http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Over the past century, advancements in computer science have consistently resulted from extensive mathematical work. Even today, innovations in the digital domain continue to be grounded in a strong mathematical foundation. To succeed in this profession, both today's students and tomorrow's computer engineers need a solid mathematical background. The goal of this book series is to offer a solid foundation of the knowledge essential to working in the digital sector. Across three volumes, it explores fundamental principles, digital information, data analysis, and optimization. Whether the reader is pursuing initial training or looking to deepen their expertise, the Mathematics for Digital Science series revisits familiar concepts, helping them refresh and expand their knowledge while also introducing equally essential, newer topics.
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 B̌zout 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.
Sciences. Computer science; Operational research and decision