The Mathematics degree is a professional option consisting primarily of courses in pure and applied mathematics aimed at developing skills in communication, quantitative analysis, abstract thinking, and modeling. Our mission is to cooperate with society to improve the quality of life for its members through the training of ethical and well-rounded mathematicians capable of solving problems in their environment and working in multidisciplinary teams, enhancing their research and creativity skills throughout their lives.
* Undergraduate tuition/fees:
The Constitution of the Republic of Ecuador in its Article 356, among other principles, establishes that third-level public higher education will be tuition/fees free. Zero cost education is linked to the academic responsibility of the students.
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To study mathematics, one must be curious, critical, analytical, and have aptitude for logical and abstract thinking.
Educational Objectives
- To solve environmental problems using mathematical foundations.
- To adapt mathematical models in order to obtain new problem-solving approaches that arise in contexts such as science, technology, industry, finance, among others.
- To collaborate in interdisciplinary groups contributing to knowledge generation.
- To pursue postgraduate programs strengthening perspectives and scope.
Learning Outcomes
- Ability to identify, formulate, and solve broadly defined technical or scientific problems using mathematical knowledge.
- Ability to formulate or design a system, process, procedure, or program to model environmental phenomena.
- Ability to develop and conduct experiments or test hypotheses, to analyze and interpret data, and to use scientific judgment to draw conclusions.
- Ability to communicate effectively to a range of audiences.
- Ability to communicate effectively in English.
- Understanding of ethical and professional responsibilities, and the impact of technical or scientific solutions in global, economic, environmental, and social contexts.
- Ability to function effectively in teams that set goals, plan tasks, meet deadlines, and analyze risk and uncertainty.
- Ability to acquire and apply new knowledge as needed, using appropriate learning strategies.
- Ability to design real solutions that propose unique value as a response to specific needs considered from the perspective of those involved.
First Year
Descripción:
In this course, students apply the Design Thinking methodology to identify, analyze real-life problems or needs, to design innovative solutions. Students work in multidisciplinary teams to present solution proposals that add value to customers/users from private companies, public organizations and non-profit organizations.
Descripción:
This course is for basic training on students who begin the Mathematics career, and so they need the development of the ability to make demonstrations for tackling deeper studies, in both mathematics and other sciences. The course consists of five chapters, which begins by introducing the principles of propositional logic. Following, these principles are applied in the verification of elementary properties of set theory. Then, it proceeds to analyze the demonstration methods, to finally use them when studying the concepts of relations and functions, and some basic topics in number theory.
Descripción:
This basic and general education subject presents grammatical structures to produce a simple paragraph based on a writing program. Additionally, it allows the identification of a specific argument in oral and written communication. It also considers learners’ personal opinions about different topics related to social, academic, and professional aspects. It includes the necessary vocabulary to make comparisons between present and past, books or movies description, creation of simple students’ profile, opinions about inventions, formal apologies and tell past events.
Descripción:
This lower division course is aimed at undergraduate students of mathematics; it prepares them to handle the axiomatic method, that is, to carry out deductive proofs starting from axioms or postulates with geometric arguments. The course introduces an axiomatic system based on a rule and a protractor and then studies properties of congruence and similarity of plane figures. Then, it introduce algebraic methods that complement synthetic methods. Finally, advanced Euclidean geometry is studied, through contemporary theorems.
Descripción:
This subject, aimed at the basic training of students in the Mathematics career, represents an approach to the concepts and techniques of the so-called differential calculus, which focuses on the concept of derivative. The course begins with a brief description of the basic fundamentals of the topology of the real line. Then, the concept of limit is studied, later that of continuity and its properties, to reach the fundamental notion that is the derivative. These concepts are applied in the solution of a significant number of practical problems in fields such as economics, engineering, physics, and mathematics. Finally, the notion of calculus of the antiderivative is introduced as a prelude to the integral.
Descripción:
Physics: Mechanics is a basic, theoretical-practical training course aimed at engineering students, with laboratory experimentation activities, which provides the fundamentals of particle mechanics, rigid bodies and fluid mechanics, in an environment of active learning.
