Throughout history, human beings have always had the need to count, to express commercial operations and to solve other problems that have arisen in the development of mathematics. We will analyze the evolution of the various sets, in such a way that each of them is contained in the next.
By counting techniques we mean any algorithm that is used to count, that is, to find the cardinal of a set. Within counting techniques, Combinatorics deserves a special treatment: variations, permutations and combinations; although we will not deal with it in this topic since they have already been treated before.
In this post we are going to study one of the most important applications of derivatives: the equation of the tangent line and the normal line; as well as the various applications that we can find. We will start by looking at the interpretation of the derivative, and then the three types of exercises that we can find:
INTRODUCTION Jules Henri Poincaré was a 19th century French mathematician who stood out not only for his mathematical work but also for his work as a physicist, theoretical scientist and philosopher. Among his most important works in Physics, those related to the theory of light and electromagnetic waves stand out.
Today we are going to study another property of functions (and/or series as we will see later). We will first study when we say that a function is bounded above and when it is bounded below, to finally be able to establish when a function is bounded.
Due to the fact that the natural numbers are infinite, it is necessary to look for a set of words, symbols and rules that allow us to determine the natural numbers and vice versa; while being able to work with them. In this post we are going to define the numbering systems, their properties and some of the most common ones, such as the one we use:
Today we are going to work with an entertaining exercise that can be done at all levels by modifying its complexity: the magic squares. The magic squares are tables, or better said, grids with integers in such a way that the sum of the figures of the rows and columns, as well as the sum of the main diagonal is always the same quantity, called the magic constant.
The algebraic language is a way of translating into symbols and numbers what we normally take to be particular expressions. In this way, unknown quantities can be manipulated with easy-to-write symbols, which allows simplifying theorems , formulating equations and inequations and studying how to solve them.
Yesterday we did a study of geometric bodies. Today we are going to continue that study, but in this case of some special geometric bodies, round bodies. Round bodies are geometric figures that have at least one of their curved faces. They are also known by the name of bodies of revolution since all of them are obtained by rotating a figure around an axis.
We already know how to do a study of a random variable depending on the type in question, we have seen how to make the frequency table and how to calculate the measures of position and dispersion. Today we are going to focus on the different ways we have to represent the data collected in the frequency tables, which will depend on the type of variable we are working with.
A fraction or broken is the division of something into parts. If we take the fraction 2/4 as an example, it is read as two fourths, and what it does is indicate two parts over the four total parts. We can see then that what gives this fraction its name is the number below which we call the denominator since we "
In the field of mathematics, a fraction or fraction is the division of something into parts. If we take the fraction ¾ as an example, it is read as three quarters, and what it does is indicate three parts over four totals. Here we can see that what gives this fraction its name is the bottom number which we call the denominator since we call the fraction "
After a long, long summer, it is necessary to return to the routine. We look back to mathematics and today we have to study the characteristics of geometric bodies, that is, the number of faces, vertices, axes of symmetry, etc. We'll start with the cube first:
By combinatorial analysis, we refer to that part of algebra that deals with the study of the groups that are formed with given elements, differing from each other, by the number of elements that are incorporated in each group, by the type of elements and by the order of their placement.
As we already know, combinatorics is the part of algebra that deals with the study of the groups that can be formed with certain elements, distinguishing between them the number of elements, their type and their order. The groupings formed can be variations, permutations or combinations.
Radiation is defined as the inverse operation of potentiation. Power is a mathematical expression that includes two named terms: base a and exponent n. It is written as follows: Reads like, “a raised to n” To better understand the definition of settlement, suppose we are given a number a and asked to calculate another, such that multiplied by itself a number b of times gives us the number a.
Combinatorics is a branch of mathematics that deals with the study of finite sets of objects that satisfy specific criteria and that is especially concerned with counting the objects in such sets. In other words, it is a part of algebra that is responsible for studying the groups that are formed, distinguishing between them the number of elements that make up each group, the type of these elements and their order.
Once the sample data we are going to study have been collected, it is necessary to group them by ordering them in the form of a table, this table is called frequency distribution orfrequency table. In this section we will focus on frequency tables for one-dimensional random variables (we will study two-dimensional random variables later).
We will call combined operations those in which several arithmetic operations appear to solve. To obtain a correct result, it is necessary to follow some rules and take into account the priority between the operations. In the first place, the present terms must be separated in order to be able to solve each of these later.
