Books
The series is planned as at least four books. Mathematical Structures I, the foundation volume, is the first — and currently the only one being written. The other three are planned but not yet drafted.
Mathematical Structures I
Status: in progress.
Mathematical Structures I is the foundation volume of the series. It establishes the language and structural apparatus — category theory, set theory, basic algebra and topology, multilinear and geometric algebra — that the other volumes are written to use rather than rebuild. It is also where the methodology of the series is set: how to think about a mathematical object, what makes a definition the right definition, how to pick the right tool for the right problem. It is the recommended entry point even if the reader’s primary interest is in calculus, linear algebra, or probability.
Planned
The next three volumes are planned, not yet drafted. They are intended to be read in parallel — each builds on the foundation in MS1, but not on the others.
- Linear Algebra and Geometric Structure
- Calculus, Analysis, and Geometry
- Probability, Expectation, and Measure
For pace and near-term plan on the work in progress, see the roadmap →.