# Groups Lecture 22

in which we find out about permutation properties of Möbius maps and start looking at cross-ratios.

# Groups Lecture 21

in which we view Möbius maps via matrices, and compose geometrically meaningful maps.

# Groups Lecture 20

in which we meet the unitary group and start exploring Möbius maps as transformations of the Riemann sphere.

# Groups Lecture 19

in which meet the orthogonal group and we rotate and reflect in two and three dimensions.

# Groups Lecture 18

in which we meet the quaternions, start exploring matrix groups and act with matrices on vectors and on matrices.

# Groups Lecture 17

in which we explore conjugacy classes in $S_n$ and $A_n$, and prove that $A_5$ is simple.

# Groups Lecture 16

in which we learn about the symmetry groups of polyhedra, and start exploring conjugacy classes in the symmetric groups $S_n$.