COMMON TERMS IN MATHEMATICS

COMMON TERMS IN MATHEMATICS

Absolute value: The magnitude of a number. It is the number with the sign (+ or -) removed and is symbolised using two vertical straight lines (|5|). Also called modulus.

Abstract number: A number with no associated units.

Acute angle: An angle with degree measure less than 90. See MathWorld: Geometry: Trigonometry: Angles.

Addition: The process of finding the sum of two numbers, which are called addend and the augend (sometimes both are called the addend).

Algorithm: Any mathematical procedure or instructions involving a set of steps to solve a problem.

Arctan: The inverse of the trigonometric function tangent shown as arctan(x) or tan-1(x). It is useful in vector conversions and calculations. See Wikipedia: Mathematics: Trigonometric Functions.

Arithmetic mean: M = (x1 + x2 + .... xn) / n (n = sample size).

Arithmetic sequence: A sequence of numbers in which each term (subsequent to the first) is generated by adding a fixed constant to its predecessor.

Associative property: A binary operation (*) is defined associative if, for a*(b*c) = (a*b)*c. For example, the operations addition and multiplication of natural numbers are associative, but subtraction and division are not.

Asymptote: A straight line that a curve approaches but never meets or crosses. The curve is said to meet the asymptote at infinity. In the equation y = 1/x, y becomes infinitely small as x increases but never reaches zero.

Axiom: Any assumption on which a mathematical theory is based.

Average: The sum of several quantities divided by the number of quantities (also called mean).

Avogadro's number: The number of molecules in one mole is called Avogadro’s number (approximately 6.022 × 1023 particles/mole).

Binary operation: An operation that is performed on just two elements of a set at a time.

Brownian motion: See an article (by Lee & Hoon) and an animation and a second one..

Butterfly effect: In a system when a small change results in an unpredictable and disproportionate disturbance, the effect causing this is called a butterfly effect.

Calculus: Branch of mathematics concerned with rates of change, gradients of curves, maximum and minimum values of functions, and the calculation of lengths, areas and volumes. It involves determining areas (integration) and tangents (differentiation), which are mutually inverse. Also called real analysis. See also Dr. Vogel's Gallery of Calculus Pathologies; MathWorld: Calculus; Wikipedia: Mathematics: Calculus; Visual Calculus; PlanetMath: Calculus; Math Archives: Calculus; Calculus Animations with Mathcad.

Cartesian coordinates: Cartesian coordinates (x,y) specify the position of a point in a plane relative to the horizontal x and the vertical y axes. The x and y axes form the basis of two-dimensional Cartesian coordinate system.

Chaos: Apparent randomness whose origins are entirely deterministic. A state of disorder and irregularity whose evolution in time, though governed by simple exact laws, is highly sensitive to starting conditions: a small variation in these conditions will produce wildly different results, so that long-term behaviour of chaotic systems cannot be predicted. This sensitivity to initial conditions is also known as the butterfly effect (when a butterfly flaps its wings in Mexico, the result may be a hurricane in Florida a month later).

Chord: A straight line joining two points on a curve or a circle. See also secant line.

Circle: A circle is defined as the set of points at a given distance (or radius) from its centre. If the coordinates of the centre of a circle on a plane is (a,b) and the radius is r, then (x-a)2 + (y-b)2 = r2. The equation that characterises a circle has the same coefficients for x2 and y2. The area of a circle is A = pr2 and circumference is C = 2pr. A circle with centre (a,b) and radius r has parametric equations: x = a + r.cos q and y = b + r.sin q (0 ≤ q ≤ 2p). A ‘tangent’ is a line, which touches a circle at one point (called the point of tangency) only. A ‘normal’ is a line, which goes through the centre of a circle and through the point of tangency (the normal is always perpendicular to the tangent). A straight line can be considered a circle; a circle with infinite radius and centre at infinity. See a Lecture Note, BBC Bitesize: Circle; Wikipedia: Mathematics: Circle; MathWorld: Geometry: Circles.

Circumference: A line or boundary that forms the perimeter of a circle.

Closure property: If the result of doing an operation on any two elements of a set is always an element of the set, then the set is closed under the operation. For example, the operations addition and multiplication of natural numbers (the set) are closed, but subtraction and division are not.

Coefficient: A number or letter before a variable in an algebraic expression that is used as a multiplier.

Common denominator: A denominator that is common to all the fractions within an equation. The smallest number that is a common multiple of the denominators of two or more fractions is the lowest (or least) common denominator (LCM).

Common factor: A whole number that divides exactly into two or more given numbers. The largest common factor for two or more numbers is their highest common factor (HCF).

Common logarithm: Logarithm with a base of 10 shown as log10 [log1010x = x].

Common ratio: In a geometric sequence, any term divided by the previous one gives the same common ratio.

Commutative property: A binary operation (*) defined on a set has the commutative property if for every two elements, a and b, a*b = b*a. For example, the operations addition and multiplication of natural numbers are commutative, but subtraction and division are not.

Complementary angles: Two angles whose sum is 90o. See also supplementary angles.

Complex numbers: A combination of real and imaginary numbers of the form a + bi where a and b are real numbers and i is the square root of -1 (see imaginary number). While real numbers can be represented as points on a line, complex numbers can only be located on a plane. See Types of Numbers.

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