,Table of Contents
Cover
Table of Contents
Title Page
Copyright Page
Preface
1 The Concept of Logic
1.1. Syllogisms
1.2. Elementary operations of propositional calculus
1.3. Tools of deductive reasoning
1.4. Quantification
1.5. Prenex forms and pure forms
2 Sets and Relationships
2.1. Generalities
2.2. Algebra of sets
2.3. Parts and partitions
2.4. Cartesian product
2.5. Binary relationships
2.6. Properties of relationships
2.7. Applications
3 Counting and Combinatorial Analysis
3.1. Set cardinals
3.2. Permutations, arrangements, combinations
3.3. Properties of binomial coefficients
3.4. Stirling’s formula
4 Boolean Algebra and Boolean Functions
4.1. Special elements of an ordered set
, 4.2. Lattice
4.3. Boolean algebra
4.4. Boolean functions
5 Logic Circuits
5.1. Canonical forms of a Boolean function
5.2. Reduction of a Boolean function
5.3. Karnaugh tables
5.4. Elementary logic circuits
5.5. A little on electronics
5.6. Construction of logical functions
5.7. A basic circuit: the binary adder
6 Arithmetic
6.1. Reminder about integers
6.2. Euclidean division
6.3. Divisibility and prime numbers
6.4. GCD and LCM
6.5. Congruencies
6.6. Elliptic curves
6.7. Identity, theorem and Bézout algorithm
7 Error Protection
7.1. General context
7.2. Linear codes
7.3. Polynomial codes
7.4. Convolutional codes
8 Encryption Systems
8.1. Substitution and transposition
8.2. Substitution methods
8.3. Transposition methods
8.4. Asymmetric systems
, 8.5. DES – secret key system
8.6. RSA – public key system
8.7. Cryptography with elliptic curves
8.8. Quantum cryptography
8.9. Appendix: The Crow and the Fox
9 Probabilities
9.1. Chance
9.2. Counting and probabilities
9.3. Events and probabilities
9.4. Statistics and probabilities
9.5. Compound probabilities
9.6. Graphs, states, transitions
9.7. Markov chains
10 Descriptive Statistics
10.1. Statistical description
10.2. Graphical representations
10.3. Position parameters
10.4. Dispersion parameters
10.5. Linear adjustment
10.6. Chronological series
10.7. Covariance and correlation
11 Probability Laws and Simulation
11.1. Random variables
11.2. Mathematical expectation, variance and standard deviation
11.3. Distribution function
11.4. Usual probability laws
11.5. General information on simulation
11.6. Generating programs
11.7. M/M/1 waiting system
Cover
Table of Contents
Title Page
Copyright Page
Preface
1 The Concept of Logic
1.1. Syllogisms
1.2. Elementary operations of propositional calculus
1.3. Tools of deductive reasoning
1.4. Quantification
1.5. Prenex forms and pure forms
2 Sets and Relationships
2.1. Generalities
2.2. Algebra of sets
2.3. Parts and partitions
2.4. Cartesian product
2.5. Binary relationships
2.6. Properties of relationships
2.7. Applications
3 Counting and Combinatorial Analysis
3.1. Set cardinals
3.2. Permutations, arrangements, combinations
3.3. Properties of binomial coefficients
3.4. Stirling’s formula
4 Boolean Algebra and Boolean Functions
4.1. Special elements of an ordered set
, 4.2. Lattice
4.3. Boolean algebra
4.4. Boolean functions
5 Logic Circuits
5.1. Canonical forms of a Boolean function
5.2. Reduction of a Boolean function
5.3. Karnaugh tables
5.4. Elementary logic circuits
5.5. A little on electronics
5.6. Construction of logical functions
5.7. A basic circuit: the binary adder
6 Arithmetic
6.1. Reminder about integers
6.2. Euclidean division
6.3. Divisibility and prime numbers
6.4. GCD and LCM
6.5. Congruencies
6.6. Elliptic curves
6.7. Identity, theorem and Bézout algorithm
7 Error Protection
7.1. General context
7.2. Linear codes
7.3. Polynomial codes
7.4. Convolutional codes
8 Encryption Systems
8.1. Substitution and transposition
8.2. Substitution methods
8.3. Transposition methods
8.4. Asymmetric systems
, 8.5. DES – secret key system
8.6. RSA – public key system
8.7. Cryptography with elliptic curves
8.8. Quantum cryptography
8.9. Appendix: The Crow and the Fox
9 Probabilities
9.1. Chance
9.2. Counting and probabilities
9.3. Events and probabilities
9.4. Statistics and probabilities
9.5. Compound probabilities
9.6. Graphs, states, transitions
9.7. Markov chains
10 Descriptive Statistics
10.1. Statistical description
10.2. Graphical representations
10.3. Position parameters
10.4. Dispersion parameters
10.5. Linear adjustment
10.6. Chronological series
10.7. Covariance and correlation
11 Probability Laws and Simulation
11.1. Random variables
11.2. Mathematical expectation, variance and standard deviation
11.3. Distribution function
11.4. Usual probability laws
11.5. General information on simulation
11.6. Generating programs
11.7. M/M/1 waiting system
