Some of Dr E. Anderson’s Courses and Course Designs
*** I. See my “Appendices: Mathematical Methods
for Basic and Foundational Quantum Gravity”, freely available online here for a 200-page graduate school course on a wide range of mathematical topics of estabilished and growing relevance in foundational and theoretical physics.
This includes brief accounts (1 to 3 graduate-level mathematics lectures apiece) for each of:
* Algebra and Discrete Mathematics
* Flat Geometry
* Manifold Geometry
* Lie Groups and Lie Algebras
* Two sets of Exercises on on the topics so far.
* More Advanced Topology and Geometry
* Configuration Space Geometry for Mechanics
* Configuration Space Geometry for Field Theory, General Relativity, Minisuperspace and Perturbations Thereabout.
* Principles of Dynamics for Finite Theories
* Principles of Dynamics for Field Theories and General Relativity
* Quotient Spaces and Stratified Manifolds
* Differential Equations Theorems
* Function Spaces, Measures and Probabilities
* Statistical Mechanics, Information and Correlation
* Stochastic Geometry
* Generalized Configuration Spaces (Spaces of Differentiable Structures, of Topological Manifolds, of Metric Spaces, Lattices of Subgroups,
Topological Spaces and Collections, Spaces of Sets) and Grainings, Information, Stochastics and Statistics outlined on most of these.
* Quantum Statistical Mechanics, Information and Correlation
* Further Algebraic Structures (Semidirect Product-, Super-, and Diffeomorphism Groups, Algebroids, Operator Algebras).
* Alternative Foundations for Mathematics (Categories, Presheaves, Sheaves and Topoi)
*** Some Graduate Course Notes
*** III. See the below for some specific ‘blackboards’ illustrating Proofs, Conceptual Outlines and Exercises: