Unit COMBINATORICS
- Course
- Mathematics
- Study-unit Code
- 55A00045
- Curriculum
- Matematica per la crittografia
- Teacher
- Marco Buratti
- Teachers
-
- Marco Buratti
- Hours
- 42 ore - Marco Buratti
- CFU
- 6
- Course Regulation
- Coorte 2020
- Offered
- 2021/22
- Learning activities
- Affine/integrativa
- Area
- Attività formative affini o integrative
- Academic discipline
- MAT/03
- Type of study-unit
- Obbligatorio (Required)
- 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 algebraic/geometrical tools and to direct the students to develop research in this area.
- 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.
Le lezioni sono accompagnate da appunti, esercizi, esempi e problemi aperti nella ricerca.
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 proof on the whole programm.
- 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.