A comprehensive and 100% online program, exclusive to TECH, with an international perspective supported by our membership with the Association for Computing Machinery" 

In an increasingly technological environment shaped by automation, artificial intelligence, and natural language processing, understanding how computational languages are constructed, interpreted, and optimized has become a key requirement for progress across multiple fields of knowledge and industry.  Human–machine interaction, the efficiency of computing systems, and the creation of new digital tools depend largely on mastery of these languages. 

This program offers a comprehensive view of the pillars that underpin computing and programming languages, enabling the acquisition of specialized competencies that enhance logical thinking, complex problem-solving, and the design of innovative solutions.  Topics such as formal semantics, language theory, automata, compilation, and other fundamental elements essential to understanding the internal functioning of computing systems are addressed in depth. 

Moreover, mastery of these contents opens opportunities in highly dynamic sectors such as artificial intelligence, programming language development, quantum computing, and software engineering. This specialization represents a strategic step for those seeking to advance their careers in academic, technical, or professional settings, particularly in contexts where profiles with a strong theoretical foundation and analytical capacity are highly valued. The conceptual depth acquired enables not only the application of existing technologies, but also the design of those of the future. 

The online format of this program allows access to up-to-date, high-level academic content from anywhere, without compromising quality or rigor. This flexibility facilitates compatibility with other professional or academic projects and promotes autonomous, rigorous learning oriented toward critical analysis. Through an interactive platform, multimedia materials, and expert guidance, an enriching educational experience is ensured that responds to the current needs of the digital and academic sectors.  In addition, a renowned International Guest Director will deliver 10 in-depth Masterclasses. 

Furthermore, thanks to TECH membership in the Association for Computing Machinery (ACM), students will have access to exclusive and up-to-date resources, such as scientific publications, specialized courses, and international conferences. Additionally, they will have the opportunity to expand their network by connecting with experts in technology, artificial intelligence, data science, and other key disciplines in the sector.

A renowned International Guest Director will deliver 10 exclusive Masterclasses on the latest trends in Computing and Programming Languages”

This Master's Degree in Computing and Programming Languages contains the most complete and up-to-date university program on the market. Its most notable features are:

• The development of practical cases presented by experts in Computing and Programming Languages
• The graphic, schematic, and practical contents with which they are created, provide scientific and practical information on the disciplines that are essential for professional practice
• Practical exercises where the self-assessment process can be carried out to improve learning
• Its special emphasis on innovative methodologies
• Theoretical lessons, questions to the expert, debate forums on controversial topics, and individual reflection assignments
• Content that is accessible from any fixed or portable device with an Internet connection

You will delve into automata theory and formal languages to understand the internal functioning of computational systems”

The faculty includes professionals from the field of Computing, who contribute their practical experience to the program, as well as renowned specialists from leading professional associations and prestigious universities.

Its multimedia content, developed using the latest educational technology, enables situated and contextualized learning—that is, a simulated environment that provides an immersive learning experience designed to prepare professionals for real-world situations.

This program is designed around Problem-Based Learning, whereby the student must try to solve the different professional practice situations that arise throughout the program. For this purpose, the professional will be assisted by an innovative interactive video system created by renowned and experienced experts.

You will work with advanced data structures to develop efficient, scalable, and performance-oriented solutions"

You will design sophisticated algorithms to solve computational problems with high demand in key technology sectors"

In a context where advances in programming languages, automata theory, and formal semantics are driving the development of new technologies, an in-depth study of these foundations is essential for innovation in areas such as quantum computing, artificial intelligence, and cybersecurity. For this reason, this syllabus integrates up-to-date and strategically structured content that enables an understanding of the internal logic of computing systems. In this way, it fosters a critical and advanced perspective on computational functioning, aligned with the digital transformations that are redefining computer science standards on a global scale.

