Reading and Research in Mathematics

Topics

• – Space and time
• – Lorenz transformations
• – Vectors and dual vectors
• – Tensors
• – Maxwell’s equations
• – Energy and momentum
• – Classic field theory
• – Gravity as geometry
• – Manifolds, vector and tensors thereon
• – Metrics
• – Differential forms
• – Integration
• – Covariant derivatives
• – Parallel transport and geodesics
• – Properties of geodesics
• – The expanding universe
• – The Riemann curvature tensor
• – Symmetries and killing vectors
• – Maximally symmetric spaces
• – Geodesic deviations