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Module 1. Algebra and discrete mathematics

1.1. Methods of test, induction and recursion

1.1.1. Variables and quantifiers
1.1.2. Test methods
1.1.3. Induction
1.1.4. Recursion

1.2. Sets and Functions

1.2.1. Sets
1.2.2. Operations with sets
1.2.3. Functions
1.2.4. Cardinality

1.3. Number theory and modular arithmetic

1.3.1. Divisibility and modular arithmetic
1.3.2. Prime numbers
1.3.3. Greatest Common Divisor and Least Common Multiple
1.3.4. Linear congruencies
1.3.5. Chinese remainder theorem
1.3.6. Fermat's little theorem
1.3.7.  Primitive root and discrete logarithm
1.3.8. Diffie-Hellman Algorithm

1.4. Matrix Operations

1.4.1.  Concept of Matrix
1.4.2. Fundamental matrix operations
1.4.3. The matrix identity and the power of a matrix
1.4.4. The zero-one matrixes
1.4.5. The transposed matrix, inverse and determinant

1.5. Relationships

1.5.1. Binary relationships and their properties
1.5.2. N-Ary Relationships
1.5.3. Representation of relationships
1.5.4. Closure of a relationship

1.6. Gaussian elimination

1.6.1. Automatic solving of equation systems
1.6.2. Naive Gaussian elimination
1.6.3. Error vector and residual vector
1.6.4. Gaussian elimination with scaled partial pivoting

1.7. Lineal Programming

1.7.1. -Lineal Programming Problems
1.7.2. Standard form
1.7.3. Distensioned form
1.7.4. Duality

1.8. Simplex algorithm

1.8.1. What is the simplex algorithm?
1.8.2. Geometric Interpretation
1.8.3. Pivoting
1.8.4. Initialization
1.8.5. Algorithm body

1.9. Graphs

1.9.1. Introduction to Graphs
1.9.2. Neighborly relations
1.9.3. Graph representation
1.9.4. Isomorphic graphs
1.9.5. Connectivity in networks

1.10. Tree

1.10.1. Introduction to Tree
1.10.2. Application of Tree
1.10.3. Tree Paths

Module 2. Calculus and numerical methods

2.1. Introduction to Analysis

2.1.1. Concept from Functions
2.1.2. Concept of limit
2.1.3. Calculation of limits
2.1.4. Continuity of functions

2.2. Derivation of functions and their applications

2.2.1. Derivative of a function
2.2.2. Geometric Interpretation
2.2.3. Physical interpretation
2.2.4. Calculation of derivatives
2.2.5. Successive derivatives
2.2.6. Derivable functions. Lateral derivatives
2.2.7. Theorems of derivable functions
2.2.8. L'Hôpital Rule
2.2.9. Relative extremes and monotony
2.2.10. Inflection points and curvature
2.2.11. Optimization problems

2.3. Study and graphical representation of functions of one variable

2.3.1. Study of a function
2.3.2. Study of polynomial functions
2.3.3. Study of Rational Functions
2.3.4. Study of irrational functions
2.3.5. Study of exponential functions
2.3.6. Study of Logarithm Functions
2.3.7. Study of trigonometric functions
2.3.8. Construction of functions from other known functions

2.4. Definite Integrals

2.4.1.  The definite integral as the limit of a sum
2.4.2.  Properties of the definite integral
2.4.3.  Immediate Integrals
2.4.4.  Mean value theorem of integral calculus
2.4.5.  Fundamental Calculus Theorem. Barrow's Rule
2.4.6.  Areas of flat enclosures
2.4.7.  Arc length of a curve
2.4.8.  Volumes of solid bodies

2.5. Indefinite integral

2.5.1.  Concept of Primitives of a Function
2.5.2.  Properties of the indefinite integral
2.5.3.  Integration by Parts
2.5.4.  Integration of Rational Functions
2.5.5.  Integration by variable change
2.5.6.  Integration by trigonometric substitutions
2.5.7.  Non-elemental integrals

2.6. Finite sequences and series

2.6.1.  Successions of Real Numbers
2.6.2.  Sets
2.6.3.  The integral criterion and the comparison criterion
2.6.4.  Alternating series
2.6.5.  Absolute convergence and quotient criterion

2.7. Fundamental principles of counting

2.7.1.  Partitioning of a set
2.7.2.  Addition principle
2.7.3.  Multiplication principle
2.7.4.  Inclusion- Exclusion Principles
2.7.5.  Distribution principle

2.8. Numerical and error analysis

2.8.1.  Origin and Evolution of Numerical Analysis
2.8.2.  Algorithms
2.8.3.  Types of Error
2.8.4.  Convergence

2.9. Numbering Systems

2.9.1.  Information representation
2.9.2.  Introduction to numerical systems
2.9.3.  Conversion from decimal system to base b
2.9.4.  Arithmetic operations in base b
2.9.5.  Conversion from b1 to b2 system
2.9.6.  Representation of numbers
2.9.7.  Floating point arithmetic
2.9.8.  Error propagation

