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Semester (Sem)
1First Semester
2Second Semester
AAnnual course
Educational activities
BIdentifying activities
Course completely offered in italian
Course completely offered in english
--Not available
Innovative teaching
The credits shown next to this symbol indicate the part of the course CFUs provided with Innovative teaching.
These CFUs include:
  • Subject taught jointly with companies or organizations
  • Blended Learning & Flipped Classroom
  • Massive Open Online Courses (MOOC)
  • Soft Skills
Course Details
Academic Year 2020/2021
School School of Industrial and Information Engineering
Name (Master of Science degree)(ord. 270) - MI (487) Mathematical Engineering
Track MCS - Computational Science and Computational Learning
Programme Year 2

Course Details
ID Code 093269
Course Type Mono-Disciplinary Course
Credits (CFU / ECTS) 5.0
Semester First Semester
Course Description ELEMENTARY NUMBER THEORY AND MODULAR ARITHMETIC: Basic notions of set theory. Natural numbers and the induction principle. Integers. Divisibility and prime numbers. Euler's function. Congruences. Integers modulo m. Euler's theorem. Fermat's little theorem. Elements of group, rings and fields. Finite fields. Chinese remainder theorem. Primality test: Wilson's theorem and its converse. ENUMERATIVE COMBINATORICS: Cardinality of a set. Basic counting principles. Binomial numbers, Stiefel's formula and other identities on binomial numbers. Permutations and selections from a set. Binomial theorem. Formal power series. Partial fractions. Generating functions. Linear homogeneous recursions. Fibonacci and Lucas numbers. Closed form of the Fibonacci numbers. Stirling numbers of the second kind. Partitions of a natural number. Ferrer's diagrams. The Tower of Hanoi problem. Principle of inclusion and exclusion. Formulas of Sylvester and Da Silva. Derangements. GRAPHS: Basic definitions. Planarity of graphs. Euler's formula. Bipartite graphs. Eulerian graphs. Hamiltonian graphs. Trees. Binary trees. Spanning trees. Vertex colorings. Chromatic number. Edge colorings. Chromatic index. K"{o}nig's theorem. Matchings in bipartite graphs. Hall's theorem. Adjacency matrix, incidence matrix with respect to an orientation, Laplacian matrix. Theorem of Poincaré. Spectrum of a graph.
Scientific-Disciplinary Sector (SSD)
Educational activities SSD Code SSD Description CFU

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Area Servizi ICT