 | Study programme 2020-2021 | Français | |
 | Algebra II | ||
Programme component of Bachelor's in Mathematics à la Faculty of Science |
| Students are asked to consult the ECTS course descriptions for each learning activity (AA) to know what special Covid-19 assessment methods are possibly planned for the end of Q3 |
|---|
| Code | Type | Head of UE | Department’s contact details | Teacher(s) |
|---|---|---|---|---|
| US-B2-SCMATH-002-M | Compulsory UE | VOLKOV Maja | S843 - Géométrie algébrique |
|
| Language of instruction | Language of assessment | HT(*) | HTPE(*) | HTPS(*) | HR(*) | HD(*) | Credits | Weighting | Term |
|---|---|---|---|---|---|---|---|---|---|
| Français | 30 | 20 | 0 | 0 | 0 | 5 | 5.00 | 2nd term |
| AA Code | Teaching Activity (AA) | HT(*) | HTPE(*) | HTPS(*) | HR(*) | HD(*) | Term | Weighting |
|---|---|---|---|---|---|---|---|---|
| S-MATH-011 | Algebra II | 30 | 20 | 0 | 0 | 0 | Q2 | 100.00% |
| Programme component |
|---|
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
Basic algebra: groups, commutative rings, fields.
This course aims to present the essential material in undergraduate basic algebra.
Content of UE
Groups: generated subgroups, factorisation of morphisms, canonical isomorphisms, centralisers, normalisers, dihedral groups, quaternion group, linear groups over finite fields.
Commutative rings: prime ideals, maximal ideals, operations on ideals, Chinese remainder theorem, PID's and UFD's.
Fields: field extensions, multiplicativity of degrees, algebraic and transcendental elements, roots of unity, minimal polynomials, extension degree computations.
Prior Experience
"Algèbre I" course.
Type of Assessment for UE in Q2
- Written examination
Q2 UE Assessment Comments
Not applicable
Type of Assessment for UE in Q3
- Written examination
Q3 UE Assessment Comments
Not applicable
Type of Teaching Activity/Activities
| AA | Type of Teaching Activity/Activities |
|---|---|
| S-MATH-011 |
|
Mode of delivery
| AA | Mode of delivery |
|---|---|
| S-MATH-011 |
|
Required Reading
| AA | |
|---|---|
| S-MATH-011 |
Required Learning Resources/Tools
| AA | Required Learning Resources/Tools |
|---|---|
| S-MATH-011 | Not applicable |
Recommended Reading
| AA | |
|---|---|
| S-MATH-011 |
Recommended Learning Resources/Tools
| AA | Recommended Learning Resources/Tools |
|---|---|
| S-MATH-011 | M.A. Armstrong, Groups and Symmetry, Undergraduate Texts in Mathematics, Springer-Verlag. D. Perrin, Cours d'Algèbre, Ellipses. A. Chambert-Loir, Algèbre corporelle, Les Editions de l'Ecole polytechnique. |
Other Recommended Reading
| AA | Other Recommended Reading |
|---|---|
| S-MATH-011 | Not applicable |
Grade Deferrals of AAs from one year to the next
| AA | Grade Deferrals of AAs from one year to the next |
|---|---|
| S-MATH-011 | Authorized |