This book is meant to complement traditional textbooks by covering the mathematics used in theoretical physics beyond that typically covered in undergraduate math and physics courses. The idea is to provide an intuitive, visual overview of these mathematical tools, with guiding end goals including but not limited to spinors and gauge theories.
The book focuses on:
- Defining and visualizing concepts and relationships between them
- Stating related results and introducing related concepts for further study
- Explaining the jargon and alternative treatments found in the literature
This means that many other aspects are omitted, including:
- Historical motivations and attributions
- Proofs of theorems and derivations of results
- Tools for practical calculations
The idea is to take advantage of the reader’s intuitive ability to grasp a concept through in most cases mathematically rigorous definitions, descriptive pictures, and related results. Such an approach permits concise coverage of a large breadth of material, hopefully providing a cross-subject synthesis while at the same time serving as a useful reference.
The book starts with generalizations of numbers (abstract algebra), moves to shapes (topology), and then adds geometric structure until arriving at fiber bundles.