The syllabus for this Postgraduate certificate has been designed and created by a team of experts in the field to respond specifically to the needs of Business Science professionals. This compendium of content has also been designed with a focus on applied learning, which will allow professionals to successfully intervene by means of a broad vision of real environments in the profession. Thus, this syllabus will become our students' main asset to successfully insert themselves into a labor market that increasingly demands more specialized professionals in Business Mathematics. 

The most complete syllabus on the market with a single purpose: To prepare the best business administrators” 

Syllabus

Business Mathematics, understood as the process involved in identifying, extracting and adequately processing the continuous and dispersed data produced in an organization's environment, is an extremely important part of business management, as it helps to analyze and predict the future of the company and the decisions that must be taken to ensure its success with a higher rate of accuracy. 

For this reason, TECH professionals have designed this complete Postgraduate certificate that aims to provide business professionals with the methodologies and procedures that govern the operation of Business Mathematics, such as algebra, matrices, integrals, and others. This will empower our students to analyze various issues that directly concern business operations.  

Throughout the training, students will analyze a multitude of practical cases through individual practice and teamwork that will facilitate an in-depth understanding of the function of Business Mathematics. This complete immersion in real situations will provide our students with a more complete and effective vision of this area and will help them understand how these operations will become the main professional asset when analyzing and predicting the status of an organization with a higher rate of success.   

Further, the content included in this Postgraduate certificate in Business Mathematics is designed to develop skills that enable more rigorous decision-making in uncertain environments. This will enable professionals to make use of various fruitful and success-oriented mathematical operations. 

This Postgraduate certificate is takes place over six weeks and is divided into a single module: 

Module 1. Business Mathematics

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

Where, When and How is it Taught?

TECH offers the possibility of developing this Postgraduate certificate in Business Mathematics completely online. Over the course of 6 weeks, 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. Business Mathematics

1.1. Basic Elements of Linear and Matrix Algebra

1.1.1. The Vector Space of IRn, Functions and Variables
1.1.2. Graphical Representation of Sets in R
1.1.3. Basic Concepts of Functions of Several Real Variables. Operations with Functions
1.1.4. Function Types
1.1.5. Weierstrass Theorem
1.1.6. Optimization with Inequality Constraints
1.1.7. Two-Variable Graphical Method
1.1.8. Function Types
1.1.9. Separate Variables
1.1.10. Polynomial Variables
1.1.11. Rational Variables
1.1.12. Quadratic Forms

1.2. Matrices: Types, Concepts and Operations

1.2.1. Basic Definitions
1.2.2. Matrix of Order m by n
1.2.3. Square Matrices
1.2.4. Identity Matrix
1.2.5. Matrix Operations
1.2.6. Matrix Addition
1.2.7. Scalar Multiplication
1.2.8. Matrix Multiplication

1.3. Transpose

1.3.1. Diagonalizable Matrix
1.3.2. Transpose Properties
1.3.3. Involution

1.4. Determinants: Calculation and Definition

1.4.1. The Concept of Determinants
1.4.2. Determinant Definition
1.4.3. Square Matrix of Order 2.3 and Greater Than 3
1.4.4. Triangular Matrices
1.4.5. Determinant of Triangular Matrices
1.4.6. Determinant of Non-Triangular Square Matrices
1.4.7. Properties of Determinants
1.4.8. Simplifying Calculations
1.4.9. Calculation in any Case

1.5. Invertible Matrices

1.5.1. Properties of Invertible Matrices
1.5.2. The Concept of Inversion
1.5.3. Definitions and Basic Concepts
1.5.4. Invertible Matrix Calculation
1.5.5. Methods and Calculation
1.5.6. Exceptions and Examples
1.5.7. Expression Matrices and Matrix Equations
1.5.8. Expression Matrices
1.5.9. Matrix Equations

1.6. Solving Systems of Equations

1.6.1. Linear Equations
1.6.2. Discussion of the System. Rouché–Capelli Theorem
1.6.3. Cramer's Rule: Solving the System
1.6.4. Homogeneous Systems
1.6.5. Vector Spaces
1.6.6. Properties of Vector Spaces
1.6.7. Linear Combination of Vectors
1.6.8. Linear Dependence and Independence
1.6.9. Coordinate Vectors
1.6.10. The Basis Theorem

