Nyimbi Odero

Series 01 · a numbered run · kept in public

Mathematics of Quantum Gravity

The mathematics a working engineer needs to read quantum gravity honestly — calculus through Lie algebras, in six lessons of five parts each.

Two theories that are each right in their own domain and cannot both be. This course builds the mathematics needed to read the contradiction first-hand, one lesson in five parts at a time.

Lesson 1: Limits, Continuity, and Differentiation

  1. Part 2: The Theory of Limits
  2. Part 3: Continuity and Its Physical Significance
  3. Part 4: The Theory of Differentiation
  4. Part 5: Applications of Derivatives in Physics

Lesson 2: Integration and Its Physical Applications

  1. Part 2: Techniques of Integration

Lesson 3: Multivariable Calculus I

  1. Part 1: Understanding Scalar Fields and Their Variations
  2. Part 2: Vector Fields and Their Properties
  3. Part 3: Integral Theorems and Their Applications
  4. Part 4: Applications to Physical Systems

Lesson 4: Multivariable Calculus II

  1. Part 1: Understanding Divergence and Curl
  2. Part 2: Vector Analysis in Curved Spaces
  3. Part 3: Integral Theorems in Curved Space
  4. Part 5: Quantum Fields in Curved Spacetime

Lesson 5: Differential Geometry I

  1. Part 1: Foundations of Differential Geometry: Manifolds and Charts
  2. Part 3: Differential Forms and Exterior Calculus
  3. Part 5: Complex Manifolds and Kähler Geometry

Lesson 6: Lie Groups and Lie Algebras

  1. Part 1: Foundations of Lie Groups: Understanding Continuous Symmetry
  2. Part 2: Lie Algebras and Infinitesimal Transformations
  3. Part 3: Representation Theory and Physical Applications
  4. Part 4: Symmetry Breaking and Physical Systems