Objectives of Programme's Learning Outcomes

• Understand "elementary" mathematics profoundly
• Understand one- and several-variable differential and integral calculus
• 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
• Address literature and interact within other scientific fields
• Have a good knowledge of related fields using mathematics

Learning Outcomes of UE

Elementary knowledge in the theory of finite groups and their unitary irreducible representations. 
Elementary notions in the theory of matrix Lie groups and their representations. Some notions of the theory of irreducible representations of complex semi-simple Lie algebras, with an emphasis on the case of sl(2,C).

UE Content: description and pedagogical relevance

Part 1. Finite groups, definitions and theory of unitary irreducible representations. Irreducible representations of the symmetric groups S_n
Part 2. Matrix Lie groups and irreducible representations of SU(2) and SO(3).

Prior Experience

Elementary knowledge of basic linear algebra and tensorial calculus.