 | Study programme 2021-2022 | Français | |
 | Group Theory | ||
Programme component of Bachelor's in Mathematics à la Faculty of Science |
| Code | Type | Head of UE | Department’s contact details | Teacher(s) |
|---|---|---|---|---|
| US-B2-SCMATH-019-M | Optional UE | BOULANGER Nicolas |
|
| Language of instruction | Language of assessment | HT(*) | HTPE(*) | HTPS(*) | HR(*) | HD(*) | Credits | Weighting | Term |
|---|---|---|---|---|---|---|---|---|---|
| Français | 30 | 20 | 0 | 0 | 0 | 4 | 4.00 | 2nd term |
| AA Code | Teaching Activity (AA) | HT(*) | HTPE(*) | HTPS(*) | HR(*) | HD(*) | Term | Weighting |
|---|---|---|---|---|---|---|---|---|
| S-PHYS-201 | Group theory | 30 | 20 | 0 | 0 | 0 | Q2 | 100.00% |
| Programme component |
|---|
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 written exam concerns the entire course.
Type of Assessment for UE in Q3
- Written examination
Q3 UE Assessment Comments
The written exam concerns the entire course.
Type of Teaching Activity/Activities
| AA | Type of Teaching Activity/Activities |
|---|---|
| S-PHYS-201 |
|
Mode of delivery
| AA | Mode of delivery |
|---|---|
| S-PHYS-201 |
|
Required Reading
| AA | |
|---|---|
| S-PHYS-201 |
Required Learning Resources/Tools
| AA | Required Learning Resources/Tools |
|---|---|
| S-PHYS-201 | PDF file of the lecture notes based on the following reference: Wu Ki Tung, "Group theory in Physics", World Scientific (1985); M. Hamermesh, "Group Theory", Dover (1989) |
Recommended Reading
| AA | |
|---|---|
| S-PHYS-201 |
Recommended Learning Resources/Tools
| AA | Recommended Learning Resources/Tools |
|---|---|
| S-PHYS-201 | Lectures notes on Moodle or Teams |
Other Recommended Reading
| AA | Other Recommended Reading |
|---|---|
| S-PHYS-201 | A. Knapp, "Lie groups: Beyond an Introduction", Birkhauser, 2nd edition (2002); Fuchs and Schweigert, "Symmetries, Lie algebras and Representations: A graduate course for Physicists", Cambridge (2003) |
Grade Deferrals of AAs from one year to the next
| AA | Grade Deferrals of AAs from one year to the next |
|---|---|
| S-PHYS-201 | Authorized |