---
title: "Differential Geometry"
subtitle: "Timeline"
format: 
    html:
        toc: true
        toc-depth: 3
---

Textbook: VDGAF by Needham

### Week 1
+ Prologue
    - Newtonian Reasoning
    - Ultimate Equality
+ Act I
    - Three different geometries
    - Angular Excess
    - Gaussian Curvature
    - Local Gauss-Bonnet Theorem

### Week 2
+ Act II: Chapter 4 - Mapping Surfaces
    - Maps
      . Projective, Conformal Steregraphic
    - Metrics
      . General Surface 
      . Metric Curvature
    
### Week 3
+ Act II: Chapter 5 - Pseudosphere & $\mathbb{H}^2$
    - Beltrami
    - Tractrix 
    - Half-plane

### Week 3
+ Act II: Chapter 6 - Isometries
+ Act III: Chapter 8 - Curvature of Plane Curves

### Week 4
+ Act III: Chapter 9 - Curves in 3-Space
+ Act III: Chapter 10 - Principal Curvatures of a Surface

### Week 5
+ Act III: Chapter 11 - Geodesics & Geodesic Curvature
+ Act III: Chapter 12 - Extrinsic Curvature of a Surface

### Week 6
+ Act III: Chapter 13 - Gauss's *Theorema Egregium*
+ Act III: Chapter 14 - Curvature of a Spike

### Week 7
+ Act III: Chapter 15 - The Shape Operator
+ Act III: Chapter 16 - Intro to Global Gauss-Bonnet Theorem

### Week 8
+ Act III: Chapter 17 - Heuristic Proof of GGB
+ Act III: Chapter 18 - Angular Excess Proof of GGB

### Week 9
+ Act III: Chapter 19 - Vector Proof of GGB
+ Act IV: Chapter 22 - Parallel Transport: Extrinsic Constructions

### Week 10
+ Act III: Chapter 23 - Intrinsic Contructions
+ Act IV: Chapter 24 - Holonomy

### Week 11
+ Act III: Chapter 25 - Intuitive Proof of *Theorema Egregium*
+ Act IV: Chapter 26 - Holonomy Proof of GGB

### Week 12
+ Act III: Chapter 27 - Proof of Metric Curvature Formula
+ Act IV: Chapter 28 -  Curvature as Force b/w Geodesics

### Week 13
+ Act III: Chapter 29
    - Covariant Derivative
    - Riemannian Curvature Tensor
+ Act III: Chapter 30
  - Tidal Forces
  - Spacetime Metric

### Week 14
+ Act IV: Forms
    - 1-forms
    - 2-forms
    - Tensors


