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**COMMON TERMS IN MATHEMATICS**

** **

**Dilara DORAK & M.Tevfik DORAK**

** **

**Please bookmark
this address: ****http://www.dorak.info/mtd/glosmath.html**** **

** **

**See
also** '**Common Concepts in
Statistics****', 'Glossary of Mathematical Mistakes' and 'CTK
Glossary of Mathematical Terms’**

**[Please
note that the best way to find an entry is to use the Find option from the Edit
menu, or CTRL + F]**

**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 = (x_{1} + x_{2}
+ .... x_{n}) / 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 × 10^{23} 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**

**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} = r^{2}.
The equation that characterises a circle has the same coefficients for x^{2}
and y^{2}. The area of a circle is A = pr^{2}
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**:

**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 log _{10}
[log_{10}10^{x} = 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 90 ^{o}. See also **

**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.**

**Composite number****: Any integer which is not a prime number, i.e., evenly
divisible by numbers other than 1 and itself. **

**Congruent****: Alike in all relevant respects.**

**Constant****: A quality of a measurement that never changes in
magnitude. **

**Coordinate****: A set of numbers that locates the position of a point
usually represented by*** (x,y***) values. **

**Cosine law**: For any triangle, the side
lengths a, b, c and corresponding opposite angles A, B, C are related as
follows: a^{2} = b^{2} + c^{2} - 2bc cosA etc. The law
of cosines is useful to determine the unknown data of a triangle if two sides
and an angle are known. See
** Wikipedia**:

**Counting number****: An element of the set C = {1,2,3,...}. **

**Cube root****: The factor of a number that, when it is cubed (i.e., x ^{3})
gives that number. **

**Curve****: A
line that is continuously bent.**

**Decimal****: A fraction having a power of ten as denominator, such as
0.34 = 34/100 (10 ^{2}) or 0.344 = 344/1000 (10^{3}). In the
continent, a comma is used as the decimal point (between the unit figure and
the numerator). **

**Degree of an angle**: A unit of angle equal
to one ninetieth of a right angle. Each degree ( ^{0 }) may be further
subdivided into 60 parts, called *minutes**
(60’)*, and in turn each minute may be subdivided into another 60
parts, called *seconds*
(60’’). Different types of angles are called acute (<90^{0})<
right (90^{0}) < obtuse (90^{0}-180^{0}) < reflex
(180^{0}-360^{0}). See also **radian **(the SI unit of
angle).

**Denominator****: The bottom number in a fraction.**

**Derivative****: The derivative at a point on a curve is the gradient of
the tangent to the curve at the given point. More technically, a function (***f'***(***x _{0}*

**Differential Equations**:
Equations containing one or more derivatives (rate of change). As such these
equations represent the relationships between the rates of change of
continuously varying quantities. The solution contains constant terms (constant
of integration) that are not present in the original differential equation. Two
general types of differential equations are ordinary differential equations
(ODE) and partial differential equations (PDE). When the function involved in
the equation depends upon only a single variable, the differential equation is
an ODE. If the function depends on several independent variables (so that its
derivatives are partial derivatives) then the differential equation is a PDE.
See **Internet Resources for Differential Equations**;
**S.O.S
Mathematics Review: Differential
Equations.**

**Diameter****: A straight line that passes from side to side thorough
the centre of a circle.**

**Differential calculus****: Differentiation is concerned with rates of change and
calculating the gradient at any point from the equation of the curve,***
y = f(x)***. **

**Differential equation****: Equations involving total or partial differentiation
coefficients and the rate of change; the difference between some quantity now
and its value an instant into the future. See also ****Wikipedia**:**
Mathematics**:** Differential Equations; Mathlets:
Differential Equation Applet; Alternative Differential
Equation Applet.**

**Digit****: In
the decimal system, the numbers 0 through 9.**

**Dimension****: Either the length and/or width of a flat surface
(two-dimensional); or the length, width, and/or height of a solid
(three-dimensional).**

