Objectives of Programme's Learning Outcomes

• Have integrated and elaborate mathematical knowledge.
• Mobilise the Bachelor's course in mathematics to address complex issues and have profound mathematical expertise to complement the knowledge developed in the Bachelor's course.
• Use prior knowledge to independently learn high-level mathematics.
• Research mathematical literature in an efficient and relevant way.
• Carry out major projects.
• Appropriately use bibliographic resources for the intended purpose.
• Present the objectives and results of a project orally and in writing.
• Communicate clearly.
• make a structured and reasoned presentation of the content and principles underlying a piece of work, mobilised skills and the conclusions it leads to.
• Adapt to different contexts.
• Demonstrate thoroughness, independence, creativity, intellectual honesty, and ethical values.

Learning Outcomes of UE

Introduction to commutative algebra.
Introduction to affine and projective algebraic geometry.
The aim of this course is to master the correspondence between algebraic geometry and commutative algebra over an algebraically closed field.

UE Content: description and pedagogical relevance

Arithmetics of polynomial rings, modules, integrality, Noetherian rings, localisation.
Hilberts Nullstellensatz, Zariski topology, topological irreducibility, regular maps, products, rational maps, dimension, smoothness.
Projective space, projective and quasi-projective objects, morphisms.

Prior Experience

Bachelor's degree Algebra courses, elementary general toplogy.