Objectives of Programme's Learning Outcomes

• Understand "elementary" mathematics profoundly
• Use vector spaces, linear applications and the techniques associated with them
• Understand and use the naive set theory
• Understand basic algebraic structures
• Manipulate previously acquired knowledge that appears in a question
• Give examples and counterexamples for definitions, properties, theorems, etc.
• Understand and produce strict mathematical reasoning
• Write clearly and concisely
• Use mathematical vocabulary and formalism appropriately
• Make sense of formal expressions
• Rely on a picture to illustrate a concept, rationale, etc.
• Solve new problems
• Abstract and manipulate theories and use these to solve problems
• Adapt an argument to a similar situation
• Use knowledge from different fields to address issues

Learning Outcomes of UE

Algebraic field theory and finite Galois theory. 
 

UE Content: description and pedagogical relevance

Algebraic field theory: field extensions, algebraic and transcendental elements, algebraic extensions, algebraic closure.
Galois theory: embeddings, Galois groups, Galois extensions, Galois correspondence, solvability. 

Prior Experience

"Algèbre II" course.