Mathematics

General objectives: to acquire the basic knowledge and techniques of the combinatorics of permutations, enumerative combinatorics, combinatorics of integer partitions, generating functions and understand its main applications. Specific objectives: Knowledge and understanding: at the end of the course the student will have acquired the basic notions and results related to Combinatorics of permutations (with particular regard to enumerations, representation with trees, cycles, linear orderings, random generation) and enumerative combinatorics (especially concerning its algebraic aspects, via generating functions). She will also know at least the set of the most significant problems in which these theories find applications. Apply knowledge and understanding: the student will be able to solve algebraic-combinatorial problems requiring the use of techniques related to the theories of combinatorics of permutations, enumerative combinatorics, of posets and integer partitions, and to discuss how problems (in non-purely mathematical environments) can be modeled by means of the acquired tools. Critical and judgmental skills: the student will have the basis to analyze how the topics of combinatorics and Algebra and Linear Algebra treated in basic courses can find applications in different fields and be an essential tool in solving concrete problems. Communication skills: The learner will have the ability to communicate rigorously the ideas and contents shown in the course. Learning skills: the acquired knowledge will allow the student to carry on an autonomous study in a possible interdisciplinary context (for those who have knowledge and interests in Applied Mathematics, Genetics, Computer Science, Data Science).