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 $S_n$.

Groups Lecture 15

in which we use actions to find sizes of groups, subgroups and stabilisers, and prove Cauchy’s Theorem.

Groups Lecture 14

in which we meet several standard actions and prove Cayley’s Theorem.

Groups Lecture 13

in which we meet orbits and stabilisers and prove the Orbit-Stabiliser Theorem.