Theory of Scalar Fields

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Tensor Products of Modules

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Covariant Derivatives and Christoffel Symbols

Covers accelerated and inertial coordinate systems, Jacobian, volume elements, covariant derivatives, Christoffel symbols, Lorentz case, and metric tensor properties.

Tensor Decomposition: Jennrich's Theorem

Covers tensor decomposition and Jennrich's theorem, focusing on tensor rank and the uniqueness of tensor decomposition.

Tensor Analysis: Coordinate Systems

Covers tensor analysis for arbitrary coordinate systems and introduces Christoffel symbols.

Scaling & Renormalization in Statistical Mechanics

Explores scaling and renormalization in statistical mechanics, emphasizing critical points and invariant properties.

Intersection of Manifolds in Exercise 8.2

Covers the intersection of manifolds in exercise 8.2 and fiscal year 8.8.

Representations of SU(2): Symmetries and Transformations

Covers the representations of SU(2) and their transformations in quantum mechanics.

Tensors & Indices Recap

Covers the basics of tensors and indices, including contravariant vectors and tensor operations.

Vectors and Tensors: Mathematical Preliminaries and Transformations

Explores mathematical preliminaries of tensors and their transformations under basis rotations.

Tensors: Motivations and Introduction

Covers the basics of tensors, including their definition, properties, and decomposition, starting with a motivating example involving Gaussian distributions.