**Engineering Mathematics**

### Career Objectives

Achieve more efficient systems and at a lower cost in the area of science and technology, applying mathematical models both in their design and in the resolution of their specific problems.

### Professional Profile

Professional with sound training in mathematics and knowledge of the scientific method that allows him to address both engineering problems as well as problems related to administrative and financial systems, through the creation of *mathematical models that simulate the behavior of that situation or functioning of the system for its programming and computer processing.

These models will be the basis for professional from other specialties to *investigate, design, produce, build, operate, maintain, estimate and manage systems with different levels of complexity.

This type of professional is necessary in companies or institutions linked to engineering that, due to their complexity, require the application of more elaborate mathematical *techniques for programming and computer processing.

Computer *simulation has become a useful part of the modeling of several natural systems in Physics, Chemistry and Biology, and in human systems such as economics and social science (Computational Sociology).

They can opt for further training, continuing studies to obtain the Master’s degree or PhD.

The Mathematical Engineer is oriented towards the application of mathematics in contrast to the Mathematical Sciences professional (Bsc in Mathematics) whose purpose is to the study and research of mathematics itself.

### Specific tasks or activities carried out in the profession

He investigates, perfects or develops mathematical *concepts, *theories and *techniques.

He carries out mathematical *logical reasoning to determine or distinguish between correct and incorrect reasoning, looking for the correct *premises and deriving the correct conclusion.

He looks for the practical application to *concepts and *theories.

He uses computer tools to solve mathematical problems, as well as developing his own systems to apply them to specific problems.

He applies *principles, mathematical *techniques and statistics to systems or practical problems in medicine, engineering, agriculture, industry and commerce.

He creates *models that simulate processes before turning them into reality and then foresee their behavior under different conditions and the consequences of said behavior. For that:

He defines the system, that is, he identifies the elements that make it up, how these elements interrelate and how they interact with each other.

He obtains a *block diagram of the system for its analysis and subsequent optimization.

He *deduces the mathematical expressions that define the system.

He sets out the *models graphically.

He explores the behavior of the system to be developed and optimizes the *model to obtain the desired behavior.

He obtains the best possible solution, within constraints on design.

He validates the response by comparing it to experimental data that has been prepared using statistical tools.

He addresses *market research needs, handling of large amounts of products, works *planning and production, process improvement and optimization, among others.

He advises on research projects in specific areas of knowledge of exact biological science, natural, legal and social science by *analyzing a problem in a logical way and *formulating *models that *simulate the behavior of different phenomena creating artificial worlds in the computer to see how a certain topic would be developed. For instance, in biology, it is very difficult to verify *hypotheses related to evolution based on natural selection because *chronological time is very long, but with the computer you can create an artificial world related to the topic, corroborate ideas and find new *paradigms.

He judges the impact, implications and consequences of the application of solutions given to the problem, discusses their importance and relevance and defends the conclusions.

He performs expositions and reports of his work.

### Occupational Field

-In development, research or planning departments of mining, fishing, forestry, chemical, energy, financial, transport, planning industries, etc.

-In development, research or planning departments of service companies such as Banks, consulting companies, distributors, etc.

-Ministries

Governmental organizations geared towards the promotion of some productive area.

-Multidisciplinary Research Centers such as Research Centers for Mining and Metallurgy, Natural Resource Information Centers and other scientific and technical fields.

-National and foreign universities.

### Estimated time of College years

5 years

### Main courses considered in the syllabus

Basic Training Courses

Algebra (2 semesters)

Professional Training Courses

Advanced Algebra

*Analytic Geometry

*Calculus (3 semesters)

*Discrete Mathematics

*Numerical Analysis (2 semesters)

*Differential Equations (3 semesters)

Systems Optimization (2 semesters)

IT

Programming (2 semesters)

Advanced Statistics

Mathematical Analysis

*Simulation (2 semesters)

Decision Analysis

Project *Formulation and *Evaluation

Quality Systems

Specialties - Industrial

Chemistry

Biology

*Physics (3 semesters)

*Industrial Engineering

Industrial Modelling

Quality Engineering and *Reengineering

Operations Management

Specialties - Finance

*Finance

*Economics

Financial and Trading Systems

*Stochastic Processes

*Financial Engineering

Financial Modelling

*Operations Research

*Business Management

Specialties

Industrial

Administrative/Financial (Actuary)

### Vocation, Skills and Interests required in the candidate to this career

### Interests

-Satisfaction for solving a mathematical problem.

-Motivation for the interpretation of mathematical expressions and the results obtained.

-Curiosity for the search for new solutions to mathematical problems.

-Motivation for games of skill.

-Natural and frequent tendency to relate the facts numerically.

-Appreciation for accuracy, precision and rigor that mathematics provides.

-Interested in what will be discussed, give importance to define it beforehand and accurately.

- Realize that mathematics has truths to know from how a supermarket works to how the cosmos is organized.

-Desire to understand a reality by finding which logical relations are perceived in it and look for ways to quantify them: “It is fascinating to be able to detect hidden patterns, connections between things, intuiting the mathematical order in them, guessing those harmonies and hidden relationships”. Jean Marie Duhamel, French mathematician (1797 – 1872).

