{"id":928,"date":"2025-08-25T12:11:48","date_gmt":"2025-08-25T09:11:48","guid":{"rendered":"https:\/\/users.utu.fi\/jkari\/?page_id=928"},"modified":"2025-08-25T12:11:48","modified_gmt":"2025-08-25T09:11:48","slug":"tilings2025-syllabus","status":"publish","type":"page","link":"https:\/\/users.utu.fi\/jkari\/tilings2025-syllabus\/","title":{"rendered":"T&amp;P course syllabus"},"content":{"rendered":"<p>&nbsp;<\/p>\n<div align=\"CENTER\">\n<h3>Autumn semester 2025<b><span style=\"color: #ff0000\"><br \/>\nTilings and Patterns<\/span><\/b><\/h3>\n<p>&nbsp;<\/p>\n<p style=\"text-align: left\">The course has two parts:<\/p>\n<ul>\n<li style=\"text-align: left\">Part 1 on Sep 8 &#8211; Oct 16,<\/li>\n<li style=\"text-align: left\">Part 2 on Oct 29 &#8211; Dec 4.<\/li>\n<\/ul>\n<p style=\"text-align: left\">The first part alone forms a 5 ects course, the two parts combined form a 10 ects course.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: left\"><b>Lectures:<\/b><\/p>\n<\/div>\n<ul>\n<li>12:15-14:00 Tuesdays in room M1 (Quantum, 2nd floor)<\/li>\n<li>12:15-14:00 Wednesdays in room M1 (Quantum, 2nd floor)<\/li>\n<li>10:15-12:00 Thursdays in room M1 (Quantum, 2nd floor)<\/li>\n<\/ul>\n<p><b>Homework sessions:<\/b><\/p>\n<ul>\n<li>14:15-16:00 Mondays in room M1 (Quantum, 2nd floor)<\/li>\n<\/ul>\n<p>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.<\/p>\n<p><b>Course Web Page:<\/b> <a href=\"http:\/\/users.utu.fi\/jkari\/tilings2025\">http:\/\/users.utu.fi\/jkari\/tilings2025<\/a><\/p>\n<p><b>Instructor: <\/b>\u00a0<a href=\"http:\/\/users.utu.fi\/jkari\">Jarkko Kari<\/a> &lt;jkari@utu.fi&gt;; office: Quantum 365, 3rd floor<\/p>\n<p><b>Textbook:<\/b><\/p>\n<ul>\n<li>No textbook. Lecture notes are posted on the course web page.<\/li>\n<\/ul>\n<p><b>About homework:<\/b><\/p>\n<ul>\n<li>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\n<ul>\n<li style=\"list-style-type: none\">\n<ul>\n<li>A, if you complete 70%-100%,<\/li>\n<li>B, if you complete 45%-70%,<\/li>\n<li>C, if you complete 25%-45%<\/li>\n<\/ul>\n<p>of the given problems.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><b>Grading the 5 ects course:<\/b><\/p>\n<ul>\n<li>An exam at the end of the first teaching period (week of Oct 20-24, date TBD)<\/li>\n<li>The 3 hour exam consists of 4 problems, each of which has a maximum score of 4 points.<\/li>\n<li>The homework activity (demo class A, B or C) and the score of the exam determine the final grade according to the following table:<\/li>\n<\/ul>\n<table class=\"MsoNormalTable\" style=\"border-collapse: collapse;border: none\" border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr style=\"height: 8.5pt\">\n<td style=\"width: 66.5pt;border: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" rowspan=\"2\" valign=\"bottom\" width=\"89\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">Final Grade<\/span><\/p>\n<\/td>\n<td style=\"width: 139.25pt;border: solid windowtext 1.0pt;border-left: none;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" colspan=\"3\" valign=\"top\" width=\"186\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">Demo class<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 8.5pt\">\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">A<\/span><\/p>\n<\/td>\n<td style=\"width: 46.45pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">B<\/span><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">C<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 8.5pt\">\n<td style=\"width: 66.5pt;border: solid windowtext 1.0pt;border-top: none;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"89\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><b><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">1<\/span><\/b><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">6-7<\/span><\/p>\n<\/td>\n<td style=\"width: 46.45pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">7<\/span><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">7-8<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 8.5pt\">\n<td style=\"width: 66.5pt;border: solid windowtext 1.0pt;border-top: none;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"89\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><b><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">2<\/span><\/b><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">8-9<\/span><\/p>\n<\/td>\n<td style=\"width: 46.45pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">8-10<\/span><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">9-10<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 8.5pt\">\n<td style=\"width: 66.5pt;border: solid windowtext 1.0pt;border-top: none;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"89\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><b><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">3<\/span><\/b><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">10-11<\/span><\/p>\n<\/td>\n<td style=\"width: 46.45pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">11<\/span><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">11-12<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 8.5pt\">\n<td style=\"width: 66.5pt;border: solid windowtext 1.0pt;border-top: none;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"89\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><b><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">4<\/span><\/b><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">12-13<\/span><\/p>\n<\/td>\n<td style=\"width: 46.45pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">12-14<\/span><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">13-14<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 8.5pt\">\n<td style=\"width: 66.5pt;border: solid windowtext 1.0pt;border-top: none;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"89\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><b><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">5<\/span><\/b><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">14-16<\/span><\/p>\n<\/td>\n<td style=\"width: 46.45pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">15-16<\/span><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">15-16<\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><b>Grading the 10 ects course:<\/b><\/p>\n<p><b>Midterms<\/b><\/p>\n<ul>\n<li>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.