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Kies de Nederlandse taal
Course module: UCSCIMATL3
UCSCIMATL3
Group Theory
Course info
Course codeUCSCIMATL3
EC2.5
Course goals
 
Content
Content
How many wallpaper patterns are there? The answer is of course infinitely many. But what happens if you restrict yourself to the possible symmetries such a pattern has. Stated otherwise, if you only study the transformations that map such a pattern into itself, are there still infinitely many? No, there are only 17 of such patterns. The set of such transformations, like rotations, reflections and translations, form what mathematicians call a group. One can show that there are only 17 of such wallpaper groups.
This lab course is an introduction into group theory. We will study groups, mainly consisting of transformations that map an object into itself. What are the possible transformations that map a cube into itself? What are the possibilities for a regular tetrahedron, an octahedron or other regular polytopes? Not only will we study these examples of particular groups, but we will also approach this in a more abstract way. When are two groups the same? Can one group be seen as a subset of a larger one? This course will give an answer to some of these questions.
Format
You will start by following a number of lectures on this subject, do exercises and thus learn more about this particular topic. At the end you will write in small groups a paper on a certain group theoretical problem and give a small presentation on this topic.
 Attendance
Due to the short duration and intensive nature of the lab course, 100% attendance is required.
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Kies de Nederlandse taal