About
What Is This Site?
Broken Symmetry is a personal research notebook where I work through foundational texts in mathematics and theoretical physics. It contains solutions to textbook problems, expository notes, and observations about connections between different areas of mathematics.
The name reflects a central theme in modern physics: interesting structure often emerges when perfect symmetry is broken. This site documents my journey through the mathematics that describes such phenomena.
Philosophy
I believe in active reading: working through problems, proving theorems yourself, and making connections between ideas. Each solution aims to be:
- Rigorous: Complete proofs with all steps justified
- Clear: Well-organized with explicit structure
- Intuitive: Explaining the "why" behind the "what"
- Connected: Linking to related ideas across mathematics
Topics Covered
Current areas of focus include:
- Group theory and symmetry
- Differential geometry and calculus on manifolds
- Linear algebra and functional analysis
- Representation theory
- Mathematical foundations of quantum mechanics
Books I'm Studying
Foundational texts in mathematics and physics that I'm working through, with solutions and expository notes.
Calculus on Manifolds
Michael Spivak (1965)
A rigorous treatment of multivariable calculus leading to differential forms and Stokes' theorem on manifolds.
Visual Group Theory
Nathan Carter (2009)
An accessible introduction to abstract algebra using visual representations, Cayley diagrams, and symmetry groups to build intuition before formalism.
Linear Algebra and Its Applications
Peter D. Lax (2007)
A sophisticated treatment of linear algebra emphasizing connections to analysis, differential equations, and numerical methods.