Math 225 Reflection Groups

The official syllabus in pdf form.

The text Finite Reflection Groups, 2nd Edition, by Grove and Benson will be referred to as GB.

Weekly problem sets will be due in class on Thursday.

Weekly Syllabus and Homework

Updated April 25, 2016.
Week Date Topics Reading Homework
1 Tue 19 Jan Regular polygons and regular polyhedra, i.e., Plantonic solids. GB 2.1, pp. 12-14
Thu 21 Jan Review of linear algebra. Inner products/Euclidean space. Orthogonal transformations in 2 dimensions. Reflections. Rotations. GB 2.2
2 Tue 26 Jan Group theory. Cyclic group. Subgroup. Coset. GB 1.1
Thu 28 Jan Quotient group. Normal subgroup. Lagrange's theorem. Homomorphism. Group action. GD 1.2
3 Tue 02 Feb Orthogonal transformations in 3 dimensions. GB 2.3 Problem Set #1
Thu 04 Feb Orthogonal transformations in 3 dimensions continued. Symmetry groups of regular polyhedra. GB 2.4
4 Tue 09 Feb Finite groups in 3 dimensions. GB 2.5 Problem Set #2
Thu 11 Feb Finite groups in 3 dimensions continued. GB 2.6
5 Tue 16 Feb All reflection groups in 3 dimensions. Crystallographic groups. GB 2.6 Problem Set #3
Thu 18 Feb Symmetric group. Cycle type. Generators.
6 Tue 23 Feb Fundamental regions. Coxeter groups. GB 3, 4.1 Problem Set #4
Thu 25 Feb Root systems. GB 4.1
7 Tue 01 Mar Bases for Coxeter groups. GB 4.1 Problem Set #5
Thu 03 Mar More bases for Coxeter groups. Fundamental regions. GB 4.1-4.2
8 Tue 08 Mar Fundamental regions for Coxeter groups. GB 4.2 Midterm review
Thu 10 Mar Coxeter graphs. GB 5.1
9 Tue 15 Mar Spring Break!
Thu 17 Mar Spring Break!
10 Tue 22 Mar Spring Break!
Thu 24 Mar Spring Break!
11 Tue 29 Mar Sylvester's criterion. Classification of Coxeter graphs. GB 5.2, Article EC Problem Set #6
Thu 31 Mar Midterm!
12 Tue 05 Apr Classification of Coxeter groups. GB 5.1
Thu 07 Apr Crystallographic Coxeter groups. GB 5.2
13 Tue 12 Apr Construction of Coxeter groups. GB 5.3 Problem Set #7
Thu 14 Apr Construction of exceptional Coxeter bases. GB 5.3, 5.4
14 Tue 19 Apr Construction of exceptional Coxeter groups. GB 5.3 Problem Set #8
Thu 21 Apr Construction of exceptional Coxeter groups. GB 5.3
15 Tue 26 Apr Orders of Coxeter groups. GB 5.4 Problem Set #9
Thu 28 Apr Orders of Coxeter groups and applications.
16 Tue 03 May Reading period. Final Exam Problems

Theorems Review
Thu 05 May Reading period.
17 Sun 08 May Final Exam!


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