This course explores group theory at the university level, but is uniquely motivated through symmetries, applications, and challenging problems. For example, before diving into the technical axioms, we'll explore their motivation through geometric symmetries.
You'll be left with a deep understanding of how group theory works and why it matters.
An introduction to Group Theory through the beauty of symmetry.
Come to know mathematical groups through symmetry.
Gain a visual understanding of how groups work.
What makes a set into a group?
Explore group axioms with cube symmetries.
The axioms, subgroups, abelian groups, homomorphisms, and quotient groups.
Dive deeper into groups by exploring some real-world applications.
See how groups tie into geometry and music.
Learn about the structure of groups within a group.
For these groups, composition order doesn't matter.
Number theory, the 15-puzzle, peg solitaire, the Rubik's cube, and more!
Use groups to unlock the secrets of integers.
Formulate winning game strategies with groups!
Apply groups to understand this perplexing toy.
From the isomorphism theorems to conjugacy classes and symmetric groups.
Explore normality, a critical ingredient in making quotient groups.
When are two groups different versions of the same thing?
Learn a wealth of information about a group by separating its elements by class.
Master the fundamentals of permutations.
Burnside's Lemma, semidirect products, and Sylow's Theorems.
Explore the interplay between a group and the set it acts upon.
Solve challenging counting and combinatorial problems with group theory.
Learn a useful technique for building larger groups from smaller ones.
Explore the structure of finite groups and uncover fascinating new relations.