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)


ALPHA: The first letter of the Greek alphabet.
BETA: Beta is the second letter of the Greek alphabet.
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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