2.10. Root computation and interpolation, solving algorithms and acceleration techniques

2.10.1.  Bisection algorithm
2.10.2.  Fixed-point algorithm
2.10.3.  Secant Method
2.10.4.  Newton-Raphson algorithm
2.10.5.  Modified secant algorithm
2.10.6.  Newton modified algorithm
2.10.7.  ∆2 of Aitken
2.10.8.  Steffersen Algorithm

Module 3. Statistics

3.1. Introduction to Statistics

3.1.1. Basic Concepts
3.1.2. Types of Variables
3.1.3. Statistical Information

3.2. Data Record Sorting and Classifying

3.2.1. Description of Variables
3.2.2. Frequency Distribution Table
3.2.3. Quantitative and Qualitative Frequency Distribution Tables

3.3. ICT Applications and Practical Systems

3.3.1. Basic Concepts
3.3.2. Data Science
3.3.3. Data Representation

3.4. Summary Statistics I

3.4.1. Descriptive Statistics
3.4.2. Centralization Measurements
3.4.3. Measures of Dispersion
3.4.4. Measures of Shape and Position

3.5. Summary Statistics II

3.5.1. Box Plots
3.5.2. Identifying Outliers
3.5.3. Transformation

3.6. Statistical Analysis of the Relationship between the Two Variables

3.6.1. Tabulation
3.6.2. Contingency Tables and Graphical Representations
3.6.3. Linear Relationship between Quantitative Variables

3.7. Time Series and Index Numbers

3.7.1. Time Series
3.7.2. Rates of Change
3.7.3. Index Numbers
3.7.4. Consumer Prices Index (CPI) and Deflated Time Series

3.8. Introduction to Probability: Calculation and Basic Concepts

3.8.1. Basic Concepts
3.8.2. Set Theory
3.8.3. Probability Calculation

3.9. Random Variables and Probability Distributions

3.9.1. Random Variables
3.9.2. Variable Measurements
3.9.3. Function of Probability

3.10. Probability Models for Random Variables

3.10.1. Probability Calculation
3.10.2.  Discrete Random Variables
3.10.3. Continuous Random Variables
3.10.4. Models Derived from Normal Distribution

Module 4. Logic in Computer Science

4.1. Justification of the Logic

4.1.1. Object of Logic Study
4.1.2. What Is Logic for?
4.1.3. Components and Types of Reasoning
4.1.4. Components of a Logic Calculation
4.1.5. Semantics
4.1.6. Justification of the Existence of a Logic
4.1.7. How to Check that a Logic is Adequate

4.2. Calculation of Natural Deduction from Statements

4.2.1. Formal Language
4.2.2. Deductive Mechanism

4.3. Formalization and Deduction Strategies for Propositional Logic

4.3.1. Formalization Strategies
4.3.2. Natural Reasoning
4.3.3. Laws and Rules
4.3.4. Axiomatic Deduction and Natural Deduction
4.3.5. Calculating Natural Deduction
4.3.6. Primitive Rules of Propositional Calculus

4.4. Semantics of Propositional Logic

4.4.1. Truth Tables
4.4.2. Equivalence
4.4.3. Tautologies and Contradictions
4.4.4. Validation of Propositional Sentences
4.4.5. Validation by Means of Truth Tables
4.4.6. Validation Using Semantic Trees
4.4.7. Validation by Refutation

4.5. Applications of Propositional Logic: Logic Circuits

4.5.1. Basic Gates
4.5.2. Circuits
4.5.3. Mathematical Models of the Circuits
4.5.4. Minimization
4.5.5. The Second Canonical Form and the Minimum Form in Product of Additions
4.5.6. Other Gates

4.6. Natural Predicate Deduction Calculus

4.6.1. Formal Language
4.6.2. Deductive Mechanism

4.7. Formalization Strategies for Predicate Logic

4.7.1. Introduction to Formalization in Predicate Logic
4.7.2. Formalization Strategies with Quantifiers

4.8. Deduction Strategies for Predicate Logic

4.8.1. Reason for Omission
4.8.2. Presentation of the New Rules
4.8.3. Predicate Logic as a Natural Deduction Calculus

4.9. Applications of Predicate Logic: Introduction to Logic Programming

4.9.1. Informal Presentation
4.9.2. Prolog Elements
4.9.3. Re-Evaluation and Cut-Off

4.10. Set Theory, Predicate Logic and Its Semantics

4.10.1. Intuitive Set Theory
4.10.2. Introduction to Predicate Semantics

A unique, key, and decisive educational experience to boost your professional development”