Commutative algebra and algebraic geometry
Summary
David Hilbert can be regarded as the founder of commutative algebra. He seems to have viewed it as an alternative approach to the function theory which was dominant at the time. The concept of module over a ring, which can be traced back to Leopold Kronecker, generalizes the theory of ideals. These methods were introduced to commutative algebra by Emmy Noether and are indispensable today.
This course is intended to serve as an introduction to the theory and methods of commutative algebra and algebraic geometry. We will also discuss some topics in arithmetic geometry such as the aritmetic of elliptic curves.
Page one of Hilbert's 1893 paper with a photo of Hilbert as background.