Master the mathematical intervention in algorithms and their role in informatics thanks to a program that will give you the keys to be part of the forefront of this field"

Why Study at TECH?

TECH is the world's largest 100% online business school. It is an elite business school, with a model based on the highest academic standards. A world-class centre for intensive managerial skills training.   

TECH is a university at the forefront of technology, and puts all its resources at the student's disposal to help them achieve entrepreneurial success"

At TECH Global University

Innovation

The university offers an online learning model that combines the latest educational technology with the most rigorous teaching methods. A unique method with the highest international recognition that will provide students with the keys to develop in a rapidly-evolving world, where innovation must be every entrepreneur’s focus.

"Microsoft Europe Success Story", for integrating the innovative, interactive multi-video system.  

The Highest Standards

Admissions criteria at TECH are not economic. Students don't need to make a large investment to study at this university. However, in order to obtain a qualification from TECH, the student's intelligence and ability will be tested to their limits. The institution's academic standards are exceptionally high...  

95% of TECH students successfully complete their studies.

Networking

Professionals from countries all over the world attend TECH, allowing students to establish a large network of contacts that may prove useful to them in the future.  

100,000+ executives trained each year, 200+ different nationalities.

Empowerment

Students will grow hand in hand with the best companies and highly regarded and influential professionals. TECH has developed strategic partnerships and a valuable network of contacts with major economic players in 7 continents.  

500+ collaborative agreements with leading companies.

Talent

This program is a unique initiative to allow students to showcase their talent in the business world. An opportunity that will allow them to voice their concerns and share their business vision. 

After completing this program, TECH helps students show the world their talent. 

Multicultural Context

While studying at TECH, students will enjoy a unique experience. Study in a multicultural context. In a program with a global vision, through which students can learn about the operating methods in different parts of the world, and gather the latest information that best adapts to their business idea. 

TECH students represent more than 200 different nationalities.   

Learn with the best

In the classroom, TECH teaching staff discuss how they have achieved success in their companies, working in a real, lively, and dynamic context. Teachers who are fully committed to offering a quality specialization that will allow students to advance in their career and stand out in the business world. 

Teachers representing 20 different nationalities. 

TECH strives for excellence and, to this end, boasts a series of characteristics that make this university unique:   

Analysis

TECH explores the student’s critical side, their ability to question things, their problem-solving skills, as well as their interpersonal skills.  

Academic Excellence

TECH offers students the best online learning methodology. The university combines the Relearning method (a postgraduate learning methodology with the highest international rating) with the Case Study. A complex balance between tradition and state-of-the-art, within the context of the most demanding academic itinerary.  

Economy of Scale

TECH is the world’s largest online university. It currently boasts a portfolio of more than 10,000 university postgraduate programs. And in today's new economy, volume + technology = a ground-breaking price. This way, TECH ensures that studying is not as expensive for students as it would be at another university.  

At TECH, you will have access to the most rigorous and up-to-date case studies in the academic community”

The Postgraduate diploma in Mathematics and Econometrics has been developed by a teaching team versed in the area that endorses the contents of the syllabus and guarantees the correct instruction of the specialists. It is a program with great flexibility as it is taught through a 100% online modality. This, together with the audiovisual contents in different formats and the Relearning methodology make the program adaptable to the personal and professional needs of the students.

Master the basic concepts of accounting and its scope to apply them in the business and financial environment with all the guarantees"

Syllabus

TECH's Postgraduate diploma in Mathematics and Econometrics is a comprehensive program designed to broaden the financial skills of graduates in Economics, Accounting and Finance, among other degrees. One of the objectives of the program is the mastery of the method of analysis and representation of operations in the accounting field, in addition to providing students with a critical view of national and international economic problems.

To achieve this, TECH teaches this subject through theoretical and practical exercises that are focused on current environments, so that students can apply them in the real financial scenario. With this in mind, the University has adopted the most innovative methodology to facilitate and guarantee the financial training of students in the shortest possible time and in the most accessible way.

In just six months, specialists will learn the keys to economic performance, applying real functions of several variables, the ordinary least squares (OLS) estimation method, residual analysis in linear prediction, as well as qualitative variables in MRLG II and Dummyvariables, among other issues. It is a program that will project the professional career of economists, supported by an expert teaching staff in the field.

