RES.18-011 | Fall 2021 | Non-Credit

Algebra I Student Notes

Student Notes

Complete Set of Algebra I Notes in One File (PDF - 2.8MB), TEX files and associated images (ZIP)

Lecture 1: Groups (PDF) (TEX)

Lecture 2: Subgroups and Cyclic Groups (PDF) (TEX)

Lecture 3: Homomorphisms and Isomorphisms (PDF) (TEX)

Lecture 4: Isomorphisms and Cosets (PDF) (TEX)

Lecture 5: The Correspondence Theorem (PDF) (TEX)

Lecture 6: Normal Subgroups and Quotient Groups (PDF) (TEX)

Lecture 7: Fields and Vector Spaces (PDF) (TEX)

Lecture 8: Dimension Formula (PDF) (TEX)

Lecture 9: Dimension Formula (continued) (PDF) (TEX)

Lecture 10: Eigenbases and the Jordan Form (PDF) (TEX)

Lecture 11: The Jordan Decomposition (PDF) (TEX)

Lecture 12: Orthogonal Matrices (PDF) (TEX)

Lecture 13: Isometries (PDF) (TEX)

Lecture 14: Symmetry Groups (PDF) (TEX)

Lecture 15: Finite and Discrete Subgroups (PDF) (TEX)

Lecture 16: Discrete Groups (PDF) (TEX)

Lecture 17: Group Actions (PDF) (TEX)

Lecture 18: Stabilizer (PDF) (TEX)

Lecture 19: Group Actions on G (PDF) (TEX)

Lecture 20: The Icosahedral Group (PDF) (TEX)

Lecture 21: Conjugacy Classes for Symmetric and Alternating Groups (PDF) (TEX)

Lecture 22: The Sylow Theorems (PDF) (TEX)

Lecture 23: Proofs and Applications of the Sylow Theorems (PDF) (TEX)

Lecture 24: Bilinear Forms (PDF) (TEX)

Lecture 25: Orthogonality (PDF) (TEX)

Lecture 26: The Projection Formula (PDF) (TEX)

Lecture 27: Euclidean and Hermitian Spaces (PDF) (TEX)

Lecture 28: The Spectral Theorem (PDF) (TEX)

Lecture 29: Linear Groups (PDF) (TEX)

Lecture 30: The Special Unitary Group \(SU_2\) (PDF) (TEX)

Lecture 31: One-Parameter Subgroups (PDF) (TEX)

Lecture 32: One-Parameter Subgroups (cont.) (PDF) (TEX)

Lecture 33: Lie Groups (PDF) (TEX)

Lecture 34: Simple Linear Groups (PDF) (TEX)

Lecture 35: Hilbert’s Third Problem (PDF) (TEX)

Course Info

As Taught In
Fall 2021
Level
Learning Resource Types
Lecture Notes