The math is a deductive logical science, which uses symbols to generate an accurate theory of deduction and inference based on definitions, axioms, postulates and rules that transform primitive elements into more complex relations and theorems. This science teaches the individual to think in a logical way and therefore to develop skills to solve problems and make decisions. Numerical skills are valued by most sectors, it can be said that in some cases they are considered essential.
What is mathematics
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Mathematics is a science that starts from a logical deduction, which allows you to study the characteristics and existing links in abstract values such as numbers, icons, geometric figures or any other symbol. Mathematics is around everything that the individual does.
It is the cornerstone of all everyday life, including mobile devices, architecture (ancient and modern), art, money, engineering, and even sports. Since its inception in history, mathematical discovery has remained at the forefront of all highly civilized societies and has been used even in the most primitive cultures. The more complex the society, the more complex the mathematical needs are.
Origin and evolution of mathematics
The origin of mathematics is closely linked to the history of one of the wisest civilizations in the world, ancient Egypt. In its history there are thousands of knowledge conceived by the mixture between magic and science. When the modern age arrived, mathematics became a secular and quantitative science.
The Sumerians were the first people to develop a counting system. Mathematicians developed arithmetic, which includes basic operations, fractions, multiplication, and square roots. The Sumerian system passed from the Akkadian Empire to the Babylonians in 300 BC. Then some 700 years later the Mayans in America developed the calendar system and became expert astronomers.
The work of mathematicians began as civilizations grew, the first to emerge was geometry, which calculates areas and volumes. Then in the 9th century the mathematician Muhammad ibn-Musa invented the Älgebra, it developed quick methods to multiply and find numbers, known as algorithms.
Some Greek mathematicians left an indelible mark on the history of mathematics, among them are Archimedes, Apollonius, Pappus, Diophantus and Euclid, all from that time, then they began to work on trigonometry, which requires the measurement of angles and the calculation of functions. trigonometric, which includes sine, cosine, tangent, and their reciprocals.
Trigonometry is based on synthetic geometry developed by mathematicians like Euclid. For example, the theorem of Ptolemy who gives rules for the chord of the sums and the differences of the angles, which correspond to the formulas of the sums and difference for the sines and cosines. In past cultures, trigonometry was applied to astronomy and to the calculation of angles in the celestial sphere.
Archimedes 3rd century BC, an illustrious mathematician and one of the most important in his time, made very relevant advances in the field of physics, mathematics and engineering. In addition to designing military weapons for the defense of his hometown Syracuse.
Among its main findings are:
- The discovery of the Archimedean Principle.
- Definition of the law of the lever.
- He made a very precise approximation of the number pi, using geometric methods.
- Calculate the area under the arc of a parabola by using infinitesimals.
Euclid, a mathematician from the time of Ancient Greece, developed a definition of mathematics, which becomes an essential tool for students, which is the Euclidean division. This consists of dividing an integer different from zero by another, with the aim of obtaining a result without having to perform the operation on paper. The Euclidean division is not only based on the simplicity of its realization, but on the possibility of carrying it out without the help of a calculator.
The mathematician John Napier (1550-1617) created the definition of the natural logarithm, represented it in a table of logarithms, through this tool the products can be transformed into sums. This resource of indispensable use in modern mathematics, is mandatory in the learning of any beginner in mathematics.
René Descartes, philosopher, scientist and mathematician, his greatest interest focused on mathematical problems and philosophy. In 1628 he settled in Holland and dedicated himself to writing Philosophical Essays, which were published in 1637. These essays are made up of four parts, which are geometry, optics, meteors and the last one by the Discourse on method, which describes his philosophical speculations.
Descartes is the creator of the use of the last letters of the alphabet to distinguish the unknown quantities and the first ones for the known ones in Algebra.
His greatest contribution in mathematics was in the systematization of analytic geometry.
He was the first to invent the classification of curves according to the type of equations that produce them and he participated in the development of the theory of equations.
Classification of mathematics
Knowledge of mathematical logic is formed by the process of classification, this represents the first steps to the study and learning of the most complex mathematical concepts.
