Please see below for lecture summaries, homework and other study material.
| Date | Topics |
| Aug.26. | Definition of groups. Groups from sets of numbers. |
| Aug.28. | Groups from modular arithmetic and linear algebra. First properties of groups. Homework 1 |
| Aug.30. | Abelian groups. Orders and multiplication tables of groups. Symmetric groups. |
| Sep.02. | Labor day; no class. |
| Sep.04. | Notation for permutations. First properties of symmetric groups. Homework 2 |
| Sep.06. | Generating sets of symmetric groups. |
| Sep.09. | Signs of permutations (via linear algebra). Dihedral groups. |
| Sep.11. | More on dihedral groups. Symmetries of the tetrahedron. Homework 3 |
| Sep.13. | Subgroups. |
| Sep.16. | Subgroups generated by subets of groups. Orders of elements in groups. |
| Sep.18. | Orders in symmetric groups. Orders of elements vs orders of subgroups. Homework 4 |
| Sep.20. | Cosets of subgroups. Lagrange's Theorem. |
| Sep.23. | Fermat's Little Theorem. Conjugation. |
| Sep.25. | Properties of conjugation. Conjugation in the symmetric group. Homework 5 |
| Sep.27. | Normal subgroups. |
| Sep.30. | Examples and properties of isomorphisms. |
| Oct.02. | Examples and non-examples of homomorphisms. Homework 6 |
| Oct.04. | Properties of homomorphisms. |
| Oct.07. | The first isomorphism theorem. |
| Oct.09. | Applications of the first isomorphism theorem. Homework 7 |
| Oct.11. | Review for midterm exam. |
| Oct.14. | Midterm. |
| Oct.16. | The correspondence theorem. Direct products. Homework 8 |
| Oct.18. | Orders of elements in direct products. Internal direct products. |
| Oct.21. | Group actions: definition and examples. |
| Oct.23. | The homomorphism associated to a group action. Cayley's theorem. Homework 9 |
| Oct.25. | Orbits and stabilizers. |
| Oct.28. | Class cancelled due to inclement weather. |
| Oct.30. | Class cancelled due to inclement weather. No homework this week. |
| Nov.01. | The orbit-stabilizer theorem. Counting the size of an orbit. |
| Nov.04. | Burnside's (orbit-counting) lemma. Counting orbits. |
| Nov.06. | More counting problems. Homework 10 |
| Nov.08. | The class equation and Cauchy's theorem. |
| Nov.11. | Statements and an application of the Sylow theorems. Preparatory lemmas. |
| Nov.13. | Proof of the Sylow theorems. Homework 11 |
| Nov.15. | Simple groups. Non-simplicity proofs using Sylow theorems. |
| Nov.18. | Finitely generated abelian groups. Invariant and elementary factors. |
| Nov.20. | Applications of the fundamental theorem of finitely generated abelian groups. Homework 12 |
| Nov.22. | Smith normal forms. |
| Dec.02. | Definition and examples of rings. |
| Dec.04. | Subrings, ideals, and ring homormorphisms. Homework 13 |
| Dec.06. | Quotient rings. Isomorphism theorems for rings. A construction of the complex field. |
| Dec.09. | Review for final exam, I. |
| Dec.09. | Review for final exam, II. |