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This is the Lecture 2.6 of the REU Apprentice program 2021 at the University of Chicago. We discuss affine transformations.

This is the Lecture 2.5 of the REU Apprentice program 2021 at the University of Chicago. We discuss cyclic groups.

This is the Lecture 2.4 of the REU Apprentice program 2021 at the University of Chicago. We discuss symmetries of regular polygons.

This is the Lecture 2.3 of the REU Apprentice program 2021 at the University of Chicago. We discuss Chasles' Theorem.

This is the Lecture 2.2 of the REU Apprentice program 2021 at the University of Chicago. We discuss rotations.

This is the Lecture 2.1 of the REU Apprentice program 2021 at the University of Chicago. We discuss isometries of the plane..

This is the seventh lecture of the REU Apprentice program 2021 at the University of Chicago. We discuss generating functions.

This is the sixth lecture of the REU Apprentice program 2021 at the University of Chicago. We discuss an explicit formula for Catalan numbers.

This is the fifth lecture of the REU Apprentice program 2021 at the University of Chicago. We begin to discuss Catalan numbers.

This is the fourth lecture of the REU Apprentice program 2021 at the University of Chicago. We discuss the cyclic structure of a permutation.

This is the third lecture of the REU Apprentice program 2021 at the University of Chicago. We discuss the cyclic structure of a permutation.

This is the second lecture of the REU Apprentice program 2021 at the University of Chicago. We discuss the group of permutations.

This is the first lecture of the REU Apprentice program 2021 at the University of Chicago

Group Theory, lecture 6.2: Second Sylow Theorem

Group Theory, lecture 6.1: First Sylow Theorem

Group Theory, lecture 5.4: Projective Geometry (II)

Group Theory, lecture 5.3: Projective Space (I)

Group Theory, lecture 5.2: Orbits and Stabilizers

Group Theory, lecture 5.1: Group actions

Group Theory, lecture 4.5: Quadratic residues

Group Theory, lecture 4.4: Abelian groups

Group Theory, lecture 4.3: Properties of Euler function

Group Theory, lecture 4.2: Euler function

Group Theory, lecture 4.1: Cyclic groups

Group Theory, lecture 3.7: Lattice of subgroups

Group Theory, lecture 3.8: Correspondence Theorem

Group Theory, lecture 3.6: First Homomorphism Theorem

Group Theory, Lecture 3.5: Quotient group

Group Theory, lecture 3.4: Normal subgroups of S4