But du cours
Provide engineering students with the essential foundations of discrete mathematics required to solve common problems across all fields of computer science.
Acquis d'apprentissage visés
- Select cryptographic tools suited to the requirements of a specification document
- Implement, from design to production deployment, a company’s IT network while integrating QoS and security considerations
- Conduct exploratory data analysis
Prérequis
Discrete Mathematics learned in high school then in CPGE/L1-L3/IUT/BTS
Programme
- Reminders: fundamentals of set theory, propositional logic, proofs
- Equivalence relations and order relations, quotient set
- Algebraic structures: groups, rings, fields
- Basic arithmetic: Euclidean division, GCD, prime numbers, Bézout's theorem, Euler's totient function
- Structure of the set Z/nZ and operations in this set
- Arithmetic theorems: Fermat-Euler, Chinese remainder theorem
- The ring K[X] of polynomials, arithmetic in K[X]
Modalités d'évaluation
Continuous assessment: two written evaluations
Bibliographie
- Richard Hammack - Book of Proofs - Available for download: http://www.people.vcu.edu/~rhamack/BookOfProof/ (Creative Commons license)
- Jacques Vélu - Mathematical Methods for Computer Science - Dunod Éditions, Sciences Sup collection
- J.P. Ramis and A. Warusfel (edited by) - Mathematics: All-in-One for the Bachelor’s Degree, Level L1 - Dunod Éditions
Supports
Slides and guided-work worksheets.