Miscelleous (2023)

Self-study notes for tensor and exterior algebra, differential forms, quaternions, and basic differential geometry.

1. Universal construction of tensor product, graded algebras, exterior algebra and volume forms, determinants.
   • MacLane Algebra (3rd ed), Chapter 16.
2. Differential forms, exterior differentiation and application to \(\mathbb R^3\).
   • Loring W. Tu, An Introduction to Manifolds (2nd ed), Chapter 3.
3. Quaternions and 3D rotation.
   • John Stillwell, Naive Lie Theory, Chapter 1.
4. Tangent and cotangent bundles, Lie derivatives.
   • Jeffrey M. Lee, Manifolds and Differential Geometry, Chapters 1-2.