**Distributive property****: A binary operation (*) is distributive over another
binary operation (^) if, a*(b^c) = (a*b)^(a*c). For example, the operation of
multiplication is distributive over the operations of addition and subtraction
in the set of natural numbers.**

**Division****: The operation of ascertaining how many times one number,
the ***divisor***, is contained in another, the ***dividend***. The result is the ***quotient***, and any number left over is called the ***remainder***. The dividend and divisor are also called the ***numerator*** and ***denominator***, respectively. **

**Dynamics****: The branch of mathematics, which studies the way in which
force produces motion. **

*e***:
Symbol for the base of natural logarithms (2.7182818285...), defined as the
limiting value of (1 + 1/m) ^{m}.**

**Equilibrium****: The state of balance between opposing forces or effects. **

**Even number****: A natural number that is divisible by two. **

**Exponent**** (****power****, ****index****): A number denoted by a small numeral placed above and to
the right of a numerical quantity, which indicates the number of times that
quantity is multiplied by itself. In the case of X ^{n}, it is said that
X is raised to the power of n. When a and b are non-zero real numbers and p and
q are integers, the following rules of power apply:**

a^{p} x a^{q}
= a^{p+q}; (a^{p})^{q} = a^{pq}; (a^{1/n})^{m}
= a^{m/n}; a^{1/2} x
b^{1/2} = (ab)^{1/2}.

**Exponential function****: A function in the form of f(x) = a ^{x} where x is
a real number, and a is positive and not 1. One exponential function is f(x) = **

**Extrapolation**: Estimating the value of a
function or a quantity outside a known range of values. See also **interpolation**.

**Factorial****: The product of a series of consecutive positive integers
from 1 to a given number (n). It is expressed with the symbol ( ! ). For
example, 5! = 5x4x3x2x1 = 120. As a rule (n!+n) is evenly divisible by n. **

**Factor****:
When two or more natural numbers are multiplied, each of the numbers is a factor
of the product. A factor is then a number by which another number is exactly
divided (a divisor). **

**Factorisation:**** Writing a number as the product of its factors which are
prime numbers.**

**Fermat's little theorem:**** If p is a prime number and b is any whole number, then b ^{p}-b
is a multiple of p (2^{3 }- 2 = 6 and is divisible by 3). **

**Fermat prime****: Any prime number in the form of 2 ^{2n} + 1 (see
also **

**Fibonacci sequence****: Sequence of integers, where each is the sum of the two preceding
it. 1,1,2,3,5,8,13,21,... The number of petals of flowers forms a Fibonacci
series. **

**Fractals****: Geometrical entities characterised by basic patterns that
are repeated at ever decreasing sizes. They are relevant to any system
involving self-similarity repeated on diminished scales (such as a fern's
structure) as in the study of chaos.**

**Fraction (quotient)****: A portion of a whole amount. The term usually applies
only to ratios of integers (like 2/3, 5/7). Fractions less than one are called ***common***, ***proper*** or ***vulgar***
fractions; and those greater than 1 are called ***improper*** fraction.**

**Function ( f)**

**Geometry** in **Wikipedia**
& **Geometry** in **MathWorld**.
See also **Geometric Fallacies**.

**Geometric mean**: G = (*x*_{1}.*x*_{2}...*x*_{n})^{1/n}
where n is the sample size. This can also be expressed as antilog ((1/n) S log *x*).
See **Applications of the Geometric Mean; Spizman, 2008: Geometric Mean in Forensic Economy**.

