Notebook
by Alex Nelson,
These are my notes on math and physics. The most popular note appears to be the one on Feynman diagrams, apparently no one bothers explaining the algoritm underpinning the calculations…
Math
- Bourbaki’s 1+1=2, 12 pages, a literate program checking the size of “1+1=2” in Bourbaki’s foundations of mathematics.
- Elementary Linear Algebra, 94 pages, a review of linear algebra, motivated by systems of linear equations, then taking a detour into the algebra of matrices, then returning to use matrices to solve linear equations and more broadly discuss vector spaces. This is based on my notes from UC Davis’s Math 22A course.
- Notes on An Algebraic Formulation of Tangent Spaces, 9 pages, specifically using germs.
- Introduction to Category Theory, 34 pages, a never-completed set of notes introducing category theory from the perspective of “Stuff, Structure, and Properties” (“neo-Structuralism”?).
From Lectures
- Notes on Lie Groups and Algebra, 91 pages, I took these notes from Albert Schwarz’s lectures, any typos or errors are mines.
- Homotopy Theory, 67 pages, notes taken during Albert Schwarz’s lectures on algebraic topology; errors are mine.
- Applied Complex Analysis, 53 pages, notes taken during Dmitry Fuchs’s lectures on advanced complex analysis; errors are mine.
- Differential Geometry of Curves and Surfaces, 55 pages, notes taken during Derek Wise’s lectures on differential geometry of curves and surfaces; errors are mine.
Physics
- Notes on Feynman Diagrams, 32 pages, presents computing amplitudes from Feynman diagrams algorithmically.
- Spontaneous Symmetry Breaking in Conformal Weyl Gravity, 9 pages, term paper for Steve Carlip’s course on general relativity
- Relativistic Quantum Mechanics, 11 pages, how to mix special relativity and quantum mechanics, using representation theory.
- Hamiltonian Field Theory, 5 pages, a brief note on the canonical formalism for fields. Purely Classical considerations only!
- Functional Methods in QFT, 25 pages, discusses “functional” approach to path integrals, and briefly how to determine Feynman rules.
- Newtonian Mechanics in a Nutshell, 9 pages, nontechnical discussion of Newtonian mechanics, specifically Newton’s laws of motion.
From Lectures
- Notes on General Relativity, 82 pages, a rather “mathy” physics introduction to the subject. (Includes exercises!)
- Notes on Quantum Gravity, 52 pages, discusses canonical approaches (both ADM and Ashtekar variables), string theory, briefly discusses Causal Dynamical Triangulations and Black Hole Thermodynamics; including “exercises”.