note: getting through calculus

• 30 July 2023
• math,
• note

The previews that got me through lower division calculus and led me to algebraic topology then algebraic geometry.

• “Fundamental Theorems of Vector Calculus”, David Royster, 1996

• Intuitive without lacking rigor: “Intro to Tensors for Students of Physics and Engineering”, NASA, Joseph Kolecki, 2002

• “Stoke’s Theorem on Manifolds”, Rick Presman, 2012

  • Oliver Knill Calculus in four dimensions.

• One of my favorite Introduction to differential forms

• An ok Calculus on Manifolds Intuition

• Brief but nice Intro Vectors, Multivariable, Topology

• Why do differential forms have a much richer structure than vector fields?

• Coordinate-free derivatives need a reason for use

• A Primer on Index Notation John Crimaldi

• What are the Differences Between a Matrix and a Tensor?

Notes: Spectral theorems, SVD, and Quadratic forms

• Ten Lessons I Wish I Had Learned Before I Started Teaching, Differential Equations, Gian-Carlo Rota

Poincare Conjecture

Thurston

• Thurston, William (1982). “Three dimensional manifolds, Kleinian groups and hyperbolic geometry”
• Hamilton, Richard (1982). Three-manifolds with positive Ricci curvature. J. Differential Geometry 17 , no. 2, 255–306.
• Hamilton, Richard (1986). Four-manifolds with positive curvature operator. J. Differential Geom. 24 , no. 2, 153–179.
• Hamilton, Richard (1986). The Ricci flow on surfaces. Mathematics and general relativity, 237–262, Contemp. Math., 71, Amer. Math. Soc., Providence, RI, 1988.

Perelman

• Perelman, Grisha (2002). “The entropy formula for the Ricci flow and its geometric applications”
• Perelman, Grisha (2003). “Ricci flow with surgery on three-manifolds”
• Perelman, Grisha (2003). “Finite extinction time for the solutions to the Ricci flow on certain three-manifolds”

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