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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 = (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.
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.
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; 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.
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: a2
= b2 + c2 - 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: Cosine
Law.
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., x3) 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 (102) or 0.344 = 344/1000 (103). 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 (<900)< right (900)
< obtuse (900-1800) < reflex (1800-3600).
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'(x0)) of a function y = f(x),
representing the rate of change of y and the
gradient of the graph at the point where x = x0, usually shown as dy/dx. The notation dy/dx suggests the ratio of two numbers dy and dx (denoting
infinitesimal changes in y and x), but it is a single number, the limit of a ratio
(k/h) as they both approach zero. Differentiation is the process of calculating
derivatives. The derivatives of all commonly occurring functions are known. See
Function,
Derivative & Integral Applet; Calculus Graphics; Mathlets: Derivative
Calculator.
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.
Extrapolation: Estimating the value of a function or a quantity
outside a known range of values.
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.
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; Differential Equations Applets.
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 Xn, 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:
ap
x aq
= ap+q; (ap)q
= apq; (a1/n)m
= am/n; a1/2 x b1/2 =
(ab)1/2.
Exponential
function: A function in the form of f(x) = ax
where x is a real number, and a is positive and not 1. One exponential function
is f(x) = ex.
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 bp-b is a multiple of p (23 - 2
= 6 and is divisible by 3).
Fermat
prime: Any prime number in the form of 22n + 1
(see also Mersenne prime).
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): The mathematical operation that
transforms a piece of data into a different one. For example, f(x) = x2 is a function transforming any number to its
square.
Geometry in Wikipedia.
Geometric
mean: G = (x1.x2...xn)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.
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 Curve
Bank: Slope.
Greek
alphabet: For list of Greek letters follow the
link.
Harmonic
mean: Of a set of numbers (y1 to yi),
the harmonic mean is the reciprocal of the arithmetic mean of the reciprocal of
the numbers [H = N / S (1/y)]. See also Wikipedia: Mathematics: Harmonic
Mean.
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 i2 + 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, x2 has derivative 2x, so 2x has x2 as
an integral. A classic application of integral is to calculate areas. Wikipedia: Mathematics: Calculus: Integral.
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.
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 (xi, yi), 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(xi - mx)(yi-my)] / [(S(x-mx))2], where mx and my are the means for xi and yi. The intercept a is obtained by my - bmx. 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)=2x1+3, but not
x2+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
logb N. Naturally, logb bx = 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 ab = b log a; log 1 = 0 and log 0 is undefined.
Logistic
model (map, sequence): Wikipedia: Logistic
Map; Cut-the
Knot: JAVA
Model; Logistic
Map (interactive).
Lowest
common multiple (LCM): The smallest non-zero
natural number that is a common multiple of two or more natural numbers
(compare with the highest common factor).
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, Mp, has
the form 2p-1, where p is a prime. If Mp
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 Fermat
prime.)
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: | u | = (a2 + b2)1/2.
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 ex =
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 a0xn + a1xn-1 + ... + an, where a0, a1,
..., an 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: Mathematics: Precalculus.
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)=2x1+3, this is a linear
expression. If n=2, it is quadratic (for example, x2 + 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 = 22 x 33 x 7
x 11. See Types
of 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: Mathematics: Pythagoras’
theorem.
Quadratic
equation: An algebraic equation of the second
degree (having one or more variables raised to the second power). The general
quadratic equation is ax2 + 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 1800 (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 nth root of a (a1/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 10q. An equivalent form is N.Eq. For
example; 365,000 is 3.65x105 or 3.65E5. See Wikipedia: Scientific
Notation.
Secant
line: A line that intersects a curve. The intercept is a chord
of the curve. Wikipedia: Mathematics: Secant
Line; Mathlets: Secant
Line; CTK
Glossary: Secant.
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 summation (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: Sine
Law.
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 180o. See
also complementary angles.
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.
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: Tangent
Law.
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; Taylor
Series and Probability Distributions; Taylor Polynomials Quiz; Taylor Polynomial Computation;
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 x3 - 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 180o. 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 (see Unit
Circle; Animations (1) (2)); 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; Trigonometry
Realms; S.O.S.
Math: Trigonometric
Identities Table; Wikipedia: Mathematics: Trigonometric
Function / Uses
of Trigonometry; Dave's
Short Trig Course (JAVA).
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 j
(y-axis unit vector). The magnitude of a vector | u | is the length of
the corresponding arrow and the direction is the angle (θ) the
vector makes with the positive x-axis. When a1 and a2
are the components of the vector a
(magnitude | a | = (a12
+ a22)1/2),
it equals to a = a1i + a2j in component form, which equals to a = | a | cos(θ)i + | a | sin(θ)j. The angle (θ)
can be found as arctan (a2 / a1). Cosine rule and sine rule
are used for conversion of vectors from one form to another. See Wikipedia: Algebra: Vector
/ Mathematics: Vector / Vector
Calculus; Eigenvector.
Vertex: The point where lines intersect.
Whole
number: Zero or any positive number with no
fractional parts.
Links to Mathematics and Statistics Sites
S.O.S
Mathematics Review: Algebra - Trigonometry - Calculus
Paul's
Online Math Notes
MathWorld:
Algebra
- Calculus
- Geometry
- Probability
- Animated
GIFs
Math Archives: Algebra - Applied Math - Calculus - Genetic Algorithms - Geometry - Mathematical Biology - Trigonometry
Cut-the-Knot
Math Glossary Real
Analysis Glossary MathWords
Adrian Sparrow's Maths Pages
Mathematical
Atlas JAVA
Programs for Mathematics Education
Mathlets Simulations Math-Physics-Engineering
Applets
Wikipedia: Mathematics PlanetMath The
Math Project on Everything2
Mathematical
Modules in Epidemiology
Financial
Mathematics Glossary
Software: MathCad Mathematica Matlab List
of Packages
Statistical
Tables
Compiled
by Dilara DORAK & M.Tevfik DORAK
Last updated
on 16 May 2007
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