Cutoff and Other Special Smooth Functions on ?n -- Algebras and Points -- Smooth Manifolds (Algebraic Definition) -- Charts and Atlases -- Smooth Maps -- Equivalence of Coordinate and Algebraic Definitions -- Spectra and Ghosts -- The Differential Calculus as a Part of Commutative Algebra -- Smooth Bundles -- Vector Bundles and Projective Modules

1. Mathematics
2. Algebra
3. Manifolds (Mathematics)
4. Complex manifolds
5. Quantum physics
6. Quantum computers
7. Spintronics
8. Mathematics
9. Manifolds and Cell Complexes (incl. Diff.Topology)
10. Algebra
11. Quantum Physics
12. Quantum Information Technology
13. Spintronics