Descripción:
The course presents students with strategies to solve common problems in various professional fields through the design and implementation of solutions based on the use of a programming language. It covers the basic principles so that the student can read and write programs; emphasizing the design and analysis of algorithms. In addition, it introduces students to the use of development and debugging tools.
Descripción:
This subject of basic formation and general education presents the grammatical structures for the production of an academic paragraph, through the development of the writing program in a transversal way. In addition, it allows the identification of specific arguments in oral and written communication, considering the production of one's own criteria on different topics of a social, academic or professional nature. The necessary vocabulary is also applied to refer to the different forms of communication, share work experiences and the use of digitl technology, tell short stories about interpersoanl relationship and personalities, and comment on the future of the environment.
Descripción:
Calculus II is a basic training course for students of the Mathematics career, which favors the development of skills for formulating and solving problems, both theoretical and practical ones, in science and engineering. It initiates with the concept of antiderivative to introduce the definite integral that allows us to calculate areas and volumes. Later, the improper integral and its applications are presented. Finally, infinite series, which is a generalization of addition, is presented, to address many problems, especially those of approximations, or of mathematical models in sciences.
Descripción:
This is an undergraduate-level introductory coursefor mathematicsstudentsabout concepts of mathematics, from a formal point of view, to model and solve problems of discrete nature and work in multidisciplinary teams. Initially, concepts related to the theory of graphs are studied, then application problems related to coloring are solved. Subsequently,Enumerative combinatorics is studied to solve counting problems. Finally, Boolean algebra and lattices are reviewed. Throughout this coursepresentsrecent applicationsinmathematics, computer science and relatedtopics.
Descripción:
This is a basic training course for students of Statistics and Mathematics, which provides theory and procedures that are useful when posing, interpreting and solving problems, both in their curricular and professional activities. It begins by introducing the notions of vector spaces and linear transformations. Following this, vector spaces with inner product and their geometric interpretation are studied. Then, the fundamentals of diagonalization are given, both of matrices and linear operators. Finally, all this is applied to the solution of problems modelled by bilinear forms.
Second Year
Descripción:
Vector calculus is a course aimed at the basic training of professionals in the areas of Engineering, Exact Sciences and Natural Sciences who developed problem-solving and problem-solving skills in the n-dimensional context. For this purpose, the course consists of 5 general themes: three-dimensional analytic geometry and functions of several variables, differential calculus of scalar and vector fields, optimization of scalar functions of several variables, line integrals and multiple integration, surface integrals and theorems of the vector theory; being the main applications of this course: the optimization of functions of several variables applied to practical problems, the calculation of lengths, area, volumes, work and flow, using objects of the plane and space.
Descripción:
In this subject, we study the development of the academic prosumer profile of the students, which should be consolidated throughout each individual's life, based on the processing of complex, holistic, and critical thinking. We aim to foster understanding and the production of academic knowledge through rigorous analysis of realities and readings from various academic/scientific sources.
Descripción:
The Statistics I course allows students to improve their ability to analyze, synthesize and solve problems, by studying the statistical foundations for obtaining information from a set of data, starting from their information gathering, procedure, analysis and interpretation of the data obtained. Also, the concept of probability will be studied as a measure of uncertainty, mathematical models of discrete and continuous random variables will be analyzed univariate and multivariate, to finally consolidate the bases of inferential statistics
Descripción:
This subject of basic instruction and general education presents grammatical topics for the elaboration of an outline and a structured composition, through the development of the writing program in a transversal way. In addition, it allows the identification of arguments in oral and written communication on contemporary and academic topics. Additionally, appropriate vocabulary is applied to discuss issues related to different cultures, places where we live, everyday news, entertainment media, and past and future opportunities.