In addition, TECH uses the Relearning methodology to bring all the knowledge and current economic tools to the specialists without the need to invest long hours of study in it. Likewise, its 100% online modality offers the possibility of adapting the study to the personal and professional needs of the students, regardless of their time availability.

This Postgraduate diploma takes place over six months and is divided into three modules:

Module 1. Mathematics
Module 2. Mathematics for Economists
Module 3. Econometrics

Where, When and How is it Taught?

TECH offers the possibility of developing this Postgraduate diploma in Mathematics and Econometrics completely online. Over the course of 6 months, you will be able to access all the contents of this program at any time, allowing you to self-manage your study time.

Module 1. Mathematics

1.1. Basic Elements of Linear and Matrix Algebra

1.1.1. The Vector Space of IRn, Functions and Variables

1.1.1.1. Graphical Representation of Sets in R
1.1.1.2. Basic Concepts of Functions of Several Real Variables. Operationswith Functions
1.1.1.3. Function Types
1.1.1.4. Weierstrass’ Theorem

1.1.2. Optimization with Inequality Constraints

1.1.2.1. Two-Variable Graphical Method

1.1.3. Function Types

1.1.3.1. Separate Variables
1.1.3.2. Polynomial Variables
1.1.3.3. Rational Variables
1.1.3.4. Quadratic Forms

1.2. Matrices: Types, Concepts and Operations

1.2.1. Basic Definitions

1.2.1.1. Matrix of Order mxn
1.2.1.2. Square Matrices
1.2.1.3. Identity Matrix

1.2.2. Matrix Operations

1.2.2.1. Matrix Addition
1.2.2.2. Scalar Multiplication
1.2.2.3. Matrix Multiplication

1.3. Transpose

1.3.1. Diagonalizable Matrix
1.3.2. Transpose Properties

1.3.2.1. Involution

1.4. Determinants: Calculation and Definition

1.4.1. The Concept of Determinants

1.4.1.1. Determinant Definition
1.4.1.2. Square Matrix of Order 2,3 and Greater Than 3

1.4.2. Triangular Matrices

1.4.2.1. Determinant of Triangular Matrices
1.4.2.2. Determinant of Non-Triangular Square Matrices

1.4.3. Properties of Determinants

1.4.3.1. Simplifying Calculations
1.4.3.2. Calculation in any Case

1.5. Invertible Matrices

1.5.1. Properties of Invertible Matrices

1.5.1.1. The Concept of Inversion
1.5.1.2. Definitions and Basic Concepts

1.5.2. Invertible Matrix Calculation

1.5.2.1. Methods and Calculation
1.5.2.2. Exceptions and Examples

1.5.3. Expression Matrices and Matrix Equations

1.5.3.1. Expression Matrices

1.5.3.2. Matrix Equations

1.6. Solving Systems of Equations

1.6.1. Linear Equations

1.6.1.1. Discussion of the System.Rouché–Capelli Theorem
1.6.1.2. Cramer's Rule: Solving the System
1.6.1.3. Homogeneous Systems

1.6.2. Vector Spaces

1.6.2.1. Properties of Vector Spaces
1.6.2.2. Linear Combination of Vectors
1.6.2.3. Linear Dependence and Independence
1.6.2.4. Coordinate Vectors
1.6.2.5. The Basis Theorem

1.7. Quadratic Forms

1.7.1. Concept and Definition of Quadratic Forms
1.7.2. Quadratic Matrices

1.7.2.1. Law of Inertia for Quadratic Forms
1.7.2.2. Study of the Sign by Eigenvalues
1.7.2.3. Study of the Sign by Minors

