Fall semester 2021
Tilings and Patterns
Lectures (28 times 2 hours) Aug 30 – Oct 15 and Oct 25 – Dec 10:
 12:1514:00 Tuesdays in room M1 (Quantum, 2nd floor)
 12:1514:00 Thursdays in room M1 (Quantum, 2nd floor)
The lectures are also streamed via zoom. The link has been emailed to registered students.
Homework sessions (13 times 2 hours) Sep 6 – Oct 15 and Oct 25 – Dec 10:
 14:1516:00 Mondays in room M3 (Quantum, 3rd floor)
The homework sessions are not streamed. Students who do not want to come to the homework session may alternatively email their solutions to the instructor before the beginning of the session. All students will get the model solutions sometime after the session.
Course Web Page: http://users.utu.fi/jkari/tilings2021
Instructor: Jarkko Kari
 Office: Quantum 365, 3rd floor
 email: jkari@utu.fi
Prerequisites:
 No formal prerequisites. Basic group theory, elementary geometry and automata theory are recommended.
Textbook:
 No texbook. Lecture notes will be posted on the course web page.
About homework:
 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%
of the given homeworks.

Midterms
 Two midterm exams: Dates TBA. (On the weeks Oct 1822 and December 1317).
 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 
1314 
1415 
1516 
2 
1518 
1619 
1720 
3 
1922 
2023 
2124 
4 
2327 
2428 
2528 
5 
2832 
2932 
2932 
Final exam:
 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.
 Dates TBA
 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 
1718 
1819 
1921 
2 
1923 
2024 
2226 
3 
2429 
2530 
2731 
4 
3034 
3135 
3236 
5 
3540 
3640 
3740 
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