rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Mathematics for digital science
    part number: Volume 1
    part name: Fundamentals
  title info:
    title: Fundamentals
  name:
    name part: Cochard, Gerard-Michel
    role:
      role term: creator
    role:
      role term: author
  name:
    name part: Hifi, Mhand
    role:
      role term: author
  type of resource: text
  origin info:
    place:
      place term: enk
    date issued: 2025
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (368 pages)
  abstract: 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.
  table of contents: 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 th…
  note: Gerard-Michel Cochard, Mhand Hifi.
  subject:
    topic: Computer science
    topic: Mathematics
  classification: QA76.9.M35 C63 2025
  classification: 004.01/51
  related item:
    title info:
      title: Sciences. Computer science; Operational research and decision
  identifier: 9781394352050
  identifier: 1394352050
  identifier: 9781789451948
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: NhCcYBP
    record creation date: 250218
    record change date: 20260214202600.4
    record identifier: in00005618720
    language of cataloging:
      language term: eng