1.8. Functions of One Variable

1.8.1. Analysis of the Behavior of a Magnitude

1.8.1.1. Local Analysis
1.8.1.2. Continuity
1.8.1.3. Restricted Continuity

1.9. Limits of Functions, Domain and Image in Real Functions

1.9.1. Multi-variable Functions

1.9.1.1. Vector of Several Variables

1.9.2. The Domain of a Function

1.9.2.1. Concept and Applications

1.9.3. Function Limits

1.9.3.1. Limits of a Function at a Point
1.9.3.2. Lateral Limits of a Function
1.9.3.3. Limits of Rational Functions

1.9.4. Indeterminacy

1.9.4.1. Indeterminacy in Functions with Roots
1.9.4.2. Indetermination 0/0

1.9.5. The Domain and Image of a Function

1.9.5.1. Concept and Characteristics
1.9.5.2. Domain and Image Calculation

1.10. Derivatives: Behavior Analysis

1.10.1. Derivatives of a Function at a Point

1.10.1.1. Concept and Characteristics
1.10.1.2. Geometric Interpretation

1.10.2. Differentiation Rules

1.10.2.1. Derivative of a Constant
1.10.2.2. Derivative of a Sum or Differentiation
1.10.2.3. Derivative of a Product
1.10.2.4. Derivative of an Opposite Function
1.10.2.5. Derivative of a Compound’s Function

1.11. Application of  Derivatives to Study Functions

1.11.1. Properties of Differentiable Functions

1.11.1.1. Maximum Theorem
1.11.1.2. Minimum Theorem
1.11.1.3. Rolle's Theorem
1.11.1.4. Mean Value Theorem
1.11.1.5. L'Hôpital's Rule

1.11.2. Valuation of Economic Quantities
1.11.3. Differentiable Functions

1.12. Function Optimization for Several Variables

1.12.1. Function Optimization

1.12.1.1. Optimization with Equality Constraint
1.12.1.2. Critical Points
1.12.1.3. Relative Extremes

1.12.2. Convex and Concave Functions

1.12.2.1. Properties of Convex and Concave Functions
1.12.2.2. Inflection Points
1.12.2.3. Growth and Decay

1.13. Antiderivatives

1.13.1. Antiderivatives

1.13.1.1. Basic Concepts
1.13.1.2. Calculation Methods

1.13.2. Immediate Integrals

1.13.2.1. Properties of Immediate Integrals

1.13.3. Integration Methods

1.13.3.1. Rational Integrals

1.14. Definite Integrals

1.14.1. Barrow's Fundamental Theorem

1.14.1.1. Definition of the Theorem
1.14.1.2. Calculation Basis
1.14.1.3. Applications of the Theorem

1.14.2. Curve Cutoff in Definite Integrals

1.14.2.1. Concept of Curve Cutoff
1.14.2.2. Calculation Basis and Operations Study
1.14.2.3. Applications of Curve Cutoff Calculation

1.14.3. Mean Value Theorem

1.14.3.1. Concept of Theorem and Closed Interval
1.14.3.2. Calculation Basis and Operations Study
1.14.3.3. Applications of the Theorem

Module 2. Mathematics for Economists

2.1. Multi-variable Functions

2.1.1. Terminology and Basic Mathematical Concepts
2.1.2. Definition of IRn in IRm Functions
2.1.3. Graphic Representation
2.1.4. Types of Functions

2.1.4.1. Scaled Functions

2.1.4.1.1 Concave Function and Its Application to Economic Research
2.1.4.1.2. Convex Function and Its Application to Economic Research
2.1.4.1.3. Level Curves

2.1.4.2. Vectorial Functions
2.1.4.3. Operations with Functions

2.2. Multi-variable Real Functions

2.2.1. Function Limits

2.2.1.1. Point Limit of an IRn in IRm Function
2.2.1.2. Directional Limits
2.2.1.3. Double Limits and Their Properties
2.2.1.4. Limit of an IRn in IRm Function

2.2.2. Continuity Study of Multi-variable Functions
2.2.3. Function Derivatives: Successive and Partial Derivatives Concept of Differential of a Function
2.2.4. Differentiation of Compound Functions: Chain Rule
2.2.5. Homogeneous Functions

2.2.5.1. Properties
2.2.5.2. Euler's Theorem and Its Economic Interpretation

2.3. Optimization

2.3.1. Definition
2.3.2. Searching and Interpreting Optimum
2.3.3. Weierstrass’ Theorem
2.3.4. Local-Global Theorem

2.4. Unconstrained and Constrained Equality Optimization

2.4.1. Taylor's Theorem Applied to Multi-variable Functions
2.4.2. Unconstrained Optimization
2.4.3. Constrained Optimization

