RES-18.012 | Spring 2022 | Undergraduate
Algebra II Student Notes

## Student Notes

Complete set of Algebra II notes in one file (PDF - 1.5 MB), TEX files and associated images (ZIP

Lecture 1: Representations (PDF) (TEX)

Lecture 2: Characters and the Direct Sum (PDF) (TEX)

Lecture 3: Irreducible Representations (PDF) (TEX)

Lecture 4: The Main Theorem (PDF) (TEX)

Lecture 5: Characters and Schur’s Lemma (PDF) (TEX)

Lecture 6: Orthonormality of Characters (PDF) (TEX)

Lecture 7: Proof of the Main Theorem (PDF) (TEX)

Lecture 8: Rings (PDF) (TEX)

Lecture 9: Building New Rings (PDF) (TEX)

Lecture 10: Ideals in Polynomial Rings (PDF) (TEX)

Lecture 11: More About Rings (PDF) (TEX)

Lecture 12: Factorization in Rings (PDF) (TEX)

Lecture 13: More Factorization (PDF) (TEX)

Lecture 14: Number Fields (PDF) (TEX)

Lecture 15: Ideal Factorization (PDF) (TEX)

Lecture 16: Uniqueness of Ideal Factorization (PDF) (TEX)

Lecture 17: Ideals in Quadratic Fields (PDF) (TEX)

Lecture 18: The Ideal Class Group (PDF) (TEX)

Lecture 19: Modules over a Ring (PDF) (TEX)

Lecture 20: Modules and Presentation Matrices (PDF) (TEX)

Lecture 21: Smith Normal Form (PDF) (TEX)

Lecture 22: Decomposition of Modules (PDF) (TEX)

Lecture 23: Noetherian Rings (PDF) (TEX)

Lecture 24: Fields (PDF) (TEX)

Lecture 25: Field Extensions (PDF) (TEX)

Lecture 26: Finite Fields (PDF) (TEX)

Lecture 27: Finite Fields (continued) (PDF) (TEX)

Lecture 28: Geometry of Function Fields (PDF) (TEX)

Lecture 29: Galois Theory (PDF) (TEX)

Lecture 30: Main Theorem of Galois Theory (PDF) (TEX)

Lecture 31: Applications of the Galois Correspondence (PDF) (TEX)

Lecture 32: Solving Polynomial Equations (PDF) (TEX)

Lecture 33: Symmetric Polynomials and the Discriminant (PDF) (TEX)

Lecture 34: Solving Polynomial Equations (continued) (PDF) (TEX)

Lecture 35: Final Remarks (PDF) (TEX)

Appendix: Dimensions of Irreducible Characters (PDF) (TEX)