**Geometric sequence****: A sequence of numbers in which each term subsequent to
the first is generated by multiplying its predecessor by a fixed constant (the ****common
ratio****).**

**Goldbach conjecture****: Every even number greater than 4 is the sum of two odd primes
(32 = 13 + 19). Every odd number greater than 7 can be expressed as the sum of
three odd prime numbers (11 = 3 + 3 + 5).**

**Gradient****: The slope of a line. The gradient of two points on a line
is calculated as rise (vertical increase) divided by run (horizontal increase),
therefore, the gradient of a line is equal to the tangent of the angle it makes
with the positive x-axis (y/x). See Mathlets:
Lines and Slopes; Curve
Bank: Slope.**

**Greek alphabet****: For list of Greek letters follow the link.**

**Harmonic mean**: Of a set of numbers (y_{1}
to y_{i}), the harmonic mean is the reciprocal of the arithmetic mean
of the reciprocal of the numbers [H = N / S
(1/y)]. See also ** Wikipedia**:

**Hierarchy of operations****: In an equation with multiple operators, operations
proceed in the following order: (brackets), exponentiation,
division/multiplication, subtraction/summation and from left to right.**

**Highest common factor (HCF)****: The greatest natural number, which is a factor of two or
more given numbers. **

**Hypotenuse****: The longest side of a right triangle, which lies opposite
the vertex of the right angle.**

*i***: The
square root of -1 (an ****imaginary
number****). **

**Identity element****: The element of a set which when combined with any element
of the same set leaves the other element unchanged (like zero in addition and
subtraction, and 1 in multiplication or division).**

**Imaginary number****: The product of a real number***
x*** and ***i***, where ***i*^{2}** + 1 = 0. A complex number in which the real part is zero.
In general, imaginary numbers are the square roots of negative numbers. See Types of Numbers.**

**Improper fraction****: A fraction whose numerator is the same as or larger than
the denominator; i.e., a fraction equal to or greater than 1.**

**Infinite****: Having no end or limits. Larger than any quantified
concept. For many purposes it may be considered as the reciprocal of zero and
shown as an 8 lying on its side (****∞****). **

**Infinitesimal****: A vanishingly small part of a quantity. It equals almost
zero. **

**Integer****: Any whole number: positive and negative whole numbers and
zero.**

**Integral calculus****: This is the inverse process to differentiation; i.e., a
function which has a given derived function. For example, x ^{2} has
derivative 2x, so 2x has x^{2} as an integral. A classic application of
integral is to calculate areas. **

**Integration****: The process of finding a function given its derived
function.**

**Intersection****: The intersection of two sets is the set of elements that
are in both sets. **

**Intercept**: A part of a line/plane cut
off by another line/plane.

**Interpolation**: Estimating the value of a
function or a quantity from known values on either side of it.

**Inverse function**: A function which 'does
the reverse' of a given function. For example, functions with the prefix arc
are inverse trigonometric functions; e.g. arcsin x for the inverse of sin(x).
See also **Wikipedia**:**
Mathematics**: **Inverse
Functions**** and Logarithmic Inverse Functions.**

**Irrational number****: A real number that cannot be expressed as the ratio of
two integers, and therefore that cannot be written as a decimal that either terminates
or repeats. The square root of 2 is an example because if it is expressed as a
ratio, it never gives 2 when multiplied by itself. The numbers ****p**** =
3.141592645..., and ***e*** = 2.7182818... are also irrational numbers. See also ****transcendental
numbers****, ****real
numbers****, and Types of Numbers.**

**Iteration****: Repeatedly performing the same sequence of steps. Simply,
solving an algebraic equation with an arbitrary value for the unknown and using
the result to solve it again, and again. **

**Least squares method**: A
method of fitting a straight line or curve based one minimisation of the sum of
squared differences (residuals) between the predicted and the observed points.
Given the data points (x_{i}, y_{i}),
it is possible to fit a straight line using a formula, which gives the y=a+bx.
The gradient of the straight line b is given by [S(x_{i}
- m_{x})(y_{i}-m_{y})]
/ [(S(x-m_{x}))^{2}],
where m_{x} and m_{y}
are the means for x_{i} and y_{i}.
The intercept a is obtained by m_{y}
- bm_{x}. See **Wikipedia**:
**Least Squares**.