2.4.3.1. Direct Method
2.4.3.2. Interpreting Lagrange Multipliers
2.4.3.2.1. Hessian Matrix

2.5. Optimization with Inequality Constraints

2.5.1. Introduction
2.5.2. Necessary First-order Conditions for the Existence of Local Optima: Kuhn-Tucker's Theorem and Its Economic Interpretation
2.5.3. Globality Theorem: Convex Programming

2.6. Lineal Programming

2.6.1. Introduction
2.6.2. Properties
2.6.3. Graphic Resolution
2.6.4. Applying Kuhn-Tucker Conditions
2.6.5. Simplex Method
2.6.6. Economic Applications

2.7. Integral Calculus: Riemann's Integral

2.7.1. Definition and Application in Economics
2.7.2. Properties
2.7.3. Integrability Conditions
2.7.4. Relation between Integrals and Derivatives
2.7.5. Integration by Parts
2.7.6. Change of Variables Integration Method

2.8. Applications of Rienmann's Integral in Business and Economics

2.8.1. Distribution Function
2.8.2. Present Value of a Cash Flow
2.8.3. Mean Value of a Function in an Enclosure
2.8.4. Pierre-Simon Laplace and His Contribution

2.9. Ordinary Differential Equations

2.9.1. Introduction
2.9.2. Definition
2.9.3. Classification
2.9.4. First Order Differential Equations

2.9.4.1. Resolution
2.9.4.2 Bernoulli’s Differential Equations

2.9.5. Exact Differential Equations

2.9.5.1. Resolution

2.9.6. Greater Than One Ordinary Differential Equations (with Constant Coefficients)

2.10. Finite Difference Equations

2.10.1. Introduction
2.10.2. Discrete Variable Functions or Discrete Functions
2.10.3. First-order Linear Finite Difference Equations with Constant Coefficients
2.10.4. Order Linear Finite Difference Equations with Constant Coefficients
2.10.5. Economic Applications

Module 3. Econometrics

3.1. The Ordinary Least Squares (OLS) Method

3.1.1. Linear Regression Models
3.1.2. Types of Content
3.1.3. General Line and OLS Estimation

3.2. OLS Method in Other Scenarios

3.2.1. Abandoning Basic Assumptions
3.2.2. Method Behavior
3.2.3. Effect of Measurement Changes

3.3. Properties of OLS Estimators

3.3.1. Moments and Properties
3.3.2. Variance Estimation
3.3.3. Matrix Forms

3.4. OLS Variance Calculation

3.4.1. Basic Concepts
3.4.2. Hypothesis Testing
3.4.3. Model Coefficients

3.5. Hypothesis Testing in Linear Regression Models

3.5.1. T-Contrast
3.5.2. F-Contrast
3.5.3. Global Contrasts

3.6. Confidence Intervals

3.6.1. Objectives
3.6.2. In a Coefficient
3.6.3. In a Combination of Coefficients

3.7. Specification Problems

3.7.1. Use and Concept
3.7.2. Types of Problems
3.7.3. Unobservable Explanatory Variables

3.8. Prediction in Linear Regression Models

3.8.1. Prediction
3.8.2. Average Value Intervals
3.8.3. Applications

3.9. Residual Analysis in Linear Prediction

3.9.1. Objectives and General Concepts
3.9.2. Analysis Tools
3.9.3. Waste Analysis

3.10. Qualitative Variables in GLRM I

3.10.1. Fundamentals
3.10.2. Models with Various Types of Information
3.10.3. Linear Metrics

3.11. Qualitative Variables in GLRM II

3.11.1. Binary Variables
3.11.2. Use of DummyVariables
3.11.3. Time Series

3.12. Autocorrelation

3.12.1. Basic Concepts
3.12.2. Consequences
3.12.3. Contrast

3.13. Heteroscedasticity

3.13.1. Concept and Contrasts
3.13.2. Consequences
3.13.3. Time Series

A unique, key, and decisive educational experience to boost your professional development and make the definitive leap"