DEFINITION Let f be a continuous function defined in a domain A, the function derivative of f is defined at the point a of the set A and is denoted by f´(a), when next limit value: If we call h=x-a, we can also write the definition as follows:
The trigonometric identities are equalities involving trigonometric functions. These identities are always useful when we need to simplify expressions that have trigonometric functions included, whatever values are assigned to the angles for which these ratios are defined.
In order to carry out a statistical study of a characteristic that we want to study in a certain population, it is necessary to analyze a sample of said population from which we can obtain specific numbers that allow us to analyze the collected data.
We are going to study a new concept of Mathematical Analysis: the composite function. A composite function is a function that is formed by the composition of two functions, that is, the function resulting from applying a function to x first and then applying a new function to this result.
In today's article we return to the branch of Statistics to talk about one of the most important discrete distributions: the Poisson distribution. This distribution is used in situations where you want to determine the number of events of a specific type that occur in a given space or time interval.
We are going to study today one of the three most famous problems of antiquity: the squaring of the circle,in fact it is considered an impossible problem, and at the end of the 19th century the mathematician Ferdinand Lindemann showed that the problem was unsolvable due to the transcendental character of the number pi.
In today's article we are going to study the representation of the quadratic functions , that is, the equations of the second degree. Taking into account that the graphs of the second degree equations correspond to the parabolas, in this post, we are going to study the characteristic elements of these.
After seeing the relative positions of two circles, today we are going to study the angles of a circle. Central angle: It is the angle that has its vertex in the center of the circumference, that is, an angle determined by two rays that have the origin in the center, and therefore they are radii of the circumference.
Not everything in mathematics is numbers, theorems, proofs, calculations… and a long etcetera of endless things that sound just as boring (although for me they are not). Today we are going to discover the literary side of a great Persian mathematician who was born in the 11th century:
Once we have seen the methods that exist to be able to solve systems of linear equations, we will also study how to solve some of the non-linear systems using these methods. It is very important to choose the right method, otherwise its resolution could be very heavy, difficult and therefore easy to make mistakes.
On previous occasions we have studied some of the characteristics of the circle, such as the points of contact, that is, the relative position of a circle and a line. But now the time has come to study more about the geometry of the circle. To start we will see some previous formal definitions:
We are going to study today the different methods for solving systems of linear equations with two unknowns. Systems of linear equations are of the form: where a, b, c, a´, b´and c´are real numbers. To solve this type of system of equations, that is, find the value of x and y that satisfies both equations;
Once we have seen the composite function, we will also study the inverse function. Since we have mentioned it before in the properties of the compound functions. On this occasion, we will study the process to obtain the inverse function, as well as see some of the most important examples of inverse functions and how they are represented.
The main mathematician who is considered the predecessor of set theory is George Cantor, a German mathematician who lived between 1845 and 1918. Set theory is a branch of mathematics that, as its name suggests, studies properties of sets. A set, according to Cantor's words, is a collection of objects that are clearly determined and differentiated both when contemplating them and in our thinking, this collection of objects constitutes a whole.
We are going to dig a little deeper into the Theory of Numbers by presenting a new concept that at the same time is well known by all: prime numbers. We don't know for sure the exact year in which the prime numbers appeared, but more than 20,000 years ago (which is said soon) it seems that they worked with them or at least knew them, due to the marks found in a bone.
We continue working on the Theory of Numbers, today it is the turn of the Diophantine equations , which, as their name indicates, are due to Diophantus, an ancient Greek mathematician whose work was of great importance and influence on later generations.
As we have mentioned in previous articles, one of the most important applications in mathematics is solving optimization problems. But what do we mean by optimization problems? How can we solve them? Do not worry, because these and other of your concerns will be resolved if you continue reading.
We have already worked numerous times with matrices and in fact, we have also talked about the rank of a matrix; but what do we mean by rank of a matrix? And how can we calculate it? These are the questions that we are going to answer in this post.
The linear programming is a method to solve optimization problems that are subject to a series of conditions or restrictions, which are given by a series of inequalities. In order to carry out the resolution of this type of problem, it is necessary to represent these restrictions in the plane, which will give rise to the feasible region , that is, the region in which the solution to our objective function will be found, which is the function that we have to maximize or min
One of the most important characteristics when making the graphical representation of a function is to study its monotony, that is, where our function increases and decreases. As well as determining the maximums and/or minimums in the event that it had them.
Thales of Miletus (630 BC – 545 BC) was one of the most famous Greek philosophers, but not only stands out for that, but like all the wise men of that time, also stood out as a scientist and mathematician, where his contributions to geometry are very important, and one of these contributions is the one we are going to focus on, the well-known “Thales Theorem”.