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Home >> Educational Materials >> Mathematics## ADDITION

Addition is the mathematical process of putting things together. The plus sign "+" means that numbers are added together. For example, in the picture on the right, there are 3 + 2 apples — meaning three apples and two other apples — which is the same as five apples, since 3 + 2 = 5. Besides counts of fruit, addition can also represent combining other physical and abstract quantities using different kinds of numbers: negative numbers, fractions, irrational numbers, vectors, and more. As a mathem## REAL NUMBERS

In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2.4871773339.... The real numbers include rational numbers, such as 42 and -23/129, and irrational numbers, such as p and the square root of 2, and can be represented as points along an infinitely long number line. A more rigorous definition of the real numbers was one of the most important developments of 19th century mathematics. Popular definitions in use t## TRIANGLE

A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A , B , and C is denoted ABC . In Euclidean geometry any three non-collinear points determine a unique triangle and a unique plane (i.e. a two-dimensional Euclidean space). Types of triangles Euler diagram of types of triangles, using the definition that isosceles triangles have at least 2 equal sides, i.e. equilateral triangles a## BEARING

In marine navigation, a bearing is the direction of one object in relation to another object, the other object usually being one's own vessel. In aircraft navigation, a bearing is the actual (corrected) compass direction of the forward course of the aircraft. In land navigation, a bearing is the angle between a line connecting two points and a north-south line, or meridian Historical definitions Land Navigation In land navigation, a bearing was traditionally defined in land surveying terms## GRAPH THEORY

In mathematics and computer science, graph theory is the study of graphs : mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of vertices. A graph may be undirected , meaning that there is no distinction between the two vertices associated with each edge, or its edges may be directed from one vertex to another; see graph (m## Calculus-Complex Numbers

Complex Numbers The complex numbers are an extension of the real numbers containing all roots of quadratic equations. If we define i to be a solution of the equation x 2 = -1, then the set C of complex numbers is represented in standard form as { a+bi | a,b Î R}. We often use the variable z = a+bi to represent a complex number. The number a is called the real part of z (Re z) while b is called the imaginary part of z (Im z). Two complex numbers are equal if and only if their real parts are equa## Trigonometric functions

Definition The trigonometric functions sometimes are also called circular functions. They are functions of an angle; they are important when studying triangles, among many other applications. Trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle (a circle that has a radius of one). Right triangle definitions A right triangle always includes a 90° (p/## COMPLEX NUMBERS

A complex number can be visually represented as a pair of numbers forming a vector on a diagram called an Argand diagram In mathematics, the complex numbers are an extension of the real numbers obtained by adjoining an imaginary unit , denoted i , which satisfies: [ 1 ] Every complex number can be written in the form a + bi , where a and b are real numbers called the real part and the imaginary part of the complex number, respectively. Complex numbers are a field, and thus have addition, subtra## Additive inverse

In mathematics, the additive inverse , or opposite , of a number n is the number that, when added to n , yields zero. The additive inverse of F is denoted - F . For example, the additive inverse of 7 is -7, because 7 + (-7) = 0, and the additive inverse of -0.3 is 0.3, because -0.3 + 0.3 = 0. In other words, the additive inverse of a number is the number's negative. For example, the additive inverse of 8 is -8, the additive inverse of 10002 is -10002 and the additive inverse of x² is -x². T## Boolean algebra

In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties of both set operations and logic operations. A Boolean algebra can be seen as a generalization of a power set algebra or a field of sets. Definition A Boolean algebra is a six-tuple consisting of a set A , equipped with two binary operations (called "meet" or "and"), (called "join" or "or"), a unary operation (called "complement" or "no## Basics of the Equation

The diagram on the right shows a basic equation. This equation is similar to problems which you may have done in ordinary mathematics such as: __ + 16 = 30 You could easily guess that __ equals 14 or do 30 - 16 to find that __ equals 14. In this problem __ stood for an unknown number; in an equation we use variables, or any letter in the alphabet. When written algebraically the problem would be: x + 16 = 30 and the answer should be written: x = 14 Solving Equations These equations can be solved## MODEL THEORY

In mathematics, model theory is the study of (classes of) mathematical structures such as groups, fields, graphs, or even models of set theory, using tools from mathematical logic. Model theory has close ties to algebra and universal algebra. This article focuses on finitary first order model theory of infinite structures. Finite model theory, which concentrates on finite structures, diverges significantly from the study of infinite structures in both the problems studied and the techniques use## COMPOUND INTEREST

Compound interest is very similar to simple interest; however, with time, the difference becomes considerably larger. This difference is because unpaid interest is added to the balance due. Put another way, the borrower is charged interest on previous interest. Assuming that no part of the principal or subsequent interest has been paid, the debt is calculated by the following formulas: where I comp is the compound interest, B 0 the initial balance, B m the balance after m periods (where m is no## Addition

This article is about addition in mathematics. For addition reaction in chemistry, see addition reaction. Addition is the mathematical operation of combining or adding two numbers to obtain an equal simple amount or total. Addition also provides a model for related processes such as joining two collections of objects into one collection. Repeated addition of the number one is the most basic form of counting. Performing addition is one of the simplest numerical tasks, accessible to infants as yo## Calculus-Multiple Integration

Multiple Integration Recall our definition of the definite integral of a function of a single variable: Let f(x) be defined on [a,b] and let x 0 ,x 1 , ¼ ,x n be a partition of [a,b]. For each [x i-1 ,x i ], let x i * Î [x i-1 ,x i ]. Then ó õ b a f(x) dx = lim max D x i ® 0 n å i = 1 f(x i * ) D x i Take a quick look at the Riemann Sum Tutorial We can extend this definition to define the integral of a function of two or more variables. Double Integral of a Function of Two Variables Let f(x,y)## Combinatorics

Combinatorics is a branch of pure mathematics concerning the study of the enumeration of discrete, finite sets. It is related to many other areas of mathematics, such as algebra, probability theory, ergodic theory and geometry, as well as to applied subjects in computer science and statistical physics. Aspects of combinatorics include "counting" the objects satisfying certain criteria ( enumerative combinatorics ), deciding when the criteria can be met, and constructing and analyzing objects me## Antecedent (logic)

An antecedent is the first half of a hypothetical proposition. Examples: If P , then Q . This is a nonlogical formulation of a hypothetical proposition. In this case, the antecedent is P , and the consequent is Q . If X is a man, then X is mortal. "X is a man" is the antecedent for this proposition. If men have walked on the moon, then I am the king of France. Here, "men have walked on the moon" is the antecedent.## Laplacian vector field

In vector calculus, a Laplacian vector field is a vector field which is both irrotational and incompressible. If the field is denoted as v , then it is described by the following differential equations: Since the curl of v is zero, it follows that v can be expressed as the gradient of a scalar potential (see irrotational field) f : . Then, since the divergence of v is also zero, it follows from equation (1) that which is equivalent to . Therefore, the potential of a Laplacian field satisfies La## Differential equation

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and of its derivatives of various orders. Differential equations play a prominent role in engineering, physics, economics and other disciplines. Visualization of airflow into a duct modelled using the Navier-Stokes equations, a set of partial differential equations. Differential equations arise in many areas of science and technology; whenever a d## Closure (mathematics)

In mathematics, a set is said to be closed under some operation if performance of that operation on members of the set always produces a member of the set. For example, the real numbers are closed under subtraction, but the natural numbers are not: 3 and 7 are both natural numbers, but the result of 3 - 7 is not. Similarly, a set is said to be closed under a collection of operations if it is closed under each of the operations individually. A set that is closed under an operation or collection$.ajax({
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