science have been adhered to, and a logical approach has been taken. Sometimes conclusions are invalid because scientific or mathematic rigor has not been adhered to. Reason and judgment are often important to reaching sound or valid conclusions.
CONIC SECTION: Any of the various geometric entities that are formed by slicing a cone (or double cone) are termed Conic Sections. The list includes: circles, ellipses, parabolas, and hyperbolas.
CONJUGATES: Conjugates multiply to simpler entities based on changing the operator between terms of each conjugate from positive to negative, or vice versa.
CONSISTENT: A system of equations is said to be consistent when it has at least one ordered pair that satisfies both equations.
CONSISTENT SYSTEM OF EQUATIONS: When a system of equations has at least one solution (and most often a unique solution) the equations are said to be Consistent.
CONSTANT: A mathematical value that never changes is said to be constant. Real numbers are constants because their value never changes. In a polynomial, a term with a variable (or variables) raised to the zero power is constant.
CONSTANTS: A monomial term that lacks a variable component.
CONTINUOUS: A function is considered Continuous if its graph has no gaps, no holes, no steps, and no cusps or discontinuities.
CONTINUOUS COMPOUNDING: When an entity experiences Continuous Compounding it grows unceasingly and constantly, that is, the addition of some portion of its size to its size happens all of the time. Bacterial growth and population growth are often considered to be functions of Continuous Compounding.
CONTINUOUS FUNCTION: When the graph of a function has no holes, no gaps, no steps, or no discontinuities, then it is considered Continuous. It may have cusps.
COORDINATE: A value associated with the location of a point is a Coordinate. In one dimension a Coordinate is a single value. In two dimensions, a point is defined by two Coordinates as an ordered pair.
COORDINATE PLANE: Two-dimensional entities are graphed or plotted in a plane, such as the rectangular plane or Cartesian Plane. Two-dimensional polar coordinates are also plotted in a plane. It requires an ordered pair to specify a location in a plane.
CORRELATION: When two variables have a strong linear relationship, either increasing proportionally or one variable decreasing as the other increases, we say there is (strong) Correlation between the variables.
CORRELATION COEFFICIENT: We typically use "r" for the Correlation Coefficient. When two variables are strongly correlated, that is, have a strong linear relationship, r will have a value that approaches either 1 or -1, depending on whether the variables increase with respect to each other.
COUNTABLE: In common language, countable just means reasonably enumerated or countable, as in there are not too many objects to physically count. In human terms, the grains of sand in the Sahara Desert are not countable. But mathematically they actually are. So Countable means something a little different to the mathematicians.
COUNTING NUMBERS: The set of counting (aka "natural") numbers can be expressed as {1,2,3,...}. This set is identical to the set of whole numbers, less the number zero. Counting numbers are not negative.
CRAMER'S RULE: Cramer's Rule provides a matrix manipulation to solve simultaneous equations.
CROSS PRODUCT: A product of vectors that generates another vector is often a Cross Product.
CUBE ROOT: The Cube Root of a real value is the number that when raised to the third power equates to the original real value.
CUBIC: A Cubic is a third-order polynomial.
DECREASING: Decreasing means to lessen in extent or scope, to be reduced. A function is considered to be Decreasing if the values in the range decrease as the values from the domain increase.
DEDUCTIVE LOGIC: Deductive Logic is employed before events have transpired, before the fact.
DEGREE OF A MONOMIAL: The degree of a monomial is the sum of the exponents of its variables.
DEGREE OF A POLYNOMIAL: The degree of a polynomial is the degree of the term of the greatest monomial degree.
DEGREE, POLYNOMIAL: The Degree of a polynomial is the order, or highest power (term) of the polynomial.
DELTA: Delta is the fourth letter of the Greek alphabet. Upper-case Delta looks like a triangle and is used to mean "the change in...".
DENOMINATOR: The Denominator of a fraction is the number on the bottom; it is the divisor of the numerator.
DEPENDENT (EQUATIONS): A system of equations that has an infinite number of solutions.
DEPENDENT EVENT: An occurrence or outcome that is affected by previous occurrences or outcomes. The probability of drawing a red or black card from a deck of cards is affected by the colors of cards previously drawn.
DEPENDENT VARIABLE: When solving an equation for a given variable, that variable becomes the dependent variable. That is, its value depends upon the domain values chosen for the other variable. The dependent variable represents the range and is graphed on the y-axis.
DETERMINANT: A Determinant is a number associated with a square matrix. It may also be a cofactor, a number associated with a square array from a larger matrix.
DIAGONAL MATRIX: A square matrix with zero values everywhere except on the main diagonal (upper left to lower right) is termed a Diagonal Matrix.
DIFFERENCE: The result of a subtraction operation. Order matters! The difference of 6 and 3 equals 3. The difference of 3 and 6 equals -3.
DIMENSION, MATRIX: The Dimension of a matrix is its order, or size. We label the order of a matrix by its number of rows then its number of columns. A 4x3 matrix is read as "a four by three matrix" and has four rows and three columns.
DIRECT PROPORTION: When variables are in Direct Proportion to one another they have the relation that as one variable grows the other either increases or decreases by a constant multiplication factor. When y = kx, we say the variables are in Direct Proportion.
DIRECT VARIATION: Also direct proportion, Direct Variation describes the relation y = kx.

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