You will design and implement domain-specific languages tailored to specific technical needs”

Module 1. Programming Fundamentals

1.1. Introduction to Programming

1.1.1. Basic Structure of a Computer
1.1.2. Software
1.1.3. Programming Languages
1.1.4. Life Cycle of a Software Application

1.2. Algorithm Design

1.2.1. Problem Solving
1.2.2. Descriptive Techniques
1.2.3. Algorithm Elements and Structure

1.3. Elements of a Program

1.3.1. C++ Origin and Features
1.3.2. Development Environment
1.3.3. Concept of Program
1.3.4. Types of Fundamental Data
1.3.5. Operators
1.3.6. Expressions
1.3.7. Statements
1.3.8. Data Input and Output

1.4. Control Sentences

1.4.1. Statements
1.4.2. Branches
1.4.3. Loops

1.5. Abstraction and Modularity: Functions

1.5.1. Modular Design
1.5.2. Concept of Function and Utility
1.5.3. Definition of a Function
1.5.4. Execution Flow in a Function Call
1.5.5. Function Prototypes
1.5.6. Results Return
1.5.7. Calling a Function: Parameters
1.5.8. Passing Parameters by Reference and by Value
1.5.9. Scope of an Identifier

1.6. Static Data Structures

1.6.1. Arrays
1.6.2. Matrices. Polyhedra
1.6.3. Searching and Sorting
1.6.4. Strings. Input/Output Functions for Strings
1.6.5. Structures. Unions
1.6.6. New Types of Data

1.7. Dynamic Data Structures: Pointers

1.7.1. Concept. Definition of Pointer
1.7.2. Pointer Operators and Operations
1.7.3. Arrays of Pointers
1.7.4. Pointers and Arrays
1.7.5. Pointers to Strings
1.7.6. Pointers to Structures
1.7.7. Multiple Indirection
1.7.8. Pointers to Functions
1.7.9. Passing Functions, Structures, and Arrays as Function Parameters

1.8. Files

1.8.1. Basic Concepts
1.8.2. File Operations
1.8.3. Types of Files
1.8.4. File Organization
1.8.5. Introduction to C++ Files
1.8.6. Managing Files

1.9. Recursion

1.9.1. Definition of Recursion
1.9.2. Types of Recursion
1.9.3. Advantages and Disadvantages
1.9.4. Considerations
1.9.5. Recursive to Iterative Conversion
1.9.6. Recursion Stack

1.10. Testing and Documentation

1.10.1. Program Testing
1.10.2. White Box Testing
1.10.3. Black Box Testing
1.10.4. Testing Tools
1.10.5. Program Documentation

Module 2. Data Structures

2.1. Introduction to C++ Programming

2.1.1. Classes, Constructors, Methods and Attributes
2.1.2. Variables
2.1.3. Conditional Expressions and Loops
2.1.4. Objects

2.2. Abstract Data Types (ADT)

2.2.1. Types of Data
2.2.2. Basic Structures and ADTs
2.2.3. Vectors and Arrays

2.3. Linear Data Structures

2.3.1. List ADT: Definition
2.3.2. Linked and Doubly Linked Lists
2.3.3. Sorted Lists
2.3.4. Lists in C++
2.3.5. ADT Stack
2.3.6. ADT Queue
2.3.7. Stack and Queue in C++

