BASIC MATH: An Introduction to Calculus

By Alix Aurora Fuentes Medina

"BASIC MATH. An Introduction to Calculus" is an easy way to learn mathematics. This textbook has four main chapters. The first chapter deals with set theory, the number system, and the real line with the Cartesian system of the plane and space. The second chapter shows some applications of set theory, permutations, combinations, relations, and functions. The third chapter illustrates translations and functional models with the types of functions: real, polynomial, constant, linear, quadratic, exponential, logarithmic, trigonometric, and inverse. The fourth chapter develops equations and inequalities, as well as linear or nonlinear systems of equations and inequalities. Finally, the fifth chapter concludes with solved recapitulation exercises.

This work is aimed at university students of traditional academic programs or distance education in economic, administrative, social, and humanistic sciences.

• Language: English
• Publisher: Lulu.com
• Release date: Jul 29, 2016
• ISBN: 9781326749736

Book preview

TABLE OF ILLUSTRATIONS

ILLUSTRATION 1.  METHODOLOGY OF SIGNIFICANT SYSTEMIC THINKING

ILLUSTRATION 2.  GRAPHIC REPRESENTATION OF THE UNIVERSAL OR REFERENTIAL SET U

ILLUSTRATION 3.  GRAPHICAL REPRESENTATION OF A SET IN A REFERENTIAL SYSTEM OR UNIVERSAL SET U

ILLUSTRATION 4.  GRAPHICAL REPRESENTATION OF TWO SETS A,B, LOCATED IN A REFERENTIAL SYSTEM U

ILLUSTRATION 5.  GRAPHIC REPRESENTATION OF THREE SETS A, B, C, IN THE REFERENTIAL SYSTEM U

ILLUSTRATION 6.  GRAPHICAL REPRESENTATION OF THE CARDINALITY OF A SET IN A UNIVERSAL SET

ILLUSTRATION 7.  GRAPHICAL REPRESENTATION OF THE CARDINALITY OF TWO SETS IN A UNIVERSAL SET

ILLUSTRATION 8.  GRAPHICAL REPRESENTATION OF THE CARDINALITY OF THREE SETS IN A UNIVERSAL SET

ILLUSTRATION 9.  GRAPHICAL REPRESENTATION OF A FUNCTIONAL MODEL WITH ONE INDEPENDENT VARIABLE

ILLUSTRATION 10.  MODEL OF THE REAL FUNCTION IN ONE VARIABLE, WITH VENN DIAGRAM

ILLUSTRATION 11.  FUNCTIONAL MODEL OF POLYNOMIAL FUNCTION IN ONE X VARIABLE

ILLUSTRATION 12.  GRAPHIC SKETCH OF A POLYNOMIAL FUNCTION IN ONE VARIABLE

ILLUSTRATION 13.  FUNCTIONAL MODEL OF THE CONSTANT FUNCTION

ILLUSTRATION 14.  GRAPHIC MODEL OF THE CONSTANT FUNCTION

ILLUSTRATION 15.  FUNCTIONAL MODEL OF THE LINEAR FUNCTION

ILLUSTRATION 16.  GRAPHIC MODEL OF THE LINEAR FUNCTION

ILLUSTRATION 17.  GRAPHICAL INTERPRETATION OF SLOPE IN THE LINEAR FUNCTION

ILLUSTRATION 18.  FUNCTIONAL MODEL OF THE QUADRATIC FUNCTION

ILLUSTRATION 19.  GRAPHS OF SOME FUNCTIONAL MODELS OF THE QUADRATIC FUNCTION

ILLUSTRATION 20.  FUNCTIONAL MODEL OF THE INVERSE FUNCTION

ILLUSTRATION 21.  FUNCTIONAL MODEL OF THE EXPONENTIAL FUNCTION

ILLUSTRATION 22.  FUNCTIONAL MODEL OF THE LOGARITHMIC FUNCTION

ILLUSTRATION 23.  DOMAIN IN ANGLES FOR TRIGONOMETRIC

FUNCTIONS

ILLUSTRATION 24.  DOMAIN IN REAL NUMBERS FOR TRIGONOMETRIC FUNCTIONS

ILLUSTRATION 25.  FUNCTIONAL MODEL OF THE SINE FUNCTION

ILLUSTRATION 26.  GRAPHICAL ANALYSIS OF THE SINE FUNCTION

ILLUSTRATION 27.  GRAPH OF THE SINE FUNCTION,

y = F(x) = sin x

ILLUSTRATION 28.  FUNCTIONAL MODEL OF THE COSINE FUNCTION

ILLUSTRATION 29.  GRAPH OF THE COSINE FUNCTION,

y= F(x) = cos x

ILLUSTRATION 30.  FUNCTIONAL MODEL OF THE TANGENT FUNCTION

ILLUSTRATION 31.  GRAPH OF THE TANGENT FUNCTION,

y = F(x) = tan x

ILLUSTRATION 32.  FUNCTIONAL MODEL OF THE COTANGENT FUNCTION

ILLUSTRATION 33. GRAPH OF THE COTANGENT FUNCTION,

y = F(x) = cot x

ILLUSTRATION 34.  FUNCTIONAL MODEL OF THE SECANT FUNCTION

ILLUSTRATION 35.  GRAPH OF THE SECANT FUNCTION,

y = F(x) = sec x

ILLUSTRATION 36.  FUNCTIONAL MODEL OF THE COSECANT FUNCTION

ILLUSTRATION 37.  GRAPH OF THE COSECANT FUNCTION,

y = F(x) = csc x

ILLUSTRATION 38.  FUNCTIONAL MODEL OF REAL FUNCTION, IN N INDEPENDENT VARIABLES

