TOPICS AND DEFINITIONS OF MATHEMATICS
The project is intended to write down - possibly using materials sent by users - and to make available in internet some synthetic and plain elementary mathematics items with the following parts
Part 1 Part 2 Part 3
NUMERICAL SETS INEQUATIONS TRIGONOMETRY
ELEMENTS OF ARITHMETICS LOGARITHMS COMPLEX NUMBERS
RELATIVE NUMBERS PROGRESSIONS HYPERBOLIC FUNCTIONS
ALGEBRA COMBINATORY CALCULUS ANALYTIC PLANE GEOMETRY
PLANE GEOMETRY MATRIX AND DETERMINANTS ANALYTIC SPATIAL GEOMETRY
SPATIAL GEOMETRY   VECTORS
MATTER PART 1
NUMERICAL SETS

Main numerical unions:
1) Natural numbers N = {0 , 1 , 2 , 3 , 4 , 5…….}

2) Integer Numbers  Z = { ..., -3, -2, -1, 0, 1 , 2 , 3 , 4 . . . . .} 

3) Rational numbers Q = { ..., -3/4,..., -2,..., -1,..., -1/3,.., 0,...,1/2,...2/3,...1,...,3/2,...,2,...,15/7,...} - Integers+ fractional

4) Real numbers: R =  the set obtained where we have all possible decimal finite and infinite, regular (rational) or less (irrational).
5) Complex numbers C= add to the set R the imaginary unit i =  .  
ELEMENTS OF ARITHMETICS Arithmetic is the study of the numbers properties and operations on them
RELATIVE NUMBERS Relative indicates the numbers that have the sign (+ or -) and their set is denoted by the letter Z.
ALGEBRA Algebra is the literal calculation, representing numbers by symbols and letters, and operations that can be performed on them. 
Classical algebra: study of algebraic equations, a tool to solve problems.
Modern algebra: deals with mathematical structures quite general, as groups
PLANE GEOMETRY That Euclidean geometry branch geared precisely to plane. The study of plane figures, based on Euclidean axioms regarding point, line, segment, plane
SPATIAL GEOMETRY Three-dimensional application extending postulates to the space and to building solids in space. By the equivalence passing to measure both surfaces and volumes of the three-dimensional  items.
  PART 2
INEQUATIONS Algebraic statement that an inequality holds between two values. Basic notations:
a > b that is a is greater than b
a < b that is a is less than b
a ≥ b that is a is equal to b or greater than b
a ≤ b that is a is equal to b or less than b
a ≠ b that is , the term a is different from b

LOGARITHMS

Notation: is said logarithm of a number 'a' in base 'b' that  number 'x' that given as exponent to the base 'b' reproduces the number 'a', that is:
PROGRESSIONS Arithmetic progression: sequence of numbers such that the difference of any two successive members of the sequence is a constant.
Geometric progression: sequence of numbers such that the quotient of any two successive members of the sequence is a constant
COMBINATORY CALCULUS Given a set S of n objects one wants to count the number of possible configurations of k objects taken from this set. We have:

- Simple permutations (without repetition) P_{n} = n \cdot (n - 1) \cdot (n-2) \cdot \dots \cdot 1 = n!
- Permutations with repetition
- Derangement :permutation of the elements of a set, such that no element appears in its original position.
- Simple dispositions (without repetition)
- Dispositions (with repetition)
MATRICES AND DETERMINANTS

MATRIX:set of numbers, real or complex, ranked according to rows and columns. It is said matrix of order m,n, where m is the number of rows and n the number of columns.
DETERMINANT:is the number associated with a square matrix (m = n). The determinant of a matrix A and is denoted by det A or with ||.
It's possible to decompose a non-square matrix into a series of products of square matrices and numbers, so as to be able to calculate their value.
Note: matrices and determinants are used to calculate the value of coefficients of systems of equations with n unknown variables.
  PART 3
TRIGONOMETRY It is a branch of mathematics that studies relationships involving lengths and angles of triangles. It comes from Greek τρίγωνον, "triangle" and μέτρον, "measure".  π (radiant equivalent of 180°)  is the Archimedes constant defined as the ratio between the measure of the length of the circumference and the length measurement of the diameter of a circle. This is very important to define the relationship of radiants-degrees and the trigonometric functions sin() cos() tg() etc..
COMPLEX NUMBERS Are the expressions  where there are both real numbers and the  imaginary unit i that is equal to the square root of -1. Then the field of complex numbers as its subfield includes the field of real numbers .
HYPERBOLIC FUNCTIONS

sinh, cosh, tanh and the derived functions are hyperbolic functions
Given an equilateral hyperbole  then tangent to the lines with equation y = x and y = -x, a symmetric hyperbolic sector with opening angle  α and area A determines an intersection point  P with the hyperbole itself. Then from this derives that

sinhx is the hyperbolic sine
coshx is the hyperbolic cosine .
PLANE ANALYTICAL GEOMETRY In classical mathematics, analytic geometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry using a two-dimensional coordinate system.
SPACE ANALYTIC GEOMETRY In classical mathematics, analytic geometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry using a three-dimensonal coordinate system.
VECTORS In physics and geometry, the euclidean vector are used to represent both magnitude and direction of physical quantities.
Depending on context,Vectors can also have a variety of different meanings 

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