2.4. Hierarchical Data Structures

2.4.1. ADT Tree
2.4.2. Paths
2.4.3. N-Ary Trees
2.4.4. Binary Trees
2.4.5. Binary Search Trees

2.5. Hierarchical Data Structures: Complex Trees

2.5.1. Perfectly Balanced or Minimum Height Trees
2.5.2. Multipath Trees
2.5.3. Bibliographic References

2.6. Priority Mounds and Queue

2.6.1. ADT Heaps
2.6.2. ADT Priority Queues

2.7. Hash Tables

2.7.1. ADT Hash Table
2.7.2. Hash Functions
2.7.3. Hash Function in Hash Tables
2.7.4. Rehashing
2.7.5. Open Hash Tables

2.8. Graphs

2.8.1. ADT Graph
2.8.2. Types of Graphs
2.8.3. Graphical Representation and Basic Operations
2.8.4. Graph Design

2.9. Algorithms and Advanced Graph Concepts

2.9.1. Problems about Graphs
2.9.2. Path Algorithms
2.9.3. Search or Path Algorithms
2.9.4. Other Algorithms

2.10. Other Data Structures

2.10.1. Sets
2.10.2. Parallel Arrays
2.10.3. Symbol Tables
2.10.4. Tries

Module 3. Algorithmics and Complexity

3.1. Introduction to Algorithm Design Strategies

3.1.1. Recursion
3.1.2. Divide and Conquer
3.1.3. Other Strategies

3.2. Efficiency and Analysis of Algorithms

3.2.1. Efficiency Measures
3.2.2. Measuring the Size of the Input
3.2.3. Measuring Execution Time
3.2.4. Worst, Best and Average Case
3.2.5. Asymptotic Notation
3.2.6. Criteria for Mathematical Analysis of Non-Recursive Algorithms
3.2.7. Mathematical Analysis of Recursive Algorithms
3.2.8. Empirical Analysis of Algorithms

3.3. Sorting Algorithms

3.3.1. Concept of Sorting
3.3.2. Bubble Sorting
3.3.3. Sorting by Selection
3.3.4. Sorting by Insertion
3.3.5. Merge Sort
3.3.6. Quick Sort

3.4. Algorithms with Trees

3.4.1. Tree Concept
3.4.2. Binary Trees
3.4.3. Tree Paths
3.4.4. Representing Expressions
3.4.5. Ordered Binary Trees
3.4.6. Balanced Binary Trees

3.5. Algorithms Using Heaps

3.5.1. Heaps
3.5.2. Heap Sort
3.5.3. Priority Queues

3.6. Graph Algorithms

3.6.1. Representation
3.6.2. Traversal in Width
3.6.3. Depth Travel
3.6.4. Topological Sorting

3.7. Greedy Algorithms

3.7.1. Greedy Strategy
3.7.2. Greedy Strategy Elements
3.7.3. Currency Exchange
3.7.4. Traveler’s Problem
3.7.5. Backpack Problem

3.8. Minimal Path Finding

3.8.1. The Minimum Path Problem
3.8.2. Negative Arcs and Cycles
3.8.3. Dijkstra's Algorithm

3.9. Greedy Algorithms on Graphs

3.9.1. Minimum Spanning Tree
3.9.2. Prim's Algorithm
3.9.3. Kruskal’s Algorithm
3.9.4. Complexity Analysis

3.10. Backtracking

3.10.1. Backtracking Algorithm
3.10.2. Alternative Techniques

Module 4. Advanced Algorithm Design

4.1. Analysis of Recursive and Divide and Conquer Algorithms

4.1.1. Posing and Solving Homogeneous and Non-Homogeneous Recurrence Equations
4.1.2. General Description of the Divide and Conquer Strategy

4.2. Amortized Analysis

4.2.1. Aggregate Analysis
4.2.2. The Accounting Method
4.2.3. The Potential Method

4.3. Dynamic Programming and Algorithms for NP Problems

4.3.1. Characteristics of Dynamic Programming
4.3.2. Backtracking 
4.3.3. Branch and Bound

4.4. Combinatorial Optimization

4.4.1. Representation
4.4.2. 1D Optimization

4.5. Randomization Algorithms

4.5.1. Examples of Randomization Algorithms
4.5.2. Buffon's Theorem
4.5.3. Monte Carlo Algorithm
4.5.4. Las Vegas Algorithm

4.6. Local Search and Candidate Search

4.6.1. Gradient Ascent
4.6.2. Hill Climbing
4.6.3. Simulated Annealing
4.6.4. Tabu Search
4.6.5. Candidate Search

4.7. Formal Verification of Programs

4.7.1. Specification of Functional Abstractions
4.7.2. The Language of First-Order Logic
4.7.3. Hoare's Formal System

4.8. Verification of Iterative Programs

4.8.1. Rules of Hoare's Formal System
4.8.2. Concept of Invariant Iterations

4.9. Numeric Methods

4.9.1. The Bisection Method
4.9.2. The Newton-Raphson Method
4.9.3. The Secant Method

4.10. Parallel Algorithms

4.10.1. Parallel Binary Operations
4.10.2. Parallel Operations with Networks
4.10.3. Parallelism in Divide and Conquer
4.10.4. Parallelism in Dynamic Programming

