Study-unit COMBINATORICS
| Course name | Mathematics |
|---|---|
| Study-unit Code | 55A00090 |
| Curriculum | Didattico-generale |
| Lecturer | Marco Buratti |
| Lecturers |
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| Hours |
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| CFU | 6 |
| Course Regulation | Coorte 2022 |
| Supplied | 2022/23 |
| Supplied other course regulation | |
| Learning activities | Affine/integrativa |
| Area | Attività formative affini o integrative |
| Sector | MAT/03 |
| Type of study-unit | Opzionale (Optional) |
| Type of learning activities | Attività formativa monodisciplinare |
| Language of instruction | Italian and also English if necessary. |
| Contents | Graphs. Combinatorial Designs. Affine and projective geometries. |
| Reference texts | A very good book where to study some of the main topics is the following. J.H. Van Lint & R.M. Wilson, A course in Combinatorics, Cambridge University Press, 1992. |
| Educational objectives | Acquisition of the combinatorial thought through the algebraic and geometrical tools studied during the first three years. Direct the students to develop research in the area of combinatorial designs. |
| Prerequisites | Algebra and Geometry for the first two years of the bachelor. |
| Teaching methods | The lectures will be accompanied by exercises, examples and open research problems. Some results will be rigorously proven. Other results will be only stated looking only at their more relevant applications. |
| Other information | In office hours and by arrangement, students will be followed in a personalized way. Attendance of the lectures is strongly suggested. |
| Learning verification modality | The exam consists of an oral discussion - whose average duration may vary from 20 minutes to half an hour - on a topic of the program chosen by the student. During the discussion it might be required to illustrate some links with other topics of the program. The discussion is finalized to verify the students' capacity for synthesis and their grasp of the whole subject. Info about how to support students with disabilities and/or DSA can be found at http://www.unipg.it/disabilita-e-dsa |
| Extended program | Graphs: Hamiltonian and Eulerian circuits; trees; Cayley graphs; colorings; graph decompositions. Combinatorial Designs: Latin squares; t-designs; Steiner designs; Fisher's theorem; resolvable designs; symmetric designs; projective planes; the theorem of Bruck-Ryser Chowla; difference sets; difference families; explicit constructions of some classes of combinatorial designs. Affine and projective geometries: Pasch's axiom; Desargues' theorem; arcs of a projective plane. |