Study programme | Français | ||
Algebra I | |||
Programme component of Bachelor's Degree in Mathematics à la Faculty of Science |
Code | Type | Head of UE | Department’s contact details | Teacher(s) |
---|---|---|---|---|
US-B1-SCMATH-002-M | Compulsory UE | MICHAUX Christian | S838 - Logique mathématique |
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Language of instruction | Language of assessment | HT(*) | HTPE(*) | HTPS(*) | HR(*) | HD(*) | Credits | Weighting | Term |
---|---|---|---|---|---|---|---|---|---|
| Français | 30 | 55 | 14 | 0 | 0 | 9.00 | 9.00 |
AA Code | Teaching Activity (AA) | HT(*) | HTPE(*) | HTPS(*) | HR(*) | HD(*) | Term | Weighting |
---|---|---|---|---|---|---|---|---|
S-MATH-705 | Algebra I (part A) | 15 | 20 | 0 | 0 | 0 | Q1 | |
S-MATH-706 | Algebra Tutorials (part A) | 0 | 0 | 7 | 0 | 0 | Q1 | |
S-MATH-707 | Algebra I (part B) | 15 | 35 | 0 | 0 | 0 | Q2 | |
S-MATH-708 | Algebra Tutorials (part B) | 0 | 0 | 7 | 0 | 0 | Q2 |
Unité d'enseignement |
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Objectives of Programme's Learning Outcomes
Learning Outcomes of UE
At the end of this course, students will be able to: use the basic techniques (morphisms, kernels, images, quotients, order of an element, order of a subgroup) in the context of group theory; apply the theorems seen for these concepts; apply these concepts in the context of permutation groups; to extend the scope of these notions in the framework of rings, to handle these concepts in polynomial rings and link them to the concept of irreducibility of a polynomial.
Content of UE
- elementatry set theory, equivalence relation, quotient by an equivalence relation;
- basic number theory on the integers (GCD, LCM, euclidean division, integers modulo) ;
- Elements of group theory (morphisms, kernels, images, quotients, order of an element, order of a subgroup);
- groups of permutations;
- elements of the theory of rings; polynomial rings, irreducibility criteria for polynomials.
Prior Experience
A first knowledge of elementary mathematics on integers, rational numbers, real numbers, complex numbers, matrices and the operations on these objects. Theses basics can be assessed during the lectures and exercices of Elementary Mathematics which take place during the firts 6 weeks of the first term.
Type of Assessment for UE in Q1
Q1 UE Assessment Comments
Not applicable
Type of Assessment for UE in Q2
Q2 UE Assessment Comments
Term 2 assessment is realized through two tests which consists of exercises; the first one is performed in groups of students (between 3 and 5); the second one is individually performed and success to this test gives waiver for the same part of the written examination. The written examination consists of exercises. All tests and examinations are open book test (except for the part about polynomials) .
Type of Assessment for UE in Q3
Q3 UE Assessment Comments
The examination covers all of the material and consists of exercises. The test is open book (with the exception of the section on polynomials).
Type of Resit Assessment for UE in Q1 (BAB1)
Q1 UE Resit Assessment Comments (BAB1)
The evaluation is based on a test which consists only of exercices the aim of which are to test the ability to use theoretical concepts encountered in group theory in a broader context. It is open book test.
Type of Teaching Activity/Activities
AA | Type of Teaching Activity/Activities |
---|---|
S-MATH-705 |
|
S-MATH-706 |
|
S-MATH-707 |
|
S-MATH-708 |
|
Mode of delivery
AA | Mode of delivery |
---|---|
S-MATH-705 |
|
S-MATH-706 |
|
S-MATH-707 |
|
S-MATH-708 |
|
Required Reading
AA | Required Reading |
---|---|
S-MATH-705 | |
S-MATH-706 | |
S-MATH-707 | |
S-MATH-708 |
Required Learning Resources/Tools
AA | Required Learning Resources/Tools |
---|---|
S-MATH-705 | Not applicable |
S-MATH-706 | Not applicable |
S-MATH-707 | The syllabus of Part A is valid for Part B. |
S-MATH-708 | The syllabus of Part A is valid for Part B. |
Recommended Reading
AA | Recommended Reading |
---|---|
S-MATH-705 | |
S-MATH-706 | |
S-MATH-707 | |
S-MATH-708 |
Recommended Learning Resources/Tools
AA | Recommended Learning Resources/Tools |
---|---|
S-MATH-705 | http://math.umons.ac.be/logic/etudiants.htm |
S-MATH-706 | http://math.umons.ac.be/logic/etudiants.htm |
S-MATH-707 | Same list as for part A |
S-MATH-708 | Identique partie A |
Other Recommended Reading
AA | Other Recommended Reading |
---|---|
S-MATH-705 | S. Lang, Structures algébriques, InterEditions, Paris. I.N. Herstein, Topics in algebra, John Wiley & Sons, London. |
S-MATH-706 | S. Lang, Structures algébriques, InterEditions, Paris. I.N. Herstein, Topics in algebra, John Wiley & Sons, London. |
S-MATH-707 | Not applicable |
S-MATH-708 | Not applicable |