T&P course syllabus

 

• 12:15-14:00 Tuesdays in room M1 (Quantum, 2nd floor)
• 12:15-14:00 Wednesdays in room M1 (Quantum, 2nd floor)
• 10:15-12:00 Thursdays in room M1 (Quantum, 2nd floor)

Homework sessions:

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

Some weeks are without some of the classes listed above. Also, sometimes the lecture and homework session times are exchanged. See the Peppi-system for a detailed list of lectures.

Course Web Page: http://users.utu.fi/jkari/tilings2025

Instructor:  Jarkko Kari <jkari@utu.fi>; office: Quantum 365, 3rd floor

Textbook:

• No textbook. Lecture notes are 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 problems.

Grading the 5 ects course:

• An exam at the end of the first teaching period (week of Oct 20-24, date TBD)
• The 3 hour exam consists of 4 problems, each of which has a maximum score of 4 points.
• The homework activity (demo class A, B or C) and the score of the exam determine the final grade according to the following table:

Final Grade	Demo class
	A	B	C
1	6-7	7	7-8
2	8-9	8-10	9-10
3	10-11	11	11-12
4	12-13	12-14	13-14
5	14-16	15-16	15-16

Grading the 10 ects course:

Midterms

• The 10 ects course has two midterm exams, at the ends of both parts. Dates TBD. The first midterm exam is the same as the final exam of the 5 ects course.
• Not mandatory on the 10 ects course. The class requirements can also be satisfied by taking a single final exam after Part 2.
• 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 10 ects course. One can take the exam more than once (even if one has passed the course) to improve the final grade.
• Date TBD
• Anyone with demo class at least C has qualified to take the exam.
• Exam (4 hours) consists 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

 

Course outline

• Symmetries in the plane
• Frieze groups and wallpaper groups
• Tilings by regular polygons, archimedean tilings
• Wang tiles
• Aperiodicity

1st midterm / Final exam of the 5 ects course

• Turing machines, computational problems concerning tilings
• Domino problem
• Interesting examples: Amman’s tiles, Penrose kites and darts, the Hat tile.

2nd midterm