Length of all activities: 6 weeks (May 9th -June 17th).

**Phase 1**, teaching sessions: Lectures on Linear Algebra, Algebras (an Algebraic Structures topic), Graph Theory, basic Differential Geometry (10:00 – 12:00 and 2:00 – 4:00) for 3 weeks, ending with a overview on basics of Category Theory; discussion/exercises 4:30 – 6:00.

**Phase 2**, research: the last 3 weeks: 10:00 – 11:00 discussion on research; for this phase the students will be divided in two groups each of which will be studying one of the Questions formulated in the project description; research time: 11:00 – 5:00; discussion: 5:15 – 6:00. Library and Internet resources and use of them: a couple of sessions with a representative of the University library (for 50 min in Phase 1, in the interval 4:30 p.m. - 6:00 p.m.); End of 4th week – reports on results; End of 6th week: presentations of the students.

The course comprises the teaching part, the first three weeks, of the Summer Research Program with the same title. It will give the background from several disciplines in Math needed for successful research activities during the last three weeks of the Program.

**Morning Session**:

- 9:30-11:00a: lecture
- 11:00-11:30a: coffee break
- 11:30a-1:00p: lecture

- 2:30-3:15p: problem solving
- 3:15–3:30p: coffee break
- 3:30–4:15p: problem solving session
- 4:15–4:30p: coffee break
- 4:30–5:00p: concluding discussion

10:00a–1:00p: discussion on the material taught during the week.