What is...Hilbert’s basis theorem?

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Goal.
Explaining basic concepts of (a classical course in) algebra in an intuitive way.

This time.
What is...Hilbert’s basis theorem? Or: Algebra meets geometry (once again).

Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.

Warning (communicated to me via email, thanks).
The polynomial at the bottom of slide 4 should should Y^3-Z^2 instead of Y^2-Z^3.

Slides.

Material used.

Conic section.

Variety.

Extra material.

How to plot varieties.

Mathematica.

#algebra
#galoistheory
#mathematics
  1. VisualMath
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