Friday, March 18, 2011

uCertify’s announces St. Patrick’s Day Sale


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patrick

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Saturday, March 12, 2011

Functions

A function is a relationship between two sets of numbers. We may think of this as a mapping; a function maps a number in one set to a number in another set. Notice that a function maps values to one and only one value. Two values in one set could map to one value, but one value must never map to two values: that would be a relation, not a function.

For example, if we write (define) a function as:
f(x) = x2
then we say:
'f of x equals x squared'
and we have
f( - 1) = 1
f(1) = 1
f(7) = 49
f(1 / 2) = 1 / 4
f(4) = 16
and so on.
Allowed mapping for a function.png

Exponentiation



Exponentiation is a mathematical operation, written as an, involving two numbers, the base 'a' and the exponent 'n'.

When n is a positive integer, exponentiation corresponds to repeated multiplication; in other words, a product of n factors of a:

a^n = \underbrace{a \times \cdots \times a}_n,

Just as multiplication by a positive integer corresponds to repeated addition:

a \times n = \underbrace{a + \cdots + a}_n.

The exponent is usually shown as a superscript to the right of the base.

The power an can be defined also when n is a negative integer, for nonzero a. No natural extension to all real a and n exists, but when the base a is a positive real number, an can be defined for all real and even complex exponents n via the exponential function ez.

Trigonometric functions can be expressed in terms of complex exponentiation.

Exponentiation where the exponent is a matrix is used for solving systems of linear differential equations.

Graphs of y=ax for various bases a: base 10 (green), base e (red), base 2 (blue), and base ½ (cyan). Each curve passes through the point (0,1) because any nonzero number raised to the power 0 is 1. At x=1, the y-value equals the base because any number raised to the power 1 is itself.

Algebra

Algebra is the branch of mathematics that concerns with the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, and number theory, algebra is one of the main branches of pure mathematics.

Elementary algebra introduces the concept of variables representing numbers. Statements based on these variables are manipulated using the rules of operations that apply to numbers, such as addition. This can be done for a variety of reasons, including equation solving. Algebra is much broader than elementary algebra. Addition and multiplication can be generalized and their precise definitions lead to structures such as groups, rings and fields, studied in the area of mathematics called abstract algebra.

In 1545, the Italian mathematician Girolamo Cardano published Ars magna -The great art, a 40-chapter masterpiece in which he gave for the first time a method for solving the general quadratic equation.

Tuesday, February 22, 2011

uCertify’s President’s Week Sale!

uCertify's President's  Day Sale


In honor of the birth anniversaries of two great men, George Washington and Abraham Lincoln, uCertify is pleased to offer fantastic savings on President’s Day!
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Tuesday, February 1, 2011

Decimal Representation


The decimal numeral system (also called base ten or occasionally denary) has ten as its base. It is the numerical base most widely used by modern civilizations.
Decimal notation often refers to a base-10 positional notation. 

Decimals also refer to decimal fractions, either separately or in contrast to vulgar fractions. In this context, a decimal is a tenth part, and decimals become a series of nested tenths. There was a notation in use like 'tenth-metre', meaning the tenth decimal of the metre, currently an Angstrom. The contrast here is between decimals and vulgar fractions, and decimal divisions and other divisions of measures, like the inch. It is possible to follow a decimal expansion with a vulgar fraction; this is done with the recent divisions of the troy ounce, which has three places of decimals, followed by a trinary place.

A decimal representation of a non-negative real number r is an expression of the form

 r=\sum_{i=0}^\infty \frac{a_i}{10^i}

where a0 is a nonnegative integer, and a1, a2, … are integers satisfying 0 ≤ ai ≤ 9, called the digits of the decimal representation. The sequence of digits specified may be finite, in which case any further digits ai are assumed to be 0. Some authors forbid decimal representations with an infinite sequence of digits 9.[1] This restriction still allows a decimal representation for each non-negative real number, but additionally makes such a representation unique. The number defined by a decimal representation is often written more briefly as

 r=a_0.a_1 a_2 a_3\dots.\,

That is to say, a0 is the integer part of r, not necessarily between 0 and 9, and a1, a2, a3, … are the digits forming the fractional part of r.
Both notations above are, by definition, the following limit of a sequence:

 r=\lim_{n\to \infty} \sum_{i=0}^n \frac{a_i}{10^i}.

Number Line

The number line



In basic mathematics, a number line is a picture of a straight line on which every point is assumed to correspond to a real number and every real number to a point.[1] Often the integers are shown as specially-marked points evenly spaced on the line. Although this image only shows the integers from −9 to 9, the line includes all real numbers, continuing "forever" in each direction, and also numbers not marked that are between the integers. It is often used as an aid in teaching simple addition and subtraction, especially involving negative numbers.

It is divided into two symmetric halves by the origin, i.e. the number zero.
In advanced mathematics, the expressions real number line, or real line are typically used to indicate the above-mentioned concept that every point on a straight line corresponds to a single real number, and vice versa.

The number line is usually represented as being horizontal. Customarily, positive numbers lie on the right side of zero, and negative numbers lie on the left side of zero. An arrowhead on either end of the drawing is meant to suggest that the line continues indefinitely in the positive and negative real numbers, denoted by \mathbb{R} . The real numbers consist of irrational numbers and rational numbers, as well as the integers, whole numbers, and the natural numbers (the counting numbers).
A line drawn through the origin at right angles to the real number line can be used to represent the imaginary numbers. This line, called imaginary line, extends the number line to a complex number plane, with points representing complex numbers.