**Linear****: A model
or function where the input and output are proportional.**

**Linear expression**: A polynomial
expression with the degree of polynomial being 1, i.e., that does not include
any terms as the power of a variable. It will be something like, f(x)=2x^{1}+3,
but not x^{2}+2x+4 (the latter is a **quadratic expression**).
Linear equations are closely related to a straight line.

**Literal numbers****: Letters representing numbers (as in algebraic equations).**

**Logarithm****: The logarithm of a number N to a given base b is the power
to which the base must be raised to produce the number N. Written as log _{b}
N. Naturally, log_{b} b^{x} = x. In any base, the following rules apply: log (ab) = log a + log b; log
(a/b) = log a - log b; log (1/a) = -log a; log a^{b} = b log a; log 1 =
0 and log 0 is undefined. See**

**Logistic model (map, sequence)**: **Wikipedia**:
**Logistic
Map**; **Cut-the Knot**: **JAVA Model**.

**Matrix**: A matrix (plural: matrices)
is a rectangular table of data. See **Basics of Matrix Algebra**; **Linear
Algebra Review**; ‘**Introduction to Matrix Algebra’ Book**; **Matrix Algebra
Tool** and **Interactive Exercises**.

**Mechanics: Study of the
forces acting on bodies, whether moving (dynamics) or stationary (statics). **

**Mersenne prime****: A Mersenne number, M _{p}, has the form 2^{p}-1,
where p is a prime. If M_{p} itself a prime, then it is called a
Mersenne prime. There are 32 such primes known (i.e., not all primes yield a
Mersenne prime). (See also **

**Mixed number****: A number that contains both a whole number and a
fraction. **

**Modulus****: The absolute value of a number regardless of its sign,
shown as | ***x*** | or mod ***x***. For a vector ***u***, the modulus | ***u*** | is used to indicate its magnitude calculated using Pythagoras’ theorem: | **

**Multiplication****: The process of finding the ***product*** of two quantities that are called the ***multiplicand*** and the ***multiplier***.**

**Natural logarithm****: Logarithm with a base of ***e***, usually abbreviated ***ln*** (***ln*** e ^{x }= x). **

**Natural number****: Any element of the set N = {0,1,2,3,...} (positive
integers). The inclusion of zero is a matter of definition. See Types of Numbers.**

**Numerator****: The top number in a fraction.**

**Obtuse angle****: An angle with a degree measure between 90 and 180. See MathWorld:
Geometry: Trigonometry: Angles: Obtuse Angle.**

**Odd number****: A natural number that is not divisible by 2. **

**Odds**: The odds of a success is
defined to be the ratio of the probability of a success to the probability of a
failure (p/(1-p)).

**Ordinate****: The vertical coordinate on a plane.**

**Origin: The point on a graph that
represents the point where the x and y axes meet: (x,y) = (0,0).**

**Parallel****: Lines or planes that are equidistant from each other and
do not intersect. **

**Perfect number****: A number which is equal to the sum of its proper
divisors. 6, 28, and 496 are the three of seven known perfect numbers. [6 is a
perfect number because its proper divisors (1,2, and 3) total 6.] See Types of Numbers.**

**Permutation****: A permutation of a sequence of objects is just a
rearrangement of them. **

**Perpendicular****: At right angles to a line or plane.**

**Pi (****p****)****: The ratio of the circumference of a circle to its
diameter. The value of ****p**** is 3.1415926, correct to seven decimal places. The sum of
the three angles of a triangle is ****p**** radians. **

**Poisson distribution**: The
probability distribution of the number of occurrences of random (usually rare
and independent) events in an interval or time or space. See a **Lecture Note**.

**Polar equation**: A system which describes a
point in the plane not by its Cartesian coordinates (x,y) but by its polar
coordinates: angular direction (**q**)
and distance r from the origin (r, **q****)**.

