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 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.
• Collaborate on mathematical subjects
• Present mathematical results orally and in a structured manner
• Demonstrate independence and their ability to work in teams.
• 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 sufficient knowledge of English in order to read and understand scientific texts, especially in the field of mathematics.
• Have a good knowledge of related fields using mathematics

Learning Outcomes of UE

The student must have learnt and should master the representation theory of finite groups. He/she must also know the basics of Lie groups and Lie algebra representation theory. In the case of SU(2), he/she must know the explicit construction and classification of all its UIR's. He/she must be able to solve elementary problems in group theory. 

Content of UE

Finite groups and their unitary irreducible representations (UIRs). Lie groups and algebras, their representations. Classification of the UIRs of SO(3) and SU(2). Haar measure. Cartan classification of semi-simple Lie algebras.

Prior Experience

Linear algebra.

Type of Assessment for UE in Q2

• Written examination

Q2 UE Assessment Comments

The exam consists of two parts. Part 1 on finite groups and Part 2 on Lie groups. 

Each of these two parts is marked over 20. The final mark is obtained by taking the geometrical mean of the two marks.
 

Type of Assessment for UE in Q3

• Written examination

Q3 UE Assessment Comments

The exam consists of two parts. Part 1 on finite groups and Part 2 on Lie groups. 

Each of these two parts are marked over 20. The final mark is obtained by taking the geometrical mean of the two marks.