<\/li>\n<li>Not mandatory on the 10 ects course. The class requirements can also be satisfied by taking a single final exam after Part 2.<\/li>\n<li>Both midterms (3 hours) consist of 4 problems, each of which has maximum score of 4 point.<\/li>\n<li>A minimum of 5 points is required in both midterms.<\/li>\n<li>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:<\/li>\n<\/ul>\n<table class=\"MsoNormalTable\" style=\"border-collapse: collapse;border: none\" border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr style=\"height: 8.5pt\">\n<td style=\"width: 66.5pt;border: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" rowspan=\"2\" valign=\"bottom\" width=\"89\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">Final Grade<\/span><\/p>\n<\/td>\n<td style=\"width: 139.25pt;border: solid windowtext 1.0pt;border-left: none;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" colspan=\"3\" valign=\"top\" width=\"186\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">Demo class<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 8.5pt\">\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">A<\/span><\/p>\n<\/td>\n<td style=\"width: 46.45pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">B<\/span><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">C<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 8.5pt\">\n<td style=\"width: 66.5pt;border: solid windowtext 1.0pt;border-top: none;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"89\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><b><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">1<\/span><\/b><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">13-14<\/span><\/p>\n<\/td>\n<td style=\"width: 46.45pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">14-15<\/span><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">15-16<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 8.5pt\">\n<td style=\"width: 66.5pt;border: solid windowtext 1.0pt;border-top: none;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"89\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><b><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">2<\/span><\/b><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">15-18<\/span><\/p>\n<\/td>\n<td style=\"width: 46.45pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">16-19<\/span><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">17-20<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 8.5pt\">\n<td style=\"width: 66.5pt;border: solid windowtext 1.0pt;border-top: none;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"89\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><b><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">3<\/span><\/b><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">19-22<\/span><\/p>\n<\/td>\n<td style=\"width: 46.45pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">20-23<\/span><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">21-24<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 8.5pt\">\n<td style=\"width: 66.5pt;border: solid windowtext 1.0pt;border-top: none;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"89\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><b><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">4<\/span><\/b><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">23-27<\/span><\/p>\n<\/td>\n<td style=\"width: 46.45pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">24-28<\/span><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">25-28<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 8.5pt\">\n<td style=\"width: 66.5pt;border: solid windowtext 1.0pt;border-top: none;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"89\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><b><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">5<\/span><\/b><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">28-32<\/span><\/p>\n<\/td>\n<td style=\"width: 46.45pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">29-32<\/span><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">29-32<\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><b>Final exam:<\/b><\/p>\n<ul>\n<li>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.<\/li>\n<li>Date TBD<\/li>\n<li>Anyone with demo class at least C has qualified to take the exam.<\/li>\n<li>Exam (4 hours) consists of 5 problems, each of which has maximum score of 8 points.