**Polygon****: A geometric figure that is bound by many straight lines such
as triangle, square, pentagon, hexagon, heptagon, octagon etc. **

**Polynomial****: An algebraic expression of the form a _{0}x^{n}
+ a_{1}x^{n-1} + ... + a_{n}, where a_{0}, a_{1},
..., a_{n} are members of a field (or ring), and n is the degree of the
polynomial. See Wikipedia:
Polynomial.
**

**Precalculus**: A foundational mathematical
discipline. Pre-calculus intends to prepare students for the study of calculus.
Pre-calculus typically includes a review of algebra, as well as an introduction
to exponential, logarithmic and trigonometric functions as preparation for the
study of calculus. See ** Wikipedia**:

**Prime factors****: Prime factors of a number are a list of prime numbers the
product of which is the number concerned. When n=1, for example, f(x)=2x ^{1}+3,
this is a linear expression. If n=2, it is quadratic (for example, x^{2}
+ 2x + 4); if n=3, it is cubic, if n=4, it is quartic and if n=5, it is
quintic.**

**Prime number****: A natural number other than 1, evenly divisible only by 1
and itself. The numbers 2,3,5,7,11,13,17,19,... Apart from 2, all primes are
odd numbers and odd primes fall into two groups: those that are one less than a
multiple of four (3,7,11,19) and those one more than a multiple of four
(5,13,17). Every natural number greater than 1 may be resolved into a product
of prime numbers; eg 8316 = 2 ^{2} x 3^{3} x 7 x 11. See Types of Numbers, Prime
Numbers.**

Probability distributions: See **Gallery of Probability Distributions** in **Engineering Statistics Handbook**.

**Product****: The result of a multiplication problem.**

**Proper divisor****: Any number divides another without leaving a remainder. **

**Proper fraction****: A fraction in which the numerator is smaller than the
denominator; i.e., a fraction smaller than 1.**

**Proportion****: A type of ratio in which the numerator is included in the
denominator. It is the ratio of a part to the whole (0.0 ≤ ****p**** ≤ 1.0) that may be expressed as a decimal fraction
(0.2), vulgar fraction (1/5) or percentage (20%). **

**Pythagoras’ Theorem**: For any right-angled
triangle, the square on the hypotenuse equals the sum of the squares on the
other two sides. See . ** Wikipedia**:

**Quadratic equation**: An algebraic equation
of the second degree (having one or more variables raised to the second power).
The general quadratic equation is ax^{2} + bx + c = 0,
in which a, b, and c are constants (or parameters) and ‘a’ is not equal to 0.

**Quotient (fraction)****: An algebraic expression in which the numerator is divided
by the denominator. Turning a fraction upside down gives the fraction’s ****reciprocal****. **

**Radian (rad)**: The SI unit for measuring an
angle formally defined as ‘the angle subtended at the centre of a circle by an
arc equal in length to the radius of the circle’ (the
angle of an entire circle is 2p radians;
p
radians equal 180^{0} (sum of the three angles of a triangle); this is
the basis of circumference of a circle formula 2pr).
Sum of angles of a triangle equals p
radians. See **an Animation of Radian**.

**Radius****: The
distance between the centre of a circle and any point on the circle's
circumference. **

**Rate****: The
relationship between two measurements of different units such as change in
distance with respect to time (miles per hour). **

**Ratio****: The
relationship between two numbers or measurements, usually with the same units
like the ratio of the width of an object to its length. The ratio a:b is
equivalent to the quotient a/b.**

**Rational number****: A number that can be expressed as the ratio of two
integers, e.g. 6/7. The set of rational numbers is denotes as ‘****Q****’ for quotient. See Types of Numbers.**

**Real number****: ****Rational**** (fractions) and ****irrational**** (numbers with non-recurring decimal representation)
numbers. The set of real numbers is denoted as ‘****R****’ for real. In computing, any number with a fractional (or
decimal) part. Basically, real numbers are all numbers except imaginary numbers
(such as the square root of -1). See Types of Numbers. **