ILLUSTRATION 39.  FUNCTIONAL MODEL OF A REAL FUNCTION IN TWO INDEPENDENT VARIABLES

ILLUSTRATION 40. ALTERNATIVE OF SOLUTION IN A SYSTEM OF LINEAR EQUATIONS WITH LOCATION AT THE CARTESIAN PLANE

ILLUSTRATION 41.  GEOMETRIC INTERPRETATION OF THE INEQUALITIES IN ONE VARIABLE ON THE REAL NUMERICAL LINE

ILLUSTRATION 42.  NOTATION OF INTERVALS ON THE REAL NUMERICAL LINE, IN THE CONTEXT OF THE INEQUALITIES IN A VARIABLE

PREFACE

A relevant need in the university environment is the learning to learn Mathematics, both in academic programs on-site as well as in distance education. In this textbook to learn to learn basic Math is oriented to the requirements in the programs of administration, humanities, economy and business in general.

These mathematical foundations for Calculus include a logical constructivist structuring easily managed with a simple presentation without losing the conceptual significant depth in the application and transfer of know-know to the know-how in the knowing-being. This compendium has particular competence in the analytic selection of the mathematical foundations and minimum requirements as prerequisites to Calculus.

For this purpose this textbook BASIC MATH. An Introduction to Calculus leads to the attainment of individual and social benefits of meaningful learning that offers autonomous learning of Mathematics. The autonomous learning motivates the learning by itself in the process of teaching - learning of Mathematics towards the logical development in the theoretical argumentation and practical applications. Also, this argues the learning to learn and the learning significantly with generation and construction of knowledge in the critical understanding, analytical - reflective of the sciences.

These considerations are included in the pedagogical model of systems thinking with implementation in the platform of the organization that learns. The platform of the organization that learns includes the five basic components of the educational model that are referring to the information, the mediator, the learning process, the learner and the environment. The dynamics of these components in the systemic environment produces outcomes and achieving objectives; these goals are fed back with personal mastery and facilitators of the thought for exploring and developing the autonomous learning toward the meaningful learning.

The significant learning allows building new conceptualizations from basic concepts. This process is essential in the structuring of the logic - constructive, step by step based on reflective and analytical arguments that enhance the ability to transfer and apply the knowledge.

In this textbook the significant learning in the logistics design of each chapter is applied, beginning with the generalities to promote the constructive development of topics, the summary and the recapitulation exercises. The recapitulation exercises seek to strengthen the conceptual and exploratory handling of the mathematical contents studied.

This approach has coverage of the domain of the curricular contents of Mathematics because it offers the learner the basic mathematics necessary to develop their skills and competencies in the understanding and uses of Mathematics in general. Mathematics apply in various fields of knowledge as working tools, logical developments, creative thinking and prospective in the innovation and research.

The pedagogy of the meaningful learning provides to the learner the basic mathematics in a simple way with value in the essential concepts and applying them without losing the conceptual depth of mathematical rigor. In this process the student may make use of the mathematical foundations necessary and sufficient to study the contents of the theory of sets and its applications; wherein the functional models emerge to later study the systems of equations and inequalities.

