Groups and Geometry
Math 466 - Fall 2019
Announcements
The solution of the Final Exam is now available.
You can see your final exam grade from odtuclass. Please stop by my office or fix an appointment by email to see your final exam paper.
Available File: Wallpaper Types.
Suggested Problems
I will assign exercise questions on a regular basis. I strongly suggest that you shall work on these questions.
A1: 1, 2, 6, 7. A2: 3, 5, 6, 7, 8. A3: 3, 6, 7, 9, 10. A4: 5, 6, 7, 8, 9. A5: 2, 4, 6, 9.A6: 2, 3, 4, 9. A7: 2, 5, 9, 12.A8: 1, 2, 3, 4. A9: 1, 2, 3, 5. A10: 1, 2, 7, 11. A11: 8, 9, 10. A12: 1, 3. A13: 2, 4. A14: 4, 5, 6. A15: 1, 2, 4, 5, 12, 14. A16: 1, 2, 8. A17: 1, 3, 4, 10, 11, 14. A18: 1, 2, 3, 4, 5, 6, 7. A19: 2, 3, 5, 6, 7, 8. A23: 8, 9, 10. A24: 1, 2, 3, 4, 8, 10. J2: 1, 3, 10, 11, 15. A25: 1, 2, 3, 4, 5, 6, 7, 8, 9. A26: 2, 4, 6, 7, 8, 9, 10.
Exams and Grading
Your final letter grade will be determined by the following items.
Midterm 1 (%30) - October 23.
Midterm 2 (%30) - November 20.
Final (%30) - January 2.
Quizes (%10): Quiz 1, Quiz 2, Quiz 3, Quiz 4, Quiz 5, Quiz 6, Quiz 7, Quiz 8, Quiz 9, Quiz 10.
Textbooks
A) Armstrong - Groups and Symmetry. Reserve, QA171.A76.
J) Johnson - Symmetries. Reserve, QA174.2.J64.
H) Humphreys - Reflection Groups and Coxeter Groups. Reserve, QA171.H833.
About the course
The aim of this course is to introduce students to the basic principles of geometric symmetries. We will study certain finitely generated groups by exploring the geometric properties of spaces on which these groups act.
Course Outline
You can find the course outline below. For each week, we will attempt to cover the indicated sections of our textbooks.
(Sep 24, Sep 26) Symmetries of Tetrahedron and Dihedral Groups (A1, A4)
(Sep 01, Oct 03) Plato's Solids and Cayley's Theorem (A8)
(Oct 08, Oct 10) Actions, Orbits, and Stabilizers (A17)
(Oct 15, Oct 17) Counting Orbits (A18)
(Oct 22, Oct 24) Exam Review and Matrix Groups (A9)
(Oct 29, Oct 31) Finite Rotation Groups (A19)
(Nov 05, Nov 07) The Euclidean Group (A24, J2)
(Nov 12, Nov 14) Lattices and Point Groups (A25)
(Nov 19, Nov 21) Exam Review and Frieze Groups (J6)
(Nov 26, Nov 28) Wallpaper Patterns (A26, J7, J8)
(Dec 03, Dec 05) Wallpaper Patterns (A26, J7, J8)
(Dec 10, Dec 12) Tessellations of the Plane (J9)
(Dec 17, Dec 19) Root Systems (H1)
(Dec 24, Dec 26) Coxeter Diagrams and Finite Reflection Groups (H2).
Make-up and NA policy:
Only one make-up examination will be offered. The excuse for not attending an examination must be proved with documents. The make-up examination will take place shortly after the final exam. If you have missed both midterms, your letter grade would be NA. If you receive NA, then you can not take the final exam and the makeup.
Attendance will be taken during the lectures. You will receive the NA grade if your attendance is less than %70.
Schedule of Lectures and Office Hours
The lectures will take place in M105 during tuesdays 10:40-12:30 and in M106 M08 during thursdays 8:40-9:30. My fixed office hours are on thursdays between 13:40-15:30 in my office, M141. If these office hours are not suitable for you, then you shall either stop by my office or send me an email in advance to fix an appointment.