As opposed to common perception, the concept of mathematics does not consist only of numbers or solving equations, there are branches of mathematics that deal with the creation of equations or the analysis of their solutions, and there are parts of this science dedicated to the creation of methods for calculations. Also, some of them have nothing to do with numbers and equations.
The classification of mathematics created by UNESCO, part of a system of applied knowledge according to the order of doctoral theses. The major divisions are coded with two digits and are called fields, in the case of mathematics it is distinguished with the number 12, its disciplines are identified with 4 digits, among them:
- 12 Mathematics.
- 1201 Algebra.
- 1202 Mathematical analysis and functional analysis.
- 1203 Computer science.
- 1204 Geometry.
- 1205 Number theory.
- 1206 Numerical analysis.
- 1207 Operational research.
- 1208 Probability.
- 1209 Statistics.
- 1210 Topology.
Arithmetic
Arithmetic is the branch of mathematics that relates to counting and figuring out how to work and manipulate whole numbers and fractions. That is, its main objective is the study of numbers, in addition to the mathematical problems that are carried out with them.
This branch of mathematics also studies elementary numerical structures and their basic operations, in addition to this, it uses the processes to carry out operations such as addition, subtraction, multiplication and division.
The calculations or arithmetic operations can be carried out in different ways, when they are simple operations, they can be done mentally or go to any other option that helps to obtain the results. At present, these operations are generally performed with the help of calculators, either physically or mentally.
Geometry
Geometry is a branch of mathematics, which is based on the study of the properties and measurements of figures in the plane and in space.
Born from land surveying, geometry was for the ancient Greeks a scientific language used in the discovery of the idealizations of objects in the external world, points and geometric lines, without thickness or thickness, immaterial, are abstractions of marks, which for example, draw a pencil on a piece of paper, or of the places where the walls of a room are.
According to the British Harold Scott MacDonald Coxeter, who specialized in geometry, “It is the most elementary of the sciences that allow man, through purely intellectual processes, to make predictions (based on observation) about the physical world. The power of geometry, in the sense of precision and utility of these deductions, is impressive and has been a powerful motivation for the study of logic in geometry "
The main branches of geometry are:
- Euclidean geometry.
- Analytic geometry.
- Projective geometry
- Differential geometry.
- Non-Euclidean geometry.
Algebra
It is the branch of mathematics that uses numbers, signs and letters to refer to the different arithmetic exercises that are performed. In it (to achieve generalization) the quantities are represented by letters, which can represent all values. Thus, "a" represents the value that the person assigns to it, although it should be noted that when in a problem we assign a certain value to a letter, that letter cannot represent, in the same problem, another value other than the one assigned to it. originally.
The symbols used in Algebra to represent quantities are numbers and letters:
The same letter can represent different values and they are differentiated through quotation marks for example, a ', a ”, a' '', which are read first, second and third or also by means of subscripts for example a1, a2, a3 that are read, subuno, subdos, subtres.
Algebra signs are of three kinds: operation signs, relationship signs, and grouping signs.
A technical definition of mathematical functions indicates that they represent the relationship of a set of inputs to a set of possible outputs, where each input is related exactly to one output.
Statistics
Statistics is a powerful auxiliary to many human sciences and activities such as: sociology, psychology, human geography, economics, etc. It is an essential tool for decision making. It is also widely used to show the quantitative aspects of a situation.
This branch of mathematics is related to the study of processes whose result is more or less unpredictable and with the way to obtain conclusions to make reasonable decisions based on such observations.
The result of the study of these processes, called random processes, can be qualitative or quantitative in nature and, in the latter case, discrete or continuous.
From the moment that man lives in society he needs statistics, since in the censuses, data collection, etc., carried out at first with a practical purpose, their numerical relationship was later investigated, taking into account the effects that produced the variations of these numbers.
The predictions statistics hardly refer to facts, but describe with considerable accuracy the overall behavior of large sets of particular events. They are predictions that, for example, are not useful to know who, among members of a population, is going to find work, or on the contrary, who is going to be left without it. But it can provide reliable estimates of the next increase or decrease in the unemployment rate for the entire population.