The reflexive process with the functional models uses learn by yourself and learning to learn towards autonomous learning with a capacity and competence in the transfer and application of this knowledge in subsequent management of Calculus, with the operations of the derivative and the integral among other mathematical concepts.

In this sense, the pedagogical application provides to the learner favorable attitudes to the self-learning wherein the learner discovers their own profound comprehension of Mathematics with intellectual motivation. With this understanding, the learner can achieve with the learning to learn and the favorable disposition to their study, the scope of academic goals with expertise and control of the processes and operations of Mathematics in general.

The positive disposition to the learning motivates the learner; who will be qualified to delve into the topics covered with coverage of any academic or research field. In this context, the learner can find bibliographic support with virtual information or physical means including of university libraries.

Therefore one of the goals of this textbook is to teach Mathematics in an easy way with the personal mastery of the contents where the learner will be competent to respond critically to the mathematical ideas with the shared vision and the breaking of mental models with which the learner will achieve the maximum advantage of individual and team learning.

In this order, each learner will discover the value of self-study based on the implementation of the meaningful learning with the learning to learn in the self-critical and creative thought towards the conceptualization, application and transfer of knowledge in general.

Consequently the methodology of the book BASIC MATH, An Introduction to Calculus as an easy way to learn to learn mathematics partitions the compendium of this textbook into four main chapters. Sequentially, the first contains Set Theory; chapter two contains the applications of Set Theory, Relations and Functions; the third chapter contains Functional Models; and the fourth chapter contains Systems of Equations and Inequalities. To finish, the fifth chapter contains the Solution of Recapitulation Exercises of each of the preceding chapters.

It is emphasized that some illustrations are present in the development and construction methodology as significant expression of visual learning; which are recorded in the corresponding table of illustrations. Therefore other charts, figures or illustrations in the development of exercises will not be included in the table of illustrations unless the author considers it relevant to emphasize its importance.

In this order, set theory arises with the mathematical language that the student will use in the construction of the relations and functions. Then, attention is focused on the development of Functional Models as object of fundamental Calculus in general. The methodology continues with the development of systems of linear or nonlinear equations and linear or nonlinear inequalities. These are guidelines via which the student will construct the minimum requirements that will ensure the optimum use of Mathematics in all other areas of knowledge.

In respect to chapter five, the pedagogy guides the student to validate the results of the exercises in each chapter. This validation strengthens the learner in their personal mastery of the learning process in an environment where the mediator provides tactics for academic strategy in reaching the proposed goals.

It is important to note that the inclusion of the solutions of the recapitulation exercises fulfill the function of reflection and verification of results for the students. The verification requires the learner's self-assessment, where the complementary guide of the teacher is crucial to impart academics with an uplifting education in values ​​and ethics.

So, chapter five is only a control parameter for the student, upon which the learning level can be self-assessed. Based on the self-assessment the necessary adjustments should be made to achieve the maximum use of the learning.

The objective of this textbook is to provide the learner in classroom programs or for distance education a logical and constructive design with the basic mathematics contents. In this way the textbook includes the minimum requirements of Mathematics for addressing Calculus with significant systemic thinking which will facilitate the analytical and reflective understanding of Mathematics.

Furthermore this objective includes the personal mastery in curricular contents of basic mathematics with critical capacity for the socialization in the shared vision and complementary team work. Also this objective involves the development of skills in logistics and mathematics operations to empower the learner in their development of the breaking of paradigms and limitations in the understanding of Mathematics.

These objectives lead to the goal that makes change possible to learn for oneself in a pleasant and creative way, with the added value of learning to learn Mathematics.

This textbook is aimed at all University freshmen in classroom programs or distance education. In this sense, the constructive and conceptual process of the issues discussed here facilitate both self-learning as well as directed learning, with arguments in the learning to learn Mathematics through a simple learning process that transforms the concepts in the learner's own knowledge.

The appropriation of knowledge is of vital importance in the autonomous learning from simplicity until complexity of the thematic contents. These thought processes develop the cognitive and metacognitive competencies in the application of sciences with the construction and generation of knowledge.