Module 5. Advanced Programming

5.1. Introduction to Object-Oriented Programming

5.1.1. Introduction to Object-Oriented Programming
5.1.2. Class Design
5.1.3. Introduction to UML for Problem Modeling

5.2. Relationships Between Classes

5.2.1. Abstraction and Inheritance
5.2.2. Advanced Inheritance Concepts
5.2.3. Polymorphism
5.2.4. Composition and Aggregation

5.3. Introduction to Design Patterns for Object-Oriented Problems

5.3.1. What Are Design Patterns?
5.3.2. Factory Pattern
5.3.3. Singleton Pattern
5.3.4. Observer Pattern
5.3.5. Composite Pattern

5.4. Exceptions

5.4.1. What Are Exceptions?
5.4.2. Exception Catching and Handling
5.4.3. Throwing Exceptions
5.4.4. Exception Creation

5.5. User Interfaces

5.5.1. Introduction to Qt
5.5.2. Positioning
5.5.3. What Are Events?
5.5.4. Events: Definition and Catching
5.5.5. User Interface Development

5.6. Introduction to Concurrent Programming

5.6.1. Introduction to Concurrent Programming
5.6.2. The Concept of Process and Thread
5.6.3. Interaction Between Processes or Threads
5.6.4. Threads in C++
5.6.5. Advantages and Disadvantages of Concurrent Programming

5.7. Thread Management and Synchronization

5.7.1. Life Cycle of a Thread
5.7.2. Thread Class
5.7.3. Thread Planning
5.7.4. Thread Groups
5.7.5. Daemon Threads
5.7.6. Synchronization
5.7.7. Locking Mechanisms
5.7.8. Communication Mechanisms
5.7.9. Monitors

5.8. Common Problems in Concurrent Programming

5.8.1. The Problem of Consuming Producers
5.8.2. The Problem of Readers and Writers
5.8.3. The Problem of the Philosophers' Dinner Party

5.9. Software Documentation and Testing

5.9.1. Why is it Important to Document Software?
5.9.2. Design Documentation
5.9.3. Documentation Tool Use

5.10. Software Testing

5.10.1. Introduction to Software Testing
5.10.2. Types of Tests
5.10.3. Unit Test
5.10.4. Integration Test
5.10.5. Validation Test
5.10.6. System Test

Module 6. Theoretical Computer Science

6.1. Mathematical Concepts Used

6.1.1. Introduction to Propositional Logic
6.1.2. Theory of Relations
6.1.3. Numerable and Non-Numerable Sets

6.2. Formal Languages and Grammars and Introduction to Turing Machines

6.2.1. Formal Languages and Grammars
6.2.2. Decision Problem
6.2.3. The Turing Machine

6.3. Extensions to Turing Machines, Constrained Turing Machines and Computers

6.3.1. Programming Techniques for Turing Machines
6.3.2. Extensions for Turing Machines
6.3.3. Restricted Turing Machines
6.3.4. Turing Machines and Computers

6.4. Indecibility

6.4.1. Non-Recursively Enumerable Language
6.4.2. A Recursively Enumerable Undecidable Problem

6.5. Other Undecidable Problems

6.5.1. Undecidable Problems for Turing Machines
6.5.2. Post Correspondence Problem (PCP)

6.6. Intractable Problems

6.6.1. The Classes P and NP
6.6.2. A NP-Complete Problem
6.6.3. Restricted Satisfiability Problem
6.6.4. Other NP-Complete Problems

6.7. Co-NP and PSPACE Problems

6.7.1. Complementary to NP Languages
6.7.2. Problems Solvable in Polynomial Space
6.7.3. Complete PSPACE Problems

6.8. Classes of Randomization-Based Languages

6.8.1. MT Model with Randomization
6.8.2. RP and ZPP Classes
6.8.3. Primality Test
6.8.4. Complexity of the Primality Test

6.9. Other Classes and Grammars

6.9.1. Probabilistic Finite Automata
6.9.2. Cellular Automata
6.9.3. McCulloch and Pitts Cells
6.9.4. Lindenmayer Grammars