Types of math
Mathematics is responsible for explaining change, quantitative relationships, and the structures of things within a framework of equations and numerical relationships. It can be said that most human activities have some kind of connection with mathematics. These links may be obvious, as in the case of engineering, physics, chemistry, among others, or they may be less noticeable, as in medicine or music.
Pure mathematics
Pure mathematics are those that study the relationships of intangible structures by themselves. Pure mathematics is the study of the basic concepts and structures that underlie mathematics. Its purpose is to seek a deeper understanding and greater knowledge of mathematics itself.
These mathematics have been divided into three specialties: analytics, which studies the continuous aspects of mathematics; geometry and algebra, which are responsible for the study of discrete aspects. The undergraduate program is designed to familiarize students with each of these areas. Students may also want to explore other topics such as logic, number theory, complex analysis, and subjects within applied mathematics.
The median in mathematics is the central number in a group of digits that have been ordered by size. When the number of terms is even, the median is obtained by calculating the average of the two central numbers.
In the mathematics exercises to obtain the median of a group of numbers, proceed as follows:
- The numbers are ordered according to their size.
- If the quantity of the term is odd, the median is the center value.
- When the quantity of the term is even, the two middle terms are added and divided by two.
Applied mathematics
Applied mathematics refers to all those mathematical tools and methods that can be used in the analysis or solutions of problems corresponding to the area of social or applied sciences. Many of these methods are effective in the study of problems in Biology, Physics, Medicine, Chemistry, Social Sciences, Engineering, Economics, among others. In order to obtain results and solutions it is necessary to have knowledge of various branches of mathematics, such as analysis, differential equations and stochastics, using analytical and numerical methods.
The mathematical model is the simplified way of representing a phenomenon or the relationship between two variables, this is done through equations, mathematical formulas or functions.
Their characteristics are:
- It gives precision and direction for the solution of the problem.
- It allows a deep understanding of the modeled system.
- It paves the way for better design or control of a system.
- It enables the efficient use of modern computing capabilities.
Mathematical Symbols
Mathematical symbols are used to perform various operations. Symbols make it easy to reference mathematical quantities and help to denote easily. It is interesting to note that all mathematics is based entirely on numbers and symbols. Mathematical symbols not only refer to different numbers but also represent the relationship between two quantities.
The mathematical symbols are:
- Addition: Represents the addition of two numbers and its sign is "+".
- Subtraction: Represents the subtraction of two numbers and its sign is "-".
- Multiplication: It represents the number of times the numbers are added and its sign is "X".
- Division: Represents the total amount divided into parts and its sign is "÷".
- Equal: Represents the balance between two expressions and is one of the most important in mathematics "=".
- Parentheses, braces and brackets: These are used to group operations when several appear in the same expression and you want to specify the order to solve them. "(), {},".
- Greater than and less than: They are used to compare quantities>, <.
- Percentage: Represents the given quantity out of a total of 100 and its sign is "%".
On the other hand, it is important to highlight the contribution of great thinkers and scientists who have left their mark on mathematics books, through their mathematical thoughts, some of them are, for example:
"No human investigation can be called science if it does not pass through mathematical tests" Leonardo Da Vinci.
"In mathematics, even the smallest errors should not be neglected" Isaac Newton.
“We cannot teach anyone anything. We can only help them discover for themselves ” Galileo Galilei.
From the beginning, the human being has had the need to count, measure and determine the shape of everything that surrounded him. The progress of human civilization and the progress of mathematics have gone hand in hand. For example, without the Greek, Arab and Hindu discoveries in trigonometry, the navigation of open oceans would have been an even more adventurous task, the trade routes from China to Europe or from Indonesia to the Americas, were held together by an invisible mathematical thread..
There is no doubt that mathematics has become the guide for the world we live in, the world that we shape and change, and of which we are a part. Mathematics is the engine that moves our industrial civilization, it is the language of science, technology and engineering, it is also essential for architecture, design, economics and medicine, in our social life, when making purchases. Also in interactive programs with math games of different levels and mathematical challenges.
