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UniMath / SymmetryBook

This book will be an undergraduate textbook written in the univalent style, taking advantage of the presence of symmetry in the logic at an early stage.
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Scope of chapter 8 #141

Open ghost opened 2 years ago

ghost commented 2 years ago

The current list of sections of chapter 8 in the Symmetry Book on fields is as follows:

  1. the algebraic hierarchy: groups, abelian groups, rings, fields
  2. vector spaces
  3. the general linear group as automorphism group
  4. determinants
  5. examples: rationals, polynomials, adding a root, field extensions
  6. ordered fields, real-closed fields, pythagorean fields, euclidean fields
  7. complex fields, quadratically closed fields, algebraically closed fields

In addition, there is this list of other topics at the beginning of the chapter: Quotients; subspaces (= ?). Bases and so. Dual space; orthogonality. (all of this depends on good implementations of subobjects). Eigen-stuff. Characteristic polynomials; Hamilton-Cayley.

However, in https://github.com/UniMath/SymmetryBook/issues/140#issuecomment-1172912984 Ulrik Buchholtz implied that covering this many topics is no longer appropriate for this book, and that the scope of this chapter would need to be narrowed down. Which topics in the list above should be kept, and which topics should be removed from the list?

DanGrayson commented 2 years ago

I would say that pythagorean fields, euclidean fields, and quadratically closed fields need not be taught. The rest is standard in undergraduate algebra courses.