topological algebra

• part 1 ... basic definitions and uniform structures, posted Jun.11 2023
• part 2 ... operator theory I: the finite-dimensional case, posted Jun.12 2023

the mathematical structures of physics

• part 1 ... classical mechanics I: hamiltonian systems, posted May.11 2023

a geometric and topological toolkit

• part 1 ... a primer on embedded manifolds, posted Jan.17 2023
• part 2 ... tangent bundles, posted Jan.18 2023
• part 3 ... the algebraic theory I: vector fields + derivations, posted Feb.20 2023
• part 4 ... the algebraic theory II: ringed spaces, posted Mar.11 2023
• part 5 ... the algebraic theory III: local geometry, vector bundles, and sheaves of modules, posted Jun.24 2023