Descripción:
This course is for basic training on students in the Mathematics career. It expands the notions of Linear Algebra I by studying topics that turn out to be very useful when studying subjects in physics, engineering, control theory and numerical methods. It begins by studying the vector structure of linear functional spaces on finite dimensional vector spaces. Then, some special topics of matrix diagonalization and basic properties of certain operators in spaces with inner product are analyzed, which allows generalizing the matrix diagonalization by canonical Jordan forms. Finally, decomposition of matrices in singular values and some applications to geometry and data science, among others, are given.
Descripción:
This basic training course is aimed at students in the Mathematics career, and provides both qualitative and quantitative techniques for the resolution of differential equations. The basic concepts of differential equations are introduced, and solution techniques are then studied in power series for ordinary differential equations, and Fourier series for partial differential equations. Finally, some application problems are solved, like the vibrating string and The Dirichlet’s problem.
Descripción:
It is a basic training subject for students from the undergraduate programs in Statistics and Mathematics. Statistical theory is studied that allows the student to analyze in a scientific and deep manner the procedures of Descriptive and Inferential Statistics, emphasizing the desirable characteristics of the obtained estimators, allowing him to apply this knowledge in the most effective way to research in his own area or cross-sectional embodiment. The connection of probability as a measure of uncertainty with the point estimators, the construction of confidence intervals and the theory of hypothesis testing is established. The emphasis of the course, more than numerical, is analytical, emphasizing conceptualization and demonstrations, looking after the applications. The sample sizes are in general finite but asymptotic approximations of the estimators and inference for large samples are also analyzed.
Descripción:
This subject of basic formation and general education, presents the grammar structures to produce a persuasive essay, through the transversal development of the writing programme. In addition, it allows students to identify specific arguments in the oral and written communication, as well as, to express their own opinions about different topics of social, academic, or professional fields. It also includes the necessary vocabulary to stablish a conversation, narrate situations of their environment, activities to reach their goals, analyze cause and effect and personal and professional opportunities.
Descripción:
This course is of professional training for students of the Mathematics career, in which the student formalizes his writing and begins a necessary stage to tackle higher demanding courses. It begins with the study of the set of real numbers, its metric topology and properties, as well as numerability, compact and connected sets of real numbers. Then, sequences and series of real numbers and real functions of real variable are introduced to start the study of lower limit, upper limit and continuity. Next, the differentiation of functions is studied, Rolle's theorem, mean value theorem and L'Hopital's rule are proved and showed its applications . Finally, the Riemann-Stieltjes integral of real functions of real variable and their properties are studied. These topics are essential for the students to enter the world of analysis.
Descripción:
This is a professional training course for math students that pays attention to classical optimization concepts and techniques for linear and nonlinear problems. The course begins with optimization concepts and classical results in convex analysis, continues with optimality conditions for problems with and without restrictions. Finally, the theory of duality is reviewed. The course gives special attention to the modeling of linear problems since many decision problems in different sectors such as industrial or government, among others, can be formulated through mathematical programming.
Descripción:
This course is for professional training on students in the Mathematics career, which require concepts and techniques that allow addressing problems from an algebraic point of view. It is focused on studying, in an abstract way, the sets endowed with binary operations, properties and functions that relate them to each other. It begins by introducing the notion of group and homomorphism, their properties and some applications. Then, the rings are studied, generalizing the properties of groups, as well as the structure of the quotient set from both groups and rings. Finally, the concepts are applied in the study of the ring of polynomials.
Third Year
Descripción:
This professional training course for students of the Mathematics career generalizes the concepts studied in Mathematical Analysis I to several variables. It begins with the study of sequences and series of functions, differentiability and integrability criteria are proved. Then, the convergence and summability criteria of the Fourier series are demonstrated to prove the Parseval identity. The continuity and differentiability of functions of several variables are also studied, including the inverse and implicit function theorems. Finally, the Riemann-Stieltjes integrability, the multiple, curvilinear and classical surfaces integrals is defined and the Green, Stokes and Gauss theorems are proved.
