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How does one teach algebraic geometry to computer scientists/engineers?

There is a 2009 book by Sumio Watanabe. It has its prerequisites, and would require plenty of adaptation. Is there anything better?

Ideally, it should involve geometrical representations of datasets, transformations of finite dimensional spaces, decision-making, searching subspaces/ boundaries, computation, and aspects of visualization.

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  • $\begingroup$ You should at least provide a link to the book that you mention, and some more indication of context, such as a list of applications for which computer scientists or engineers might want to know some algebraic geometry. $\endgroup$
    – Neil Strickland
    Commented Jun 9, 2023 at 10:55
  • $\begingroup$ Added a bit. Applications to optimization methods would additionally qualify. $\endgroup$
    – A Mani
    Commented Jun 9, 2023 at 11:25
  • $\begingroup$ Kiran Kedlaya had a course on Weil Cohomology in practice that had some (theoretical) computer scientists attend. $\endgroup$
    – Mark Schultz-Wu
    Commented Jun 9, 2023 at 17:31
  • $\begingroup$ Your list of topics is a little confusing to me. You could easily fill a course on those topics without ever mentioning algebraic geometry. Is your goal really to teach algebraic geometry, as algebraic geometers understand the subject? Or is the goal to give a crash course to help students understand specific papers in these applied areas that use the language of algebraic geometry? These are very different goals, and I don't think it's realistic to try to do both. $\endgroup$
    – Timothy Chow
    Commented Jun 10, 2023 at 3:53
  • $\begingroup$ Possibly related: How to explain to an engineer what algebraic geometry is? $\endgroup$
    – Timothy Chow
    Commented Jun 10, 2023 at 3:54

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You might try

S. S. Abhyankar: Algebraic geometry for scientists and engineers, Mathematical Surveys and Monographs, 35. Providence, RI: American Mathematical Society (ISBN 0-8218-1535-0). xiii, 295 p. (1990). ZBL0709.14001.

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