6.10. Advanced Computing Systems

6.10.1. Membrane Computing: P-Systems
6.10.2. DNA Computing
6.10.3. Quantum Computing

Module 7. Automata Theory and Formal Languages

7.1. Introduction to Automata Theory

7.1.1. Why Study Automata Theory?
7.1.2. Introduction to Formal Demonstrations
7.1.3. Other Forms of Demonstration
7.1.4. Mathematical Induction
7.1.5. Alphabets, Strings and Languages

7.2. Deterministic Finite Automata

7.2.1. Introduction to Finite Automata
7.2.2. Deterministic Finite Automata

7.3. Non-Deterministic Finite Automata

7.3.1. Non-Deterministic Finite Automata
7.3.2. Equivalence Between DFA and NFA
7.3.3. Finite Automata with ε-Transitions

7.4. Languages and Regular Expressions (I)

7.4.1. Languages and Regular Expressions
7.4.2. Finite Automata and Regular Expressions

7.5. Languages and Regular Expressions (II)

7.5.1. Conversion of Regular Expressions into Automata
7.5.2. Applications of Regular Expressions
7.5.3. Algebra of Regular Expressions

7.6. Pumping and Closure Lemma of Regular Languages

7.6.1. Pumping Lemma
7.6.2. Closure Properties of Regular Languages

7.7. Equivalence and Minimization of Automata

7.7.1. Equivalence of Finite Automata
7.7.2. Minimization of Finite Automata

7.8. Context-Free Grammars (CFGs)

7.8.1. Context-Free Grammars
7.8.2. Derivation Trees
7.8.3. Applications of CFGs
7.8.4. Ambiguity in Grammars and Languages

7.9. Pushdown Automata and CFGs

7.9.1. Definition of Pushdown Automata
7.9.2. Languages Accepted by a Pushdown Automaton
7.9.3. Equivalence Between Pushdown Automata and CFGs
7.9.4. Deterministic Pushdown Automaton

7.10. Normal Forms, the Pumping Lemma for CFGs, and Properties of Context-Free Languages

7.10.1. Normal Forms for CFGs
7.10.2. Pumping Lemma
7.10.3. Closure Properties of Languages
7.10.4. Decision Properties of Context-Free Languages

Module 8. Language Processors

8.1. Introduction to the Compilation Process

8.1.1. Compilation and Interpretation
8.1.2. Compiler Execution Environment
8.1.3. Analysis Process
8.1.4. Synthesis Process

8.2. Lexical Analyzer

8.2.1. What Is a Lexical Analyzer?
8.2.2. Implementation of the Lexical Analyzer
8.2.3. Semantic Actions
8.2.4. Error Recovery
8.2.5. Implementation Issues

8.3. Syntactic Analysis

8.3.1. What Is a Parser?
8.3.2. Previous Concepts
8.3.3. Top-Down Analyzers
8.3.4. Bottom-Up Analyzers

8.4. Top-Down Parsing and Bottom-Up Parsing

8.4.1. LL(1) Parser
8.4.2. LR(0) Parser
8.4.3. Parser Example

8.5. Advanced Bottom-Up Parsing

8.5.1. SLR Parser
8.5.2. LR(1) Parser
8.5.3. LR(k) Parser
8.5.4. LALR Parser

8.6. Semantic Analysis (I)

8.6.1. Syntax-Driven Translation
8.6.2. Table of Symbols

8.7. Semantic Analysis (II)

8.7.1. Type Checking
8.7.2. The Type Subsystem
8.7.3. Type Equivalence and Conversions

8.8. Code Generation and Execution Environment

8.8.1. Design Aspects
8.8.2. Execution Environment
8.8.3. Memory Organization
8.8.4. Memory Allocation

8.9. Intermediate Code Generation

8.9.1. Syntax-Driven Translation
8.9.2. Intermediate Representations
8.9.3. Examples of Translations

8.10. Code Optimization

8.10.1. Register Allocation
8.10.2. Elimination of Dead Assignments
8.10.3. Compile-Time Execution
8.10.4. Expression Reordering
8.10.5. Loop Optimization

