Glossary - A's

Abelian group A group that is also commutative.

Abscissa The horizontal coordinate in a two-dimensional system of rectangular coordinates, usually denoted by x.

Absolute value

Accuracy One speaks of an accurate statement in the sense that it is true and correct, or of an accurate computation in the sense that it contains no numerical error. Accurate to a certain decimal place means that all digits preceding and including the given one are correct.

Acre A unit commonly used in the United States system for measuring land. It contains 43,560 sq. ft.

Acute angle An angle whose measure is smaller than a right angle.

Acute triangle A triangle with three acute angles.

Adam's apportionment plan An apportionment plan in which the representation of an geographical area is determined by finding the quotient of the number of people in that area divided by the total number of people and then the result is rounded as follows: Any quotient with a decimal portion must be rounded up to the next whole number.

Addition One of the fundamental undefined operations applied to the set of counting numbers.

Addition law of exponents
To multiply two numbers with like bases, add the exponents; that is,
b^mbⁿ = b^m+n .

Addition law of logarithms
The logarithm of the product of two numbers is the sum of the logarithms of those numbers.  In symbols,
                                     log_b(AB) = log_bA + log_bB

Addition method The method of solution of a system of equations in which the coefficients of one of the variables are opposites so that when the equations are added, one of the variables is eliminated.

Addition of integers If the integers to be added have the same sign, the answer will also have that same sign and will have a magnitude equal to the sum of the absolute values of the given integers. If the integers to be added have opposite signs, the answer will have the sign of the integer with the larger absolute value, and will have a magnitude equal to the difference of the absolute values. Finally, if one or both of the given integers is 0, use the property that n + 0 = n for any integer n.

Addition of matrices [M] + [N] =[S] if and only if [M] and [N] are the same order and the entries of [S] are found by adding the corresponding entries of [M] and [N].

Addition of rational numbers

Addition principle

Addition property (of equations) The solution of an equation is unchanged by adding the same number to both sides of the equation.

Addition property of inequality The solution of an inequality is unchanged if you add the same number to both sides of the inequality.

Addition property of probabilities
For any events E and F, the probability of their union can be found by
                          P(E or F) = P(E) + P(F) - P(E and F)

Additive identity The number 0, which has the property that a + 0 = a for any number a.

Additive inverse See Opposite. The additive inverse of a matrix [M] is denoted by [M] and is defined by (1)[M].

Add-on interest It is a method of calculating interest and installments on a loan. The amount of interest is calculated according to the formula I = Prt and is then added to the amount of the loan. This sum, divided by the number of payments, is the amount of monthly payment.

Address Designation of the location of data within internal memory or on a magnetic disk or tape.

Adjacent angles Two angles are adjacent if they share a common side.

Adjacent side In a right triangle, an every angle is made up of two sides; one of those sides is the hypotenuse, and the other side is called the adjacent side.

Adjusted balance method A method of calculating credit card interest using the formula
I = Prt in which P is the balance owed after the current payment is subtracted.

Alabama Paradox An increase in the total numbers of items to be apportioned resulting in a loss for a group is called the Alabama Paradox

Algebra A generalization of arithmetic. Letters called variables are used to denote numbers, which are related by laws that hold (or are assumed) for any of the numbers in the set. The four main processes of algebra are (1) simplify, (2) evaluate, (3) factor, and
(4) solve.

Algebraic expression Any meaningful combination of numbers, variables, and signs of operation.

Alternate exterior angles Two alternate angles are angles on opposite sides of a transversal cutting two parallel lines, each having one of the lines for one of its sides. They are alternate exterior angles if neither lies between the two lines cut by the transversal.

Alternate interior angles Two alternate angles are angles on opposite sides of a transversal cutting two parallel lines, each having one of the lines for one of its sides. They are alternate interior angles if both lie between the two lines cut by the transversal.

Alternating series A series that alternates in sign.

Amortization The process of paying off a debt by systematically making partial payments until the debt (principal) and interest are repaid.

Amortization schedule A table showing the schedule of payments of a loan detailing the amount of each payment that goes to repay the principal and how much goes to pay interest.

Amortized loan A loan that is fully paid off with the last periodic payment.

Analytic geometry The geometry in which position is represented analytically (or by coordinates) and algebraic methods of reasoning are used for the most part.

And See Conjunction. In everyday usage, it is used to join together elements that are connected in two sets simultaneously.

