{"product_id":"mathematics-for-digital-science-1-fundamentals-hardback-9781789451948","title":"Mathematics for Digital Science 1; Fundamentals (Hardback) 9781789451948","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eMathematics for Digital Science 1\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eFundamentals\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eGérard-Michel Cochard (Author), Mhand Hifi (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781789451948, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 4 February 2025\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e368 pages\u003cbr\u003e23.5 x 15.6 x 2.3 cm, 0.68 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eOver 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.\u003c\/p\u003e \u003cp\u003eThe 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 \u003ci\u003eMathematics for Digital Science\u003c\/i\u003e series revisits familiar concepts, helping them refresh and expand their knowledge while also introducing equally essential, newer topics.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003ePreface ix\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 1. The Concept of Logic 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1. Syllogisms 1\u003c\/p\u003e \u003cp\u003e1.2. Elementary operations of propositional calculus 5\u003c\/p\u003e \u003cp\u003e1.2.1. Negation 5\u003c\/p\u003e \u003cp\u003e1.2.2. Conjunction 6\u003c\/p\u003e \u003cp\u003e1.2.3. Disjunction 7\u003c\/p\u003e \u003cp\u003e1.2.4. Conditional 8\u003c\/p\u003e \u003cp\u003e1.2.5. Biconditional 10\u003c\/p\u003e \u003cp\u003e1.2.6. Tautologies 10\u003c\/p\u003e \u003cp\u003e1.3. Tools of deductive reasoning 14\u003c\/p\u003e \u003cp\u003e1.4. Quantification 17\u003c\/p\u003e \u003cp\u003e1.5. Prenex forms and pure forms 20\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2. Sets and Relationships 25\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1. Generalities 25\u003c\/p\u003e \u003cp\u003e2.2. Algebra of sets 29\u003c\/p\u003e \u003cp\u003e2.3. Parts and partitions 30\u003c\/p\u003e \u003cp\u003e2.4. Cartesian product 31\u003c\/p\u003e \u003cp\u003e2.5. Binary relationships 32\u003c\/p\u003e \u003cp\u003e2.6. Properties of relationships 35\u003c\/p\u003e \u003cp\u003e2.7. Applications 42\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3. Counting and Combinatorial Analysis 47\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1. Set cardinals 47\u003c\/p\u003e \u003cp\u003e3.2. Permutations, arrangements, combinations 48\u003c\/p\u003e \u003cp\u003e3.3. Properties of binomial coefficients 51\u003c\/p\u003e \u003cp\u003e3.4. Stirling's formula 54\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4. Boolean Algebra and Boolean Functions 61\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1. Special elements of an ordered set 61\u003c\/p\u003e \u003cp\u003e4.2. Lattice 66\u003c\/p\u003e \u003cp\u003e4.3. Boolean algebra 68\u003c\/p\u003e \u003cp\u003e4.4. Boolean functions 72\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5. Logic Circuits 75\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1. Canonical forms of a Boolean function 75\u003c\/p\u003e \u003cp\u003e5.2. Reduction of a Boolean function 80\u003c\/p\u003e \u003cp\u003e5.3. Karnaugh tables 84\u003c\/p\u003e \u003cp\u003e5.4. Elementary logic circuits 87\u003c\/p\u003e \u003cp\u003e5.5. A little on electronics 