Module 9. Computer Graphics and Visualization

9.1. Color Theory

9.1.1. Properties of Light
9.1.2. Color Models
9.1.3. The CIE Standard
9.1.4. Profiling

9.2. Output Primitives

9.2.1. The Video Driver
9.2.2. Line Drawing Algorithms
9.2.3. Circle Drawing Algorithms
9.2.4. Filling Algorithms

9.3. 2D Transformations and 2D Coordinate Systems and 2D Clipping

9.3.1. Basic Geometric Transformations
9.3.2. Homogeneous Coordinates
9.3.3. Inverse Transformation
9.3.4. Composition of Transformations
9.3.5. Other Transformations
9.3.6. Coordinate Change
9.3.7. 2D Coordinate Systems
9.3.8. Coordinate Change
9.3.9. Standardization
9.3.10. Trimming Algorithms

9.4. 3D Transformations

9.4.1. Translation
9.4.2. Rotation
9.4.3. Scaling
9.4.4. Reflection
9.4.5. Shearing

9.5. Display and Change of 3D Coordinates

9.5.1. 3D Coordinate Systems
9.5.2. Visualization
9.5.3. Coordinate Change
9.5.4. Projection and Normalization

9.6. 3D Projection and Clipping

9.6.1. Orthogonal Projection
9.6.2. Oblique Parallel Projection
9.6.3. Perspective Projection
9.6.4. 3D Clipping Algorithms

9.7. Hidden Surface Removal

9.7.1. Back-Face Removal
9.7.2. Z-Buffer
9.7.3. Painter Algorithm
9.7.4. Warnock Algorithm
9.7.5. Hidden Line Detection

9.8. Interpolation and Parametric Curves

9.8.1. Interpolation and Polynomial Approximation
9.8.2. Parametric Representation
9.8.3. Lagrange Polynomial
9.8.4. Natural Cubic Splines
9.8.5. Basic Functions
9.8.6. Matrix Representation

9.9. Bézier Curves

9.9.1. Algebraic Construction
9.9.2. Matrix Form
9.9.3. Composition
9.9.4. Geometric Construction
9.9.5. Drawing Algorithm

9.10. B-Splines

9.10.1. The Local Control Problem
9.10.2. Uniform Cubic B-Splines
9.10.3. Basis Functions and Control Points
9.10.4. Derivative to the Origin and Multiplicity
9.10.5. Matrix Representation
9.10.6. Non-Uniform B-Splines

Module 10. Bioinspired Computing

10.1. Introduction to Bioinspired Computing

10.1.1. Introduction to Bioinspired Computing

10.2. Social Adaptation Algorithms

10.2.1. Bioinspired Computation Based on Ant Colonies
10.2.2. Variants of Ant Colony Algorithms
10.2.3. Particle Cloud Computing

10.3. Genetic Algorithms

10.3.1. General Structure
10.3.2. Implementations of the Major Operators

10.4. Space Exploration and Exploitation Strategies for Genetic Algorithms

10.4.1. CHC Algorithm
10.4.2. Multimodal Problems

10.5. Evolutionary Computing Models (I)

10.5.1. Evolutionary Strategies
10.5.2. Evolutionary Programming
10.5.3. Algorithms Based on Differential Evolution

10.6. Evolutionary Computing Models (II)

10.6.1. Evolutionary Models Based on Estimation of Distributions (EDA)
10.6.2. Genetic Programming

10.7. Evolutionary Programming Applied to Learning Problems

10.7.1. Rules-Based Learning
10.7.2. Evolutionary Methods in Instance Selection Problems

10.8. Multi-Objective Problems

10.8.1. Concept of Dominance
10.8.2. Application of Evolutionary Algorithms to Multi-Objective Problems

10.9. Neural Networks (I)

10.9.1. Introduction to Neural Networks
10.9.2. Practical Example with Neural Networks

10.10. Neural Networks (II)

10.10.1. Use Cases of Neural Networks in Medical Research
10.10.2. Use Cases of Neural Networks in Economics
10.10.3. Use Cases of Neural Networks in Artificial Vision

You will develop skills for the formal and semantic analysis of programs, significantly improving software efficiency”