<\/li>\n<li>Homework activity (demo class A, B or C) and the score of the final exam determine the final grade according to the following table:<\/li>\n<\/ul>\n<table class=\"MsoNormalTable\" style=\"border-collapse: collapse;border: none\" border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr style=\"height: 8.5pt\">\n<td style=\"width: 66.5pt;border: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" rowspan=\"2\" valign=\"bottom\" width=\"89\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">Final Grade <\/span><\/p>\n<\/td>\n<td style=\"width: 139.25pt;border: solid windowtext 1.0pt;border-left: none;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" colspan=\"3\" valign=\"top\" width=\"186\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">Demo class<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 8.5pt\">\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">A<\/span><\/p>\n<\/td>\n<td style=\"width: 46.45pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">B<\/span><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">C<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 8.5pt\">\n<td style=\"width: 66.5pt;border: solid windowtext 1.0pt;border-top: none;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"89\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><b><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">1<\/span><\/b><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">17-18<\/span><\/p>\n<\/td>\n<td style=\"width: 46.45pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">18-19<\/span><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">19-21<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 8.5pt\">\n<td style=\"width: 66.5pt;border: solid windowtext 1.0pt;border-top: none;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"89\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><b><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">2<\/span><\/b><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">19-23<\/span><\/p>\n<\/td>\n<td style=\"width: 46.45pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">20-24<\/span><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">22-26<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 8.5pt\">\n<td style=\"width: 66.5pt;border: solid windowtext 1.0pt;border-top: none;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"89\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><b><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">3<\/span><\/b><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">24-29<\/span><\/p>\n<\/td>\n<td style=\"width: 46.45pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">25-30<\/span><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">27-31<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 8.5pt\">\n<td style=\"width: 66.5pt;border: solid windowtext 1.0pt;border-top: none;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"89\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><b><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">4<\/span><\/b><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">30-34<\/span><\/p>\n<\/td>\n<td style=\"width: 46.45pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">31-35<\/span><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">32-36<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 8.5pt\">\n<td style=\"width: 66.5pt;border: solid windowtext 1.0pt;border-top: none;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"89\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><b><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">5<\/span><\/b><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">35-40<\/span><\/p>\n<\/td>\n<td style=\"width: 46.45pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">36-40<\/span><\/p>\n<\/td>\n<td style=\"width: 46.4pt;border-top: none;border-left: none;border-bottom: solid windowtext 1.0pt;border-right: solid windowtext 1.0pt;padding: 0cm 1.5pt 0cm 1.5pt;height: 8.5pt\" valign=\"top\" width=\"62\">\n<p class=\"MsoNormal\" style=\"text-align: center\" align=\"center\"><span lang=\"EN-AU\" style=\"font-size: 9.0pt;font-family: Arial;color: black\">37-40<\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p><big><b>Course outline<\/b><\/big><\/p>\n<ul>\n<li>Symmetries in the plane<\/li>\n<li>Frieze groups and wallpaper groups<\/li>\n<li>Tilings by regular polygons, archimedean tilings<\/li>\n<li>Wang tiles<\/li>\n<li>Aperiodicity<\/li>\n<\/ul>\n<p>1st midterm \/ Final exam of the 5 ects course<!--(Oct 19 at 9:00am, room IX or X)--><\/p>\n<ul>\n<li>Turing machines, computational problems concerning tilings<\/li>\n<li>Domino problem<\/li>\n<li>Interesting examples: Amman&#8217;s tiles, Penrose kites and darts, the Hat tile.<\/li>\n<\/ul>\n<p>2nd midterm<\/p>\n","protected":false},"excerpt":{"rendered":"<p>&nbsp; Autumn semester 2025 Tilings and Patterns &nbsp; The course has two parts: Part 1 on Sep 8 &#8211; Oct 16, Part 2 on Oct 29 &#8211; Dec 4. The first part alone forms a 5 ects course, the two parts combined form a 10 ects course. &nbsp; Lectures: 12:15-14:00 Tuesdays in room M1 (Quantum,&hellip; <a class=\"more-link\" href=\"https:\/\/users.utu.fi\/jkari\/tilings2025-syllabus\/\">Continue reading <span class=\"screen-reader-text\">T&amp;P course syllabus<\/span><\/a><\/p>\n","protected":false},"author":6330,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-928","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/users.utu.fi\/jkari\/wp-json\/wp\/v2\/pages\/928","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/users.utu.fi\/jkari\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/users.utu.fi\/jkari\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/users.utu.fi\/jkari\/wp-json\/wp\/v2\/users\/6330"}],"replies":[{"embeddable":true,"href":"https:\/\/users.utu.fi\/jkari\/wp-json\/wp\/v2\/comments?post=928"}],"version-history":[{"count":7,"href":"https:\/\/users.utu.fi\/jkari\/wp-json\/wp\/v2\/pages\/928\/revisions"}],"predecessor-version":[{"id":937,"href":"https:\/\/users.utu.fi\/jkari\/wp-json\/wp\/v2\/pages\/928\/revisions\/937"}],"wp:attachment":[{"href":"https:\/\/users.utu.fi\/jkari\/wp-json\/wp\/v2\/media?parent=928"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}