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 2021
Offered
2022/23
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 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.
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