Epigraph:  THE KNOW-KNOW DISCOVERS IN BEING THE SIMPLICITY OF DOING

Alix Fuentes

INTRODUCTION

The structuring of the textbook, BASIC MATH An Introduction to Calculus is an easy way to learn to learn Mathematics and is cemented by the pedagogical approach of the organization that learns, which is prospected in the five dimensions of Peter Senge. These dimensions correspond to breaking mental models, shared vision with personal mastery, team learning and systemic thinking. These dimensions are logistically fused with the five components of the educational model.

The educational model contains information, the learning process, the learner, the mediator and the environment; to generate and build a new concept to use in this mathematical production, with the pedagogical approach of significant systemic thinking. This new approach uses skills and higher order cognitive and metacognitive competencies; with which thought executes the mental processing, which transforms the information and prior knowledge of the environment and the learner.

Significant systemic thinking is executed by building and generating new knowledge, strengthened by feedback and relearning in the orientation of the mediator. The Mediator is represented as a teacher, or a textbook, or document, or a smart team, or in general any teaching aid in the learning process. This new pedagogical vision produces added value to learning, where the learner learns to learn with leadership and innovation in understanding and qualitative or quantitative uses of Mathematics.

Then the systemic model poses a didactic implementation that integrates the LEARNING PROCESS, ENVIRONMENT, INFORMATION, LEARNER, and MEDIATOR, with the individual variables of each learner, in the infinite space of innovative and creative thinking. This model produces, in systemic ideas, explicable outputs, understandings, and interpretations, with the capacity to be applied to theories or concepts. Consequently this model links the personal experience of the mediator and learner, with the academic and the practical, in different references of everyday intellect, research and development of sciences.

This approach recuperates the value of self-learning of Mathematics in a constructive process that combines the psychological basis with the student's individual dimension; the sociological foundation with the social dimension; and the anthropological foundation with the dimension of cultural being.

Other added values ​​are expected to be obtained through the interrelationships of the generation and use of knowledge with the innovation, self-critical and creative thinking culture. In this context, the following are suggested considerations applied to the learning process of Mathematics:

The environment or source of resources corresponds to the external environment of the learner, and the mediator. The mathematical and non-mathematical prerequisites are acclimated in this environment, alongside the arrangement of the learner with preconceived fears; knowledge, previous experiences and expectations.

The mediator is the teacher or facilitator of pedagogical action with the learner. Mediation includes the design and construction of strategies, tactics and learning spaces in the teaching-learning process, providing the resources that enhance autonomous learning with self-checking, self-regulation and self-reflection.

The technology in the educational process in the new millennium constitutes a determining factor in education and intellectual development of mankind. In this regard, the intervention of computers, computing, and updates to information systems in virtual or real spaces is vital. Likewise the innovation in the design and methodological construction is an important facilitator in the teaching-learning process for the learner; who accesses the learning process from its technological, academic, reflective, analytical, and logical options.

The information is an input variable to the model of significant systemic thinking. The information in this model behaves as an independent variable taken from the environment. The information is transformed into understanding, interpretation, transfer and use of intellect, for discovering in the invention of humanity, arguments that give functionality to the teaching-learning process in alternatives of the design, and construction of knowledge.

The learner, or student, is the protagonist of this pedagogical model. The learner has in their individuality, the prior knowledge, feelings and emotions; along with all the components of the human condition which addresses the learning process. In this learning process, the mediator intervenes to facilitate and encourage the development of competencies, skills, knowledge and logical constructs in a specific environment for each case.

The learning process acts with significant systemic thinking in the know-know, know-how and know-being. This learning process transforms and transfers the information obtained from the environment with self-learning or team learning for producing added-value in construction and generation of knowledge.

Pedagogic action of this textbook is designed to encourage the habit of learning to learn Mathematics focused on learner's learning process as a proposal of learning by doing. This action is reflected in every idea that it is made up of, to auto-enable the motivation that relates with itself in mental processes. These mental processes contain the identification, concepts, definitions, descriptions, application, and proper execution; along with the self-assessment and self-criticism with the option of being judge and party, for regulating and overcoming failings, towards improvement as a function in the scope of goals.

Consequently the conceptual basis of the pedagogical approach of systemic thinking is centered on three pillars, as follows:

LEARN BY ONESELF.

LEARN TO LEARN.

LEARN SIGNIFICANTLY.

Through these three pillars, individual and social benefits of autonomous learning are achieved. These benefits are a principle of growth and intellectual motivation in the various forms of the organizations that learn. These are valid from University academics until the dawn of and development of pure and applied sciences.

