T&P course syllabus 2021

 

Fall semester 2021
Tilings and Patterns

 

Lectures (28 times 2 hours)  Aug 30 – Oct 15 and Oct 25 – Dec 10:

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

  • 14:15-16:00 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 18-22 and December 13-17).
  • 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

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

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