The Postgraduate certificate in Financial Mathematics is an innovative program that is taught through a 100% online modality to allow for flexible follow-up. Thanks to its pedagogical methods, TECH offers a complete and rigorous program that is developed in only 12 academic weeks and with downloadable content, which specialists can access at any time and place.

Expand your financial skills by analyzing real function behaviors and contribute to an organization's business performance” 

Syllabus

The Postgraduate certificate in Financial Mathematics of TECH is a comprehensive and rigorous program aimed at graduates in Economics, Business Management and Finance, among other degrees, to expand and update their financial knowledge in matrices, their types and concepts, the resolution of systems of equations, as well as functions optimization for several variables, among many other issues.

TECH achieves this by providing students with theoretical and practical exercises that, in addition to academic instruction, can also be applied in economic practice. For this reason, the University has adopted the most innovative methodology to facilitate and guarantee the financial qualification of students in the shortest possible time and in the most accessible way.  

Over the course of 3 months, students will analyze everything from the basic elements of linear and matrix algebra to functions of several variables and their economic applications. This is a 
complete immersion in the field of Financial Mathematics.

A qualification that, in addition, is based on 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.  

In addition, TECH has experts in the sector who are aware of all business opportunities to ensure that enrolled students acquire superior skills in the economic and financial field. All this, through a 100% online format that offers the possibility of adapting the study to the personal and professional needs of both those specialists who are already working in the sector, as well as those who are not yet part of it. 

This Postgraduate certificate takes place over 12 weeks and is divided into 2 modules: 

Module 1. Mathematics
Module 2. Mathematics for Economists

Where, When and How is it Taught?

TECH offers students the opportunity to take this Postgraduate certificate in Financial Mathematics entirely online. Throughout the 3 months of the educational program, 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. others

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. Operations with Functions
1.1.1.3. Function Types
1.1.1.4. Weierstrass Theorem

1.2.1. Optimization with Inequality Constraints

1.2.1.1. 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. Order Matrix mxn
1.2.1.2. Square Matrices
1.2.1.3. Identity Matrix
1.2.2.4. Matrix Operations
1.2.2.5. Matrix Addition
1.2.2.6. Scalar Multiplication
1.2.2.7. Matrix Multiplication

1.3. Transpose

1.3.1. Diagonalizable Matrix
1.3.2. Transpose Properties

1.3.2.1. Involution

1.4. Determinant: 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. Simplification of Calculation Functions
1.4.3.2. Calculation in any Case

1.5. Invertable Matrices

1.5.1. Properties of Invertable Matrices

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

1.5.2. Invertable 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 an Compounds 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 withEquality 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 and Closed Interval Theorem
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 a 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 a 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. Economic Applications

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

This program has been designed under the fundamentals of a group of experts who will instruct graduates in Economics, Accounting and Finance, among other economic areas, so that they will be more competitive in the labor and business environment and master the keys to intervene in micro and macroeconomics. All this, with a contextualized vision and with future perspectives that guarantee the success of the finance specialists enrolled in the program. 

Learn about the function of the elements of systems of equations such as the Rouché-Fobenius theorem and master homogeneous systems, thanks to TECH”

TECH makes the goals of their students their own goals too.
Working together to achieve them.

The Postgraduate certificate in Financial Mathematics qualifies student to: 

1. Know the basic elements that make up business mathematics: linear and matrix algebra, matrices, matrix transposition, calculus, matrix inversion, systems of equations, etc. 
2. Understand the different techniques and mathematical methods used within the financial framework of a company  
3. Apply mathematical techniques and methods to the financial framework of the company 
4. Recognize the economic realities in one or more differential equations from an economic perspective 
5. Interpret the results of optimization problems 
6. Evaluate the possible consequences of alternative actions