Particularly, significant learning with curriculum content domain of Mathematics is guided in this textbook with the following considerations:

Know-know is knowing one’s learning, where knowledge resignifies with self-reflective, regulative and creatives processes in information processing. The knowledge is appropriated with the critical review of the fundamentals of sciences, technology management and language pertinent to each science, and in general to reasoning of the scientific knowledge.

Know-how is to apply and visualize the utility with transfer of information. This action is performed for the humanization of sciences, description and interpretation of phenomena, and foundation of the scientific method in the validation of truth of the sciences, among others.

Know-being is linking personal experiences in the humanization of sciences with determination of values ​​of democracy, freedom, self-reflection, self-regulation, self-determination and autonomy. In the know-being, the understanding of reality is supported, in addition to the observation in scientific experiments to produce arguments that empower new theories and the development of sciences.

The efficiency of this pedagogical approach involves an adequate mathematical implementation of the INPUT VARIABLES with the necessary information of the defined environment. The PROCESSING transforms the information in the products generated, by the action of the systemic thought of the learner and the mediator who interact with the environment. The OUTPUT VARIABLES generate learning products, which FEEDBACK to the learner in the systemic model.

The achievement of goals needs self-assessment, for regulating the results with the relearn; and the LEARNING TO LEARN as an added value of this methodology towards autonomous learning in the teaching and learning of Mathematics for oneself in the learning processes.

Considering one of the goals of the systemic thinking teaching model in learning to learn and learn for yourself, the goals that indicate our path are located with the prior location of where we are, and the strategy of how we will achieve the goals in each conceptual management is designed in the learning process.

Below is an essential sketch that illustrates the methodology of significant systemic thinking as a creative proposal in the development of this textbook. These values ​​seek to facilitate mathematical learning with leadership in the intellectual enthusiasm of the learner.

ILLUSTRATION 1.  METHODOLOGY OF SIGNIFICANT SYSTEMIC THINKING

CHAPTER 1… CHAPTER 1 SET THEORY

SPECIFIC OBJECTIVES

Handle in the ideas the generation and transfer of knowledge through of the set theory to relearn with self-critical reflection.

Learn to learn the essential foundations of set theory through of the understanding their language, symbology and operationalization, for obtaining the conceptualization and interpretation of the real number system alongside the significant systemic thinking of the dimensions.

Construct the mathematical foundation of the plane and Cartesian space, through the application of Cartesian product in the real numbers and the concept of a straight line, to understand the Cartesian diagrams, from the point of view of the theory of sets.

CHAPTER 1.  SET THEORY

GENERAL OBJECTIVE

Learn to learn the theory of sets through the conceptualization of ideas in mathematical language, to learn for oneself with analytical logic the construction of the real number system and the Cartesian product, along with the concepts of dimensions in the plane and space real.

GENERALITIES OF THE SET THEORY

The theory of sets includes in the formalization of this approach to teaching at least four large pillars that make reference to the reasoning, analysis, language and logic discipline.

These pillars are essential to address the Calculus, and its structure contains mathematical arguments to the encounter of the fascinating world of Differential and Integral Calculus. Consequently the theory of sets is a facilitator of growth and intellectual development wherein the learner will reach various goals in the formulation and solution of problems of knowledge.

In this respect the Mathematics have a specialized language with symbols and propositions among others, in our world cognitive and metacognitive. This language enables unified communications with theories in mathematical terms, and in general formal expressions of Mathematics.

For these reasons this approach poses some common terms of mathematical language to use in this textbook, BASIC MATH. An Introduction to Calculus , as follows.

THEORY

A theory is a set of ideas or abstractions of something that are related with rules or laws, for producing the construction and generation of knowledge in a given context.

One theory is expressed by a linguistic medium, to which the communication of knowledge is embodied in mankind. Accordingly a theory contains in its structuring, symbols and propositions among others.

SYMBOLS

The symbols are basic elements or primitive of communication, created by man to describe or communicate everything that surrounds him, and attracts the attention. A symbol is represented by an ordered pair, where the first component is signifier or object, and the second component is the meaning or idea. Then the symbol is defined as follows:

Symbol = (signifier, meaning) = (Object, idea)

OBJECT: is the recipient or signifier of the symbol for itself, so the object has no meaning; and often the object is of a material nature, expressed in words.