**Reciprocal****: The multiplicative inverse of a number (i.e., 1/x). It
can be shown with a negative index (x ^{-1}).**

**Reflex angle****: An angle with a degree measure between 180 and 360. See MathWorld:
Geometry: Trigonometry: Angles: Reflex Angle.**

**Repeating decimal****: A decimal that can be written using a horizontal bar to
show the repeating digits. **

**Right angle****: An angle with a degree measure 90. An angle which is not
an right angle is called oblique angle. See MathWorld:
Geometry: Trigonometry: Angles: Right
Angle. **

**Root**: If, when a number is raised
to the power of n gives the answer a, then this number is the n^{th} root
of a (a^{1/n}).

**Rounding****: To give a close approximation of a number by dropping the
least significant numbers. For example 15.88 can be rounded up to 15.9 (or 16)
and 15.12 can be rounded down to 15.1 (or 15).**

**Scalar****: A
real number and also a quantity that has magnitude but no direction, such as
mass and density. See Wikipedia: Scalar.
**

**Scientific notation (exponential notation, standard form**):
One way of writing very small or very large numbers. In this notation, numbers
are shown as (0<N<10) x 10^{q}. An equivalent form is N.Eq. For
example; 365,000 is 3.65x10^{5} or 3.65E5. See **Wikipedia**:
**Scientific Notation**.

**Secant line**: A line that intersects a
curve. The **intercept** is a **chord** of the curve. ** Wikipedia**:

**Sequence****: An ordered set of numbers derived according to a rule,
each member being determined either directly or from the preceding terms. See Real Analysis Glossary: Sequences & Context.**

**Sigma (S, s )****: Represents ****s****ummation (****S****, ****s****). See Greek Letters.**

**Significant figure (s.f.)**: The specific
degree of accuracy denoted by the number of digits used. For example 434.64 has
five s.f. but at 3 s.f. accuracy it would be shown as ‘435 (to 3 s.f.)’. From
the left, the first nonzero digit in a number is the first significant figure,
after the first significant number, all digits, including zeros, count as
significant numbers (Both 0.3 and 0.0003 have 1 s.f.; both 0.0303 and 0.303000
have 3 s.f.). If a number has to be reduced to a lower s.f., the usual rounding
rules apply (2045.678 becomes 2046 to 4 s.f. and 2045.7 to 5 s.f.). The final
zero even in a whole number is not a s.f. as it only shows the order of
magnitude of the number (2343.2 is shown as 2340 to 3 s.f.).

**Sine law**: For any triangle, the side
lengths a, b, c and corresponding opposite angles A, B, C are related as
follows: sin A / a = sin B / b = sin C / c. The law of sines is useful for
computing the lengths of the unknown sides in a triangle if two angles and one
side are known. See **Wikipedia**: **Law
of Sines**.

**Skew lines****: Two lines in three-dimensional space, which do not lie in
the same plane (and do not intersect). **

**Stationary point****: Point at which the derivative of a function is zero. Includes
maximum and minimum turning points, but not all stationary points are turning
points. **

**Straight line**: A straight line is
characterised by an equation (y = a + bx), where a is the intercept and b is
the gradient/slope. One of the methods for fitting a straight line is the **least
squares method**.

**Subtend****: To lie opposite and mark out the limits of an angle.**

**Subtraction****: The inverse operation of addition. In the notation a - b
= c, the terms a, b, and c are called the ***minuend***, ***subtrahend*** and ***difference***, respectively.**

**Supplementary angles****: Two angles whose sum is 180 ^{o}. See also **

**Tangent**: The tangent of an angle in a
right-angled triangle is the ratio of the lengths of the side opposite to the side
adjacent [tan(x) = sin(x) / cos(x)]. A tangent line is a line, which touches a
given curve at a single point. The slope of a tangent line can be approximated
by a secant line. See
**Wikipedia**:
**Tangent**;
**MathWorld**:
**Tangent**;
**Mathlets**:
**Tangent Lines**.

