Preface -- Chapter 1. The Concept of Logic -- 1.1. Syllogisms -- 1.2. Elementary operations of propositional calculus -- 1.2.1. Negation -- 1.2.2. Conjunction -- 1.2.3. Disjunction -- 1.2.4. Conditional -- 1.2.5. Biconditional -- 1.2.6. Tautologies -- 1.3. Tools of deductive reasoning -- 1.4. Quantification -- 1.5. Prenex forms and pure forms -- Chapter 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 -- Chapter 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 -- Chapter 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 -- Chapter 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 -- Chapter 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 -- Chapter 7. Error Protection -- 7.1. General context -- 7.2. Linear codes -- 7.3. Polynomial codes -- 7.4. Convolutional codes -- Chapter 8. Encryption Systems -- 8.1. Substitution and transposition -- 8.2. Substitution methods -- 8.2.1. Replacement of a symbol by a symbol -- 8.2.2. The code: replacement of a word by a word -- 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 -- Chapter 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 -- 9.7.1. Definition -- 9.7.2. Transition matrix -- 9.7.3. Evolution rules -- 9.7.4. Ergodicity -- Chapter 10. Descriptive Statistics -- 10.1. Statistical description -- 10.1.1. A little vocabulary -- 10.1.2. Tabular presentation and frequency -- 10.1.3. Two-dimensional series -- 10.2. Graphical representations -- 10.2.1. Bar charts -- 10.2.2. Histograms -- 10.2.3. Cumulative diagrams -- 10.2.4. Polar diagrams -- 10.2.5. Pie charts -- 10.2.6. Figurative diagrams -- 10.2.7. Point clouds -- 10.3. Position parameters -- 10.3.1. Mode -- 10.3.2. Median -- 10.3.3. Averages -- 10.3.4. Comparison of position parameters -- 10.4. Dispersion parameters -- 10.4.1. Range, interquartile range, mean range -- 10.4.2. Variance and standard deviation -- 10.4.3. Coefficient of variation and concentration index -- 10.5. Linear adjustment -- 10.5.1. Principle of adjustment -- 10.5.2. Linear adjustment -- 10.6. Chronological series -- 10.6.1. Introduction -- 10.6.2. Study of the general trend -- 10.6.3. Study of seasonal variations -- 10.7. Covariance and correlation -- 10.7.1. Regression lines -- 10.7.2. Linear correlation -- Chapter 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 -- 11.4.1. Uniform law -- 11.4.2. Binomial or Bernoulli's law -- 11.4.3. Poisson's law -- 11.4.4. Exponential law -- 11.4.5. Normal law -- 11.5. General information on simulation -- 11.5.1. Weak law of large numbers -- 11.5.2. Some simulations -- 11.5.3. Generation of random numbers -- 11.6. Generating programs -- 11.6.1. Usual laws -- 11.6.2. Any probability law -- 11.7. M/M/1 waiting system -- 11.7.1. Theoretical study -- 11.7.2. Simulation -- 11.8. Appendices -- 11.8.1. Appendix 1: Table for Poisson's law -- 11.8.2. Appendix 2: Table for normal law -- 11.8.3. Appendix 3: Buffon's needle -- 11.8.4. Appendix 4: Results for M/M/1 -- References -- List of Authors -- Index.