IDEA: is the meaning of the symbol and frequently expresses the meaning of the word.

PROPOSITIONS

The propositions are a particular species of symbols, which complies with the following considerations:

The signifier is a grammatical sentence containing at least a subject and a verb.

The meaning must be true or false but not both.

Most used prepositions in mathematical language are:

AXIOMA.

THEOREM.

PARADOXES.

AXIOM: is a proposition whose meaning has been accepted as true by an explicit agreement.

THEOREM: is a proposition whose truth or falsity can be demonstrated by a logical process, supported by previously accepted axioms.

PARADOXES: are propositions that contain contradictions. Are usually contradictory propositions that seem to be true.

ONE THEORY INCLUDES ACTIONS IN ITS STRUCTURE HIGHLIGHTING THE FOLLOWING:

Gather symbols or of communication primitive elements.

Specify rules for constructing composite elements from primitive elements.

Integrate the axiomatic context of the theory for establishing the ground rules consistent with the general principles associated with the primitive elements and compounds of language.

Determine construction criteria, inference or deduction which allow to identify if a composite element of the language, is sufficient or necessary immediate consequence of other, or others language elements.

Produce the definitions and abbreviations of the primitive or compounds elements of the language.

Formulate theorems to develop the theory, supported by the axioms and rules of inference, through a process demonstrative.

1.2.  NOTION OF SET

A set is not defined by the property of having elements because the empty set has no elements, and yet it is a set. The sets are not real entities, but rather ideas created by the human mind expressed in the language of symbols, as primitive elements of a theory. Then when talking about a real entity, in reality, it is talking of the ideas that have been built of the real entity, through perception and observation, among other mental processes.

Consequently the real objects are abstracted in thought as a collection of ideas that happen to be abstractions or representations in the mind of the real properties of the entity.

This reflection leads to that in Mathematics, a set is the meeting of these well-defined abstractions in the ideas and formalized in the axiomatic set theory.

The abstraction is handled with adequate ideas to the entity being one of them the set idea. This set idea is created in Mathematics for understanding the universe of our ideas with the conceptual formality in the axiomatic set theory. This formality describes in the language of sets among others, the comprehension to or extension of a set, allowing the learner to evaluate whether the meeting of abstractions, is well or poorly defined.

PRINCIPLE OF THE EXCLUDED THIRD

In attention to the principle of the excluded third, a set cannot be and not be simultaneously an element of itself; with which it is accepted that all the sets are divided into two disjoint groups:

Sets that are normal sets.

Sets that are abnormal sets.

NORMAL SET

It is said that the set A is a normal set, if A is a set and is not a an element of itself.

Example 1.

The set whose elements are the fingers of the right hand, is not a finger of the right hand.

ABNORMAL SET

A set A, is abnormal, when the same set A, is one of its elements.

Example 2.

Set A, is equal to the set of x such that x is a set that can be described with less than a thousand words.

Solution:

One solution is the set A whose elements are all sets that can be described with less than a thousand words; symbolically is:

A = { x | x is a set that can be described with less than a thousand words}

Noting that the set A, has been described with less than a thousand words; and consequently in this example the same set A, is one of its elements, reason why the set A is a set abnormal.

The majority of sets are normal sets, and these are the most common in the scope of the objectives of this textbook because the normal sets will be required in the understanding of the relations and functional models.

It is noteworthy that the sets have been classified into normal and abnormal without explicitly defining a set, because among others, up to this point has not been established a suitable border to the concept of a set.

This process constructive of the theory of sets leads to make use of the resource FORMAL LANGUAGE OF THE THEORY OF SETS; this language does not define what is a set, but whether define the delimitation and structure of the axiomatic set theory. In this sense, the ideas come alive on the notion of set, with capacity to build other ideas more elaborated in the generation and construction of knowledge.

1.3.  SET THEORY

Set theory is a formal language of Mathematics based on the characterization of a set as ideas or abstractions that are structured to build other ideas through them more elaborate and complex. This language is expressed in symbol with propositions, axioms, theorems, lemmas, corollaries, paradoxes, inference criteria and definitions among others, to communicate and develop part of the study of Mathematics.

The significant learning in the theory of sets will allow to the learner to find the location logistics of the relations and functions. These functions will be subject of the operations of Differentiation and Integration in the study of Calculus.

On the objectives of