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Table of Contents
Part I FOUNDATIONS
LOGIC
Propositional logic
Models
Formulas
Truth-tables
Valid formulas
Demonstration
Predicates
Models with predicates
Valid consequence
Demonstration with predicates
Formal theories
Definitions
Summary
This book provides the main definitions and theorems in mathematics essential for theoretical physicists. It covers foundational topics like mathematical logic, set theory, algebra, analysis, differential geometry, Lie algebras, representation theory, fiber bundles, and functional analysis. The book aims to offer a comprehensive collection of precise definitions and results in advanced mathematics, with a focus on clarity and accessibility for readers. It is self-contained, precise, easy to use, comprehensive, and pedagogical. The author emphasizes a step-by-step approach to presenting concepts in the most general settings to extend the scope of results. The book also introduces significant new results such as distributions over vector bundles, functional derivatives, and more.