**Lectures** (28 times 2 hours)
Sep 5 - Dec 14:

- 10:15-12:00 Tuesdays in room M1 (Quantum, 2nd floor)

- 12:15-14:00 Thursdays in room M1 (Quantum, 2nd floor)

- (Exceptions: no classes on the weeks Sep 18-22 and Oct 23-27. Two lectures will be scheduled later.)

- 14:15-16:00 Mondays in room M1 (Quantum, 2nd floor)

- (Exceptions: no homeworks on Sep 18 and Oct 23. One homework will be scheduled later.)

**Course Web Page:**

**Instructor:**

- Jarkko Kari
- Office: Quantum 365, 3rd floor

- email: jkari@utu.fi,

- tel: (02) 333 5616.

- Office hours: Wednesday 10:15-11:00am

- No formal prerequisites. Basic group theory, elementary geometry and automata theory are recommended.

- No texbook. Lecture notes will be posted on the course web page.

- Presence is mandatory. Absence is permitted only if agreed with the lecturer (ask beforehand if possible).
- To pass the course, at least 25% of the homework problems must be completed. The more problems you solve, the more credit towards the final grade you get: You get demo class
- A, if you complete 70%-100%,
- B, if you complete 45%-70%,
- C, if you complete 25%-45%

- Two midterms:
- Oct 25 (room IX or X, luonnontieteidentalo I) at 9:00-12:00
- Dec 18 (room IX or X, luonnontieteidentalo I) at 9:00-12:00

- Not mandatory. The class requirements can also be satisfied by taking a single final exam.
**Registration though internet (NettiOpsu) is required at least one week before the exam.**- Both midterms (3 hours) consist of 4 problems, each of which has maximum score of 4 point.
- A minimum of 5 points is required in both midterms.
- Homework activity (demo class A, B or C) and the combined score of the two midterms determine the final grade according to the following table:

Final Grade

Demo class

A

B

C

**1**13-14

14-15

15-16

**2**15-18

16-19

17-20

**3**19-22

20-23

21-24

**4**23-27

24-28

25-28

**5**28-32

29-32

29-32

- An alternative way to pass the class. One can take the exam more than once (even if one has passed the course) to improve the final grade.
- Available exam dates in the Spring term: Monday January 8, Monday February 5, Monday March 12.
- Registration though internet (NettiOpsu) is required at least one week before the exam.
- Anyone with democlass at least C has qualified to take the exam within one year.
- Exams (4 hours) consist of 5 problems, each of which has maximum score of 8 points.
- Homework activity (demo class A, B or C) and the score of the final exam determine the final grade according to the following table:

Final Grade

Demo class

A

B

C

**1**17-18

18-19

19-21

**2**19-23

20-24

22-26

**3**24-29

25-30

27-31

**4**30-34

31-35

32-36

**5**35-40

36-40

37-40

**Tentative course outline**

- Symmetries in the plane
- Frieze groups and wallpaper groups
- Tilings by regular polygons, archimedean tilings
- Wang tiles
- 1st midterm

- Aperiodicity, quasiperiodicity
- Turing machines, computational problems concerning tilings
- Domino problem
- Penrose kites and darts, and other interesting examples

- 2nd midterm