Algebra I

Course Description

This undergraduate level Algebra I course covers groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear groups.

Lecture Notes

Assignments (no solutions)

Exams (no solutions)

Course Description

This undergraduate level Algebra I course covers groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear groups.

Lecture Notes

The topic names represent the content of the handouts.

The Matrix Exponential (PDF)

Geometry of the Special Unitary Group (PDF)

The Spectral Theorem (PDF)

Symmetric Forms (PDF)

Geometry of C² (PDF)

Stereographic projection of the Hopf Fibration Matlab Program (PDF) (Courtesy of Huan Yao. Used with permission.)

Plane Crystallographic Groups with Point Group D₁ (PDF)

Isometries (PDF)

The Multiplicative Group of Integers Modulo (PDF)

Permutations (PDF)

Permutation Matrices (PDF)

Normal Subgroups of SL₂ (PDF)

The Alternating Group (PDF)

Rotations and Isometries (PDF)

Congruence of Integers (PDF)

Greatest Common Divisor and Least Common Multiple (PDF)

Related articles

• Lie Algebra Modules
• Linear Lie Algebras
• Orthogonal and Symplectic Lie Algebras
• Where Do Linearly Compact Vector Spaces Come From?
• The Manga Guide to Linear Algebra
• Diagrams/Dev/Transformations
• Finite noncommutative probability, the Born rule, and wave function collapse
• Algebra Touch On The Road
• Some notes on Weyl quantisation
• Noncommutative probability