**Tangent law**: For any triangle, the
side lengths a, b, c and corresponding opposite angles A, B, C are related as
follows: (a+b) / (a-b) = {tan[1/2(A+B)]} / {tan[1/2(A-B)]}. See **Wikipedia**:
**Law
of Tangents**.

**Taylor
Expansions**: A special kind of power series used as a basis of
approximation. A **Taylor expansion** (series) is the sum of functions based
on continually increasing derivatives (till one gets a zero value) if they
exist. The accuracy of the approximation improves as the order of the
approximation is increased (like fourth derivative or fifth). As the
nonlinearity of the function increases the higher order terms become more
important (i.e., the error increases as fewer terms of the Taylor series are
included in the approximation). The main use of Taylor polynomial
approximations is not to estimate the value of a function at a given point
(this can be done by a calculator) but to approximate functions over an
interval (representing complicated nonlinear functions as series
‘infinite polynomials’ makes life easier; see for example: **Applications of
Taylor Series**). **Maclaurin’s expansion** is a special case of Taylor’s
expansion. **Wikipedia**:
**Taylor Series**; **MathWorld**:
**Taylor Series**; a Lecture Note on **Taylor Expansions by Luca Sbano**; **Taylor Polynomials Quizzes**; **Taylor Series Applet**;
**Taylor
Polynomials Applet**; **Mathlets:**
**Taylor Polynomials**; **Visual
Calculus**: **Taylor Polynomials**.

**Transcendental number****: A real number that does not satisfy any algebraic
equation with integral coefficients, such as x ^{3} - 5x + 11 = 0. All
transcendental numbers are irrational and most irrational numbers
(non-repeating, non-terminating decimals) are transcendental. Transcendental
functions (such as exponential, sine and cosine functions) can burst into chaos
under certain circumstances. See Types of Numbers. **

**Triangle****: A three-sided figure that can take several shapes. The
three inside angles add up to 180 ^{o}. Triangles are divided into three
basic types: obtuse, right and acute; they are also named by the
characteristics of their sides: equilateral, isosceles, and scalene. The area
of a triangle is 1/2 x perpendicular height x base.**

**Trigonometry**: The branch of mathematics
that is concerned with the trigonometric functions. Trigonometric identities
are the results that hold true for all angles. Sin, Cos and Tan are
trigonometric ratios; Cosec, Sec and Cot are reciprocal of trigonometric
ratios; Arcsin (sin^{-1}), Arccos (cos^{-1}) and Arctan (tan^{-1})
are inverse of trigonometric functions. See **Syvum
Math**: **Trigonometric Functions**; **CTK:
Trigonometric Functions**; **Trigonometry Realms**; **S.O.S. Math**:
**Trigonometric Identities Table**; ** Wikipedia**:

**Union****: The
union of two sets is the set of elements that are in either of the two sets
(compare with intersection).**

**Unit****: A
standard measurement. **

**Variable****: An amount whose value can change. **

**Vector**: A quantity characterised by a
magnitude and a direction represented by (1) column form: two numbers
(components) in a 2x1 matrix; (2) geometric form: by arrows in the (x,y)-plane;
or (3) component form: the Cartesian unit vectors ** i** (x-axis unit
vector) and

**Vertex****: The
point where lines intersect.**

**Whole number****: Zero or any positive number with no fractional parts.**

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Statistics Sites**

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**Mathematical Modules in
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**Software: Sage (open source) MathCad Mathematica Matlab Maple List of Packages
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Tables (Normal distribution, Critical values of t, F, X ^{2})
StatSoft: Statistical
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by ***Dilara DORAK & ****M.Tevfik DORAK**

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*Last updated on 1 July 2013*

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