Descripción:
This is a professional course for mathematics students that focuses on intrisic cualitative properties of the spaces, which are independent of its size, position and form. That is, to say, generalices the properties of proximities of those spaces with metric or distance. It starts introducing the notion of a topological space, limits of sequences and functions, and the continuity in these spaces. Then, the concept of connectedness and compactness is presented including the Tychonoff theorem and the Stone-Cech compactification theorem. After that, the separation and countability axioms are studied. Finally the completness of a metric space is analyzed and these concepts are applied to determine the metrizability of a topological space.
Descripción:
The course is aimed at training Mathematics students, providing some mathematical methods to solve science problems, which have been formulated in terms of differential equations. The content is approached starting with the essential aspects of abstract mathematical modeling for the definition of some notable problems in the sciences. Later, the variational method based on distribution theory and the spectral method for the approximation of solutions to typical boundary value problems of the sciences are developed.
Descripción:
This subject is of professional formation for the students of the Mathematics degree. It begins with the study of the effects of the distinct error sources. Then, direct and iterative numerical methods for solving linear equation systems are used. Next, function approximation theory and formulas for numerical differentiation e integration are examined. Finally, ordinary and partial differential equations are solved numerically. During the practical sessions of the subject, workshops are carried out, in which numerical methods are applied using the software.
Descripción:
This transversal course addresses the conditions required to innovate and the process associated with developing an innovation from an entrepreneurial point of view. Subsequently, topics such as the identification of opportunities, value creation, and prototyping and validation of products/services proposals are reviewed, as well as the elements of the business model and financial considerations that are essential for the feasibility and adoption of an innovation. Finally, entrepreneurial competences and process associated with the development and adoption of an innovation are studied.
Descripción:
This professional training course is aimed at students of the Mathematics career. The theory of measure and integration is a branch of modern mathematics which deals, in general terms, with techniques for measure more complex sets. The course begins with Lebesgue's notion of outer measure of a set, then it moves on to Lebesgue's measure. This concept is the appropriate framework to develop the notion of measurable function, which allows defining the Lebesgue integral. Thus, it is possible to solve a wide range of problems by using the pointwise convergence of integrable functions according to Lebesgue and fundamentally the Lp spaces, a wide range of problems.
Descripción:
This course is of professional training for students of the Mathematics career. It provides the fundamentals of the study of complex variable functions through analogies with real variable calculus and algebra, thus establishing contact with an advanced mathematical theory. It begins with the structure and basic properties of the set of complex numbers. Then, limit and continuity of complex variable functions as well as analytical functions are studied. Next, complex integration and complex series are analyzed. Finally, the calculation of residuals is carried out and applications are given.
Descripción:
This course is part of the professional training for the students in the mathematics degree. The course provides techniques for efficiently implementing mathematical models in computational intensive environments that simulate problems arising from applied science. The content starts with the essentials of computer systems and the efficient implementation of computational programs. Then, it is covered the approaches for parallel computing to be used in high-performance computers to solve computationally demanding problems from science and engineering. Lastly, the course covers some basic data science techniques for obtaining relevant information from a data set to analyze real phenomena.
Fourth Year
Descripción:
This transversal training course for all students of the institution has five chapters. It introduces the key principles of sustainability and the path to sustainable development. Addresses ecological principles by deepen into biodiversity, ecosystems, human population and ecosystem services. Study the fundamentals of renewable and non-renewable resources as well as the alternatives for sustainable use. Analyzes environmental quality specifically in the air, water and soil components, delving into issues such as climate change, eutrophication and deforestation. Finally, it emphasizes on the economic axis with topics such as circular economy and on the social axis on topics such as governance and urban planning.
Descripción:
This upper division subject is aimed at students of Mathematics who require methods to analyze ordinary differential equations that, due to their complexity, cannot be analytically integrated using classical quantitative methods. It complements what has been learned in Differential Equations I by introducing qualitative methods that allow obtaining properties of the solutions of a differential equation without the need to know an explicit formula. The course begins with the theory of existence of solutions; it continues with the analysis of the linear and non-linear differential equations to later study their stability. Finally, topological techniques are introduced for the study of planar vector fields.