93\u003c\/p\u003e \u003cp\u003e5.6. Construction of logical functions 97\u003c\/p\u003e \u003cp\u003e5.7. A basic circuit: the binary adder 100\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 6. Arithmetic 103\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1. Reminder about integers 103\u003c\/p\u003e \u003cp\u003e6.2. Euclidean division 104\u003c\/p\u003e \u003cp\u003e6.3. Divisibility and prime numbers 106\u003c\/p\u003e \u003cp\u003e6.4. GCD and LCM 112\u003c\/p\u003e \u003cp\u003e6.5. Congruencies 116\u003c\/p\u003e \u003cp\u003e6.6. Elliptic curves 121\u003c\/p\u003e \u003cp\u003e6.7. Identity, theorem and Bézout algorithm 127\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 7. Error Protection 131\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1. General context 131\u003c\/p\u003e \u003cp\u003e7.2. Linear codes 136\u003c\/p\u003e \u003cp\u003e7.3. Polynomial codes 140\u003c\/p\u003e \u003cp\u003e7.4. Convolutional codes 142\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 8. Encryption Systems 145\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1. Substitution and transposition 145\u003c\/p\u003e \u003cp\u003e8.2. Substitution methods 147\u003c\/p\u003e \u003cp\u003e8.2.1. Replacement of a symbol by a symbol 147\u003c\/p\u003e \u003cp\u003e8.2.2. The code: replacement of a word by a word 157\u003c\/p\u003e \u003cp\u003e8.3. Transposition methods 158\u003c\/p\u003e \u003cp\u003e8.4. Asymmetric systems 159\u003c\/p\u003e \u003cp\u003e8.5. DES -- secret key system 160\u003c\/p\u003e \u003cp\u003e8.6. RSA -- public key system 165\u003c\/p\u003e \u003cp\u003e8.7. Cryptography with elliptic curves 167\u003c\/p\u003e \u003cp\u003e8.8. Quantum cryptography 169\u003c\/p\u003e \u003cp\u003e8.9. Appendix: the Crow and the Fox 176\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 9. Probabilities 177\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1. Chance 177\u003c\/p\u003e \u003cp\u003e9.2. Counting and probabilities 178\u003c\/p\u003e \u003cp\u003e9.3. Events and probabilities 183\u003c\/p\u003e \u003cp\u003e9.4. Statistics and probabilities 189\u003c\/p\u003e \u003cp\u003e9.5. Compound probabilities 191\u003c\/p\u003e \u003cp\u003e9.6. Graphs, states, transitions 195\u003c\/p\u003e \u003cp\u003e9.7. Markov chains 199\u003c\/p\u003e \u003cp\u003e9.7.1. Definition 199\u003c\/p\u003e \u003cp\u003e9.7.2. Transition matrix 201\u003c\/p\u003e \u003cp\u003e9.7.3. Evolution rules 205\u003c\/p\u003e \u003cp\u003e9.7.4. Ergodicity 206\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 10. Descriptive Statistics 213\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1. Statistical description 213\u003c\/p\u003e \u003cp\u003e10.1.1. A little vocabulary 213\u003c\/p\u003e \u003cp\u003e10.1.2. Tabular presentation and frequency 215\u003c\/p\u003e \u003cp\u003e10.1.3. Two-dimensional series 219\u003c\/p\u003e \u003cp\u003e10.2. Graphical representations 220\u003c\/p\u003e \u003cp\u003e10.2.1. Bar charts 220\u003c\/p\u003e \u003cp\u003e10.2.2. Histograms 222\u003c\/p\u003e \u003cp\u003e10.2.3. Cumulative diagrams 223\u003c\/p\u003e \u003cp\u003e10.2.4. Polar diagrams 226\u003c\/p\u003e \u003cp\u003e10.2.5. Pie charts 227\u003c\/p\u003e \u003cp\u003e10.2.6. Figurative diagrams 227\u003c\/p\u003e \u003cp\u003e10.2.7. Point clouds 228\u003c\/p\u003e \u003cp\u003e10.3. Position parameters 229\u003c\/p\u003e \u003cp\u003e10.3.1. Mode 229\u003c\/p\u003e \u003cp\u003e10.3.2. Median 230\u003c\/p\u003e \u003cp\u003e10.3.3. Averages 235\u003c\/p\u003e \u003cp\u003e10.3.4. Comparison of position parameters 237\u003c\/p\u003e \u003cp\u003e10.4. Dispersion parameters 238\u003c\/p\u003e \u003cp\u003e10.4.1. Range, interquartile range, mean range 238\u003c\/p\u003e \u003cp\u003e10.4.2. Variance and standard deviation 240\u003c\/p\u003e \u003cp\u003e10.4.3. Coefficient of variation and concentration index 242\u003c\/p\u003e \u003cp\u003e10.5. Linear adjustment 243\u003c\/p\u003e \u003cp\u003e10.5.1. Principle of adjustment 243\u003c\/p\u003e \u003cp\u003e10.5.2. Linear adjustment 248\u003c\/p\u003e \u003cp\u003e10.6. Chronological series 254\u003c\/p\u003e \u003cp\u003e10.6.1. Introduction 254\u003c\/p\u003e \u003cp\u003e10.6.2. Study of the general trend 257\u003c\/p\u003e \u003cp\u003e10.6.3. Study of seasonal variations 260\u003c\/p\u003e \u003cp\u003e10.7. Covariance and correlation 265\u003c\/p\u003e \u003cp\u003e10.7.1. Regression lines 265\u003c\/p\u003e \u003cp\u003e10.7.2. Linear correlation 268\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 11. Probability Laws and Simulation 273\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1. Random variables 273\u003c\/p\u003e \u003cp\u003e11.2. Mathematical expectation, variance and standard deviation 283\u003c\/p\u003e \u003cp\u003e11.3. Distribution function 287\u003c\/p\u003e \u003cp\u003e11.4. Usual probability laws 289\u003c\/p\u003e \u003cp\u003e11.4.1. Uniform law 289\u003c\/p\u003e \u003cp\u003e11.4.2. Binomial or Bernoulli's law 290\u003c\/p\u003e \u003cp\u003e11.4.3. Poisson's law 293\u003c\/p\u003e \u003cp\u003e11.4.4. Exponential law 294\u003c\/p\u003e \u003cp\u003e11.4.5. Normal law 298\u003c\/p\u003e \u003cp\u003e11.5. General information on simulation 305\u003c\/p\u003e \u003cp\u003e11.5.1. Weak law of large numbers 305\u003c\/p\u003e \u003cp\u003e11.5.2. Some simulations 308\u003c\/p\u003e \u003cp\u003e11.5.3. Generation of random numbers 313\u003c\/p\u003e \u003cp\u003e11.6. Generating programs 316\u003c\/p\u003e \u003cp\u003e11.6.1. Usual laws 317\u003c\/p\u003e \u003cp\u003e11.6.2. Any probability law 318\u003c\/p\u003e \u003cp\u003e11.7. M\/M\/1 waiting system 320\u003c\/p\u003e \u003cp\u003e11.7.1. Theoretical study 322\u003c\/p\u003e \u003cp\u003e11.7.2. Simulation 326\u003c\/p\u003e \u003cp\u003e11.8. Appendices 333\u003c\/p\u003e \u003cp\u003e11.8.1. Appendix 1: Table for Poisson's law 333\u003c\/p\u003e \u003cp\u003e11.8.2. Appendix 2: Table for normal law 334\u003c\/p\u003e \u003cp\u003e11.8.3. Appendix 3: Buffon's needle 335\u003c\/p\u003e \u003cp\u003e11.8.4. Appendix 4: Results for M\/M\/1 337\u003c\/p\u003e \u003cp\u003eReferences 339\u003c\/p\u003e \u003cp\u003eList of Authors 341\u003c\/p\u003e \u003cp\u003eIndex 343\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Computer science [\u003ca title=\"See our other books on Computer science\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Computer%20science%20%5BUY%5D%22\"\u003eUY\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley-ISTE","offers":[{"title":"Brand New","offer_id":52446824792344,"sku":"9781789451948","price":91.69,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781789451948.jpg?v=1785114846","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/mathematics-for-digital-science-1-fundamentals-hardback-9781789451948","provider":"Freshly Printed Books","version":"1.0","type":"link"}