1.7. Quadratic Forms

1.7.1. Concept and Definition of Quadratic Forms
1.7.2. Quadratic Matrices
1.7.3. Law of Inertia for Quadratic Forms
1.7.4. Study of the Sign by Eigenvalues
1.7.5. Study of the Sign by Minors

1.8. Functions of One Variable

1.8.1. Analysis of the Behavior of a Magnitude
1.8.2. Local Analysis
1.8.3. Continuity
1.8.4. Restricted Continuity

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

1.9.1. Functions of Several Variables
1.9.2. Vector of Several Variables
1.9.3. The Domain of a Function
1.9.4. Concept and Applications
1.9.5. Function Limits
1.9.6. Limits of a Function at a Point
1.9.7. Lateral Limits of a Function
1.9.8. Limits of Rational Functions
1.9.9. Indeterminacy
1.9.10. Indeterminacy in Functions with Roots
1.9.11. Indetermination 0/0
1.9.12. The Domain and Image of a Function
1.9.13. Concept and Characteristics
1.9.14. Domain and Image Calculation

1.10. Derivatives: Behavior Analysis

1.10.1. Derivatives of a Function at a Point
1.10.2. Concept and Characteristics
1.10.3. Geometric Interpretation
1.10.4. Differentiation Rules
1.10.5. Derivative of a Constant
1.10.6. Derivative of a Sum or Differentiation
1.10.7. Derivative of a Product
1.10.8. Derivative of an Opposite Function
1.10.9. Derivative of a Compound Function

1.11. Application of Derivatives to Study Functions

1.11.1. Properties of Differentiable Functions 
1.11.2. Maximum Theorem
1.11.3. Minimum Theorem
1.11.4. Rolle's Theorem
1.11.5. Mean Value Theorem
1.11.6. L'Hôpital's Rule
1.11.7. Valuation of Economic Quantities
1.11.8. Differentiable Functions

1.12. Function Optimization for Several Variables

1.12.1. Function Optimization 
1.12.2. Optimization with Equality Constraint
1.12.3. Critical Points
1.12.4. Relative Extremes
1.12.5. Convex and Concave Functions
1.12.6. Properties of Convex and Concave Functions
1.12.7. Inflection Points
1.12.8. Growth and Decay

1.13. Antiderivatives

1.13.1. Antiderivatives
1.13.2. Basic Concepts
1.13.3. Calculation Methods
1.13.4. Immediate Integrals
1.13.5. Properties of Immediate Integrals
1.13.6. Integration Methods
1.13.7. Rational Integrals

1.14. Definite Integrals

1.14.1. Barrow's Fundamental Theorem
1.14.2. Definition of the Theorem
1.14.3. Calculation Basis
1.14.4. Applications of the Theorem
1.14.5. Curve Cutoff in Definite Integrals
1.14.6. Concept of Curve Cutoff
1.14.7. Calculation Basis and Operations Study
1.14.8. Applications of Curve Cutoff Calculation
1.14.9. Mean Value Theorem
1.14.10. Concept and Closed Interval Theorem
1.14.11. Calculation Basis and Operations Study
1.14.12. Applications of the Theorem

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

The objectives for this program are based on meeting the educational needs of Business Science professionals in the field of business accounting in various sectors and at various scales. In this sense, a complete and optimal program has been realistically established to lead students to academic excellence and encourage them to efficiently advance in their professional careers. For all these reasons, this specialization will be a journey of personal and professional growth for our students that will lead them to the highest quality in expert intervention in business calculations.   

International experience, ethical commitment, and business acumen are some of the most sought-after characteristics in executives in the digital age”  

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

The Postgraduate certificate in Business Mathematics qualifies students to:

1. Achieve a global and general vision of the function of business mathematics and its implication in companies 
2. Know the basic elements that make up business mathematics: linear and matrix algebra, matrices, matrix transposition, calculus, matrix inversion, systems of equations, etc. 
3. Understand the different techniques and mathematical methods used within the financial framework of a company 
4. Apply mathematical techniques and methods to the financial framework of the company