Descripción:
The functional analysis course is a professional training course for students of the Mathematics career, it has a unifying character and a high degree of abstraction. It begins by dealing with Banach spaces and their structure. Then, the Hahn-Banach theorem is studied with its diverse applications and after that, cases of weak convergences are presented. Finally, the theorems of open application, closed graph and compact and self-attached operators are analyzed; with all this information, techniques and methods are developed in such way that can be applied to other branches of science, such as differential equations, theoretical physics, econometrics, probabilities, among others.
Descripción:
The subject is aimed at students at level 400-1 of the Statistics career of the FCNM. The purpose of this course is that the students acquire the ability to recognize their strengths and weaknesses for the benefit of their personal, academic and work development through the knowledge of the predominant type of intelligence, the application of a decision-making process for the elaboration of a matrix that allows them in turn to become people with high command of the effective communication process before an audience.
Descripción:
Differential Geometry is senior course of professional training subject for students of the Mathematics career. The course constitutes an introduction to classical differential geometry, using mathematical analysis to study the metric properties of curves both in the plane and in the space, as well as fundamental aspects of surfaces theory, to arrive at the Gauss-Bonnet theorem. Finally, some elements of manifolds theory are presented as an introduction to differential topology and advanced differential geometry. The historical aspects of the subject and its applications to physics and other branches of mathematics are considered.
Descripción:
In this end of career course, the student carries out a project where the application of the profile declared for the career is evidenced, developing processes that require creativity, organization and relevance which get them involved in a professional design experience. In the first part of the course, the needs of the customer/user are identified, the problem/opportunity is defined, data is collected and critical factors are analyzed. In the second part, alternative solutions are created, framing them acording to the regulations and restrictions of each user. It concludes with the design of the feasible solution and the analysis of results.
Additional
ARTS, SPORTS AND LANGUAGES ELECTIVE COURSES
1 credits - 1.9 ECTS
HUMANITIES ELECTIVE COURSES
1 credits - 1.9 ECTS
SELECTED ELECTIVE COURSE
3 credits - 3.8 ECTS
SELECTED ELECTIVE COURSE
3 credits - 3.8 ECTS
SELECTED ELECTIVE COURSE
3 credits - 3.8 ECTS
Upon completing the degree, you will be able to formulate problems, analyze them, and develop and apply strategies for their solution in relation to challenges that arise routinely in today's world. Additionally, you will be able to work effectively in multidisciplinary teams, engage in research, participate in postgraduate programs to strengthen your perspectives and scope, and take on positions in fields such as finance, industry, public administration, and generally, social sciences, particularly in health and education.
Occupational Profile
The skills of mathematicians help them excel in many directions. They can pursue postgraduate studies, pursue careers in the business, scientific, or technical fields, or in disciplines such as social services, education, and public administration. Jobs they can access include:
-Algorithm and mathematical model developer.
-Business and risk analyst in different financial institutions.
-Affiliated expert in scientific or technological research institutions.
-Scientific advisor in different areas.
-Manager in private and public sector companies.
-University professor
-Successfully complete a minimum of 59 credits in PROFESSIONAL TRAINING AND ITINERARY.
-Successfully complete a minimum of 23 credits in GENERAL EDUCATION.
-Successfully complete a minimum of 23 credits in MATHEMATICS AND BASIC SCIENCES.
-Provide a minimum of 336 hours of pre-professional internship experience.
-Pass the graduation process, equivalent to 8 credits.
The Capstone Project is a culminating requirement for graduation. These projects provide students with the experience of applying acquired knowledge and skills to the needs of society, with a focus on sustainability.
The IDEAR Fair showcases all Capstone projects, offering students a valuable opportunity to showcase their work and hone soft skills such as communication and teamwork. It is also a space for students to network with potential clients and future employers.
Explore all of the Capstone projects completed by the Mathematics program.
DID YOU KNOW?
Did you know that the fascinating aspect of a mathematics career is that it forms the foundation of everything? This career is highly valued in the business and academic worlds due to its diverse applications.