AND-gate An electrical circuit that simulates conjunction; that is, the circuit is on when two switches are on.

Angle Two rays or segments with a common endpoint.

Angle of depression The angle between the line of sight to an object below measured from a horizontal.

Angle of elevation The angle between the line of sight to an object above measured from a horizontal.

Annual compounding In the compound interest formula, it is when n = 1.

Annual percentage rate The percentage rate charged on a loan based on the actual amount owed and the actual time it is owed. The approximation formula for annual percentage rate (APR) is APR = 2Nr/(N + 1).

Annuity A sequence of payments into or out of an interest-bearing account. If the payments are made into an interest-bearing account at the end of each time period, and if the frequency of payments is the same as the frequency of compounding, the annuity is called an ordinary annuity.

Antecedent See Conditional.

Antiderivative

Apportionment The problem of apportioning a legislative body.

Approval Voting The approval voting method allows each voter to cast one vote for each candidate who meets with his or her approval. The candidate with the most votes is declared the winner.

APR Abbreviation for annual percentage rate. See Compound interest formula.

Arc Part of the circumference of a circle.

Area A number describing the two-dimensional content of a set. Specifically, it is the number of square units enclosed in a plane figure.

Area formulas

Area function
The function that is the area below the x-axis, above by a function y = f (x), on the left by the y-axis, and on the right by the vertical line x = t. 

Area under a curve

Argument
(1) The statements and conclusion as a form of logical reasoning.
(2) In a logarithmic expression, log_bN, it is the number N.

Arithmetic mean
The arithmetic mean of the numbers a and b is (a + b)/2.

Arithmetic sequence
A sequence, each term of which is equal to the sum of the preceding term and a constant, written a₁, a₂ = a₁+ d, a₃ = a₁ + 2d, ...; the nth term of an arithmetic sequence is
a₁ + (n - 1)d, where a₁ is the first term and d is the common difference. Also called an arithmetic progression.  See also Sequence.

Arithmetic series
The indicated sum of the terms of an arithmetic sequencE. The sum of the terms is denoted by A₁and
                          A_n = (n/2)(a₁ + a_n)     or        A_n = (n/2)[2a₁ + (n - 1)d]

Arrangement Same as permutation.

Array An arrangement of items into rows and columns. See Matrix.

Arrow's impossibility theorem No social choice rule satisfies all six of the following conditions.

1. Unrestricted domain Any set of rankings possible; if there are n candidates, then there are n! possible rankings.
2. Decisiveness Given any set of individual rankings, the method produces a winner.
3. Symmetry and transitive The voting system should be symmetric and transitive over the set of all outcomes.
4. Independence of irrelevant alternatives If a voter prefers A to B with C as a possible choice, then the voter still prefers A to B when C is not a possible choice.
5. Pareto principle If each voter prefers A over B, then the group chooses A over B .
6. There should be no dictator.

Artificial intelligence A field of study devoted to computer simulation of human intelligence.

ASCII code A standard computer code used to facilitate the interchange of information among various types of computer equipment.

Assignment A computer term for setting the value of one variable to match the value of another.

Associative property
A property of grouping that applies to certain operations (addition and multiplication, for example, but not to subtraction or division): If a, b, and c are real numbers, then
                       (a + b) + c = a + (b + c)      and     (ab)c = a(bc)

Assuming the antecedent Same as direct reasoning.

Assuming the consequent A logical fallacy; same as the fallacy of the converse.

Augmented matrix A matrix that results after affixing an additional column to an existing matrix.

Average A single number that is used to typify or represent a set of numbers. In this book, it refers to the mean, median, or mode.

Average daily balance method A method of calculating credit card interest using the formula I = Prt in which P is the average daily balance owed for a current month, and t is the number of days in the month divided by 365.

Average rate of change

Axes The intersecting lines of a Cartesian coordinate system. The horizontal axis is called the x-axis, and the vertical axis is called the y -axis. The axes divide the plane into four parts called quadrants.

Axiom A statement that is accepted without proof.

Axis of a parabola The line through the focus of a parabola drawn perpendicular to the directrix.

Axis of symmetry A curve is symmetric with respect to a line, called the axis of symmetry, if for any point P on the curve, there is a point Q also on the curve such that the axis of symmetry is the perpendicular bisector of the line segment PQ .

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