- Give value to coherently chain the arguments and detect logical incorrectness. “To achieve that the concepts combine and work together harmoniously, to make everything fall into its place, in a fatal way"

Jean Marie Duhamel, French mathematician (1797-1872).

-Interest and appreciation for Science and Technology.

-Tendency to the use of guidelines, schematization and graphs for the analysis of a situation.

### Skills

-Ability to understand concepts and use the symbols that represent them.

- Ability to follow a mathematical reasoning and retain it mentally while the reasoning lasts.

-Ease to take a real situation to a scheme.

-Capacity to reason from the facts of a phenomenon to reach the laws that govern it.

-Skill for calculation.

-Ability for teamwork.

### Vocation

Foster scientific-technological changes in society that contribute to the improvement of processes, technology, services, environment and quality of life.

### Candidate Personality

-Critical

-Methodical

-Persistent

-Organized

### Work Scope

Urban

Work with reports, graphs, schemes and statistics, using the computer as a mean.

### Related Careers

-Mathematical Science (Bachelor of Science in Mathematics), Actuary, Computer Science, Statistical Science (Bachelor of Science in Statistics), Mathematics Pedagogy (Secondary Education).

Glossary of Terms

*Numerical Analysis: Numerical Analysis is the branch of mathematics in charge of designing *algorithms to simulate more complex mathematical processes applied to real world processes through numbers and mathematical rules.

*Algorithms: List of operations that allows finding the solution to a problem.

*Analyze logically: *Logical Reasoning: It is captured through the observation of a reality, a drawing, a diagram, the functioning of something, behavior, etc. Ability to analyze proposals or complex situations, predict consequences and be able to solve the problem in a consistent way.

*Calculus, *Differential Equations: Part of mathematics that takes charge of the dynamic factors of reality, dealing with concepts like derivatives and antiderivatives (or integral), where the derivative of a function gives the notion of how quickly a function grows (or decreases) at a certain point.

*Concepts: Ideas that lead to a better understanding of a thing, phenomenon or situation.

*Block Diagram: Graphical representation of the internal functioning of a system that is made through blocks and their relations that define the organization of the internal process of the system, its inputs and outputs.

*Deduce: Starting from a general principle to conclude in a particular one or drawing the consequences of a principle. Example: If a physical law is exposed (general principle), and it is requested to give an example where this law can be applied (particular case). In this case, a deduction is made; a particular case is deduced from a general fact.

*Economics: Science which subject of study is the social organization of the economic activity, in which it tries to quantify the main existing relations between the different variables of an economic model through statistical techniques and mathematics.

*Project Evaluation: Useful concepts and methods in decision making associated with economical aspects of a project. Such as: Analysis of development alternatives of the project, financing, depreciation (decrease in the value or price of equipment) taxes, among other factors.

*Finance: It deals with the collection and determination of the cash flow (inflows or outflows of money) required by the company, in addition to the distribution and management of those funds in order to maximize the economical value of the company.

*Physics: Waves and Optics; Electricity and Magnetism; Material Science and Technology (relate the structure of the material at atomic and molecular level to its macroscopic physical properties.); Thermodynamics (Force and movement generated by heat phenomena); Fluid Mechanics (behavior of fluids both in Statics (no motion) and Dynamics (in motion); among other topics.

*Project Formulation: Shape the project; describe it in clear and precise terms.

*Formulate: To shape, describe.

*Analytic Geometry: It is the one that deals with geometrical problems through graphs with the use of coordinates. This is achieved by transforming them into algebraic problems.

*Management: Manage: Make the inquiries and procedures to carry out a project.

*Hypothesis: Initial proposal that will be later submitted to veracity.

*Financial Engineering: Mathematical concepts and techniques applied to the analysis, comparison and evaluation of financial alternatives of engineering projects to choose the most economical possible.

*Industrial Engineering: Engineering that analyzes, plans, designs, optimizes and controls the processes of products and services, considering economical, technical and social aspects.

*Market Research: Process of gathering, recording and analyzing the information related to the commercialization of goods and services.

*Operations Research: Subject that gathers practical applications of decision making in organizations.

*Investigate: Examine something carefully, find out, inform yourself, ask questions, run errands to discover, search.

*Discrete Mathematics: It is the part of mathematics in charge of the study of discrete sets; that is, the study of processes to which elements can be counted one by one separately.

Unlike continuous mathematics that is responsible for processes which response is continuous (as a line) and its variation as well.

*Mathematical Model: It is the mathematical representation of relationships between entities, variables or operations to study the behavior of complex systems in situations that are difficult to observe in reality.

*Paradigm: Model accepted by everyone as true.

*Planning: Plan: Submit the development of any activity to a detailed plan.

*Premises: Statement proven previously or given as true, which serves as the basis for an argument.

*Principles: Fundamentals, base, foundations.

*Stochastic Processes: Statistical study of processes which result is not possible to predict.

*Reengineering: Radical redesign of processes within an organization to achieve improvements in performance, cost, quality, service and speed.

*Simulation: Software that tries to be a replica of reality phenomena to carry out an exploratory work with it.

*Techniques: Procedures, methods, ways of doing something.

*Theory: Proposition or attempt to temporarily explain a phenomenon or a sequence of phenomena that have occurred.

*Chronological Time: Time we measure with clocks; it is called like this to differentiate it from weather.

GO BACK