Study programme 2023-2024 | Français | ||
Algebra I | |||
Programme component of Bachelor's in Mathematics (MONS) (day schedule) 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 | 69 | 16 | 0 | 0 | 10 | 10.00 | 1st term |
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 | |
S-MATH-666 | Complex numbers | 0 | 14 | 2 | 0 | 0 | Q1 |
Programme component |
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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 (if times allows it);
- extend the scope of these notions in the framework of rings ;
- handle these concepts in polynomial rings and link them to the concept of irreducibility of a polynomial.
UE Content: description and pedagogical relevance
- 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 (subgroups, 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 first 6 weeks of the first term.
Type(s) and mode(s) of Q1 UE assessment
Q1 UE Assessment Comments
Term 1 evaluation is based on a test on complex numbers and on a written open-book test (not compulsory). This second test 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.
Method of calculating the overall mark for the Q1 UE assessment
Mark from the Complex Numbers part (it counts for 10% of the final mark).
Type(s) and mode(s) of Q1 UE resit assessment (BAB1)
Q1 UE Resit Assessment Comments (BAB1)
The evaluation is based on a test which consists only of exercices (complex numbers).
Method of calculating the overall mark for the Q1 UE resit assessment
Idem Q1.
Type(s) and mode(s) of Q2 UE assessment
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 partial test gives waiver for the same part of the written examination. The written examination consists of exercises on the differnts parts (theoretical exercices, groups, groups of permutations and polynomial rings). All tests and examinations except the part "theoretical exrecices are open-book test.
Method of calculating the overall mark for the Q2 UE assessment
Global mark from the written examination. It counts for 90% of the final mark.
Type(s) and mode(s) of Q3 UE assessment
Q3 UE Assessment Comments
The examination covers all of the material and consists of exercises. Rules are the same as for Q2
Method of calculating the overall mark for the Q3 UE assessment
idem Q2.
Type of Teaching Activity/Activities
AA | Type of Teaching Activity/Activities |
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S-MATH-705 |
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S-MATH-706 |
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S-MATH-707 |
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S-MATH-708 |
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S-MATH-666 |
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Mode of delivery
AA | Mode of delivery |
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S-MATH-705 |
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S-MATH-706 |
|
S-MATH-707 |
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S-MATH-708 |
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S-MATH-666 |
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Required Reading
AA | Required Reading |
---|---|
S-MATH-705 | Notes d'exercices - Algèbre - Maurice Boffa et Christian Michaux |
S-MATH-706 | |
S-MATH-707 | |
S-MATH-708 | |
S-MATH-666 |
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. |
S-MATH-666 | Website of "elementary mathematics": http://math.umons.ac.be/anum/fr/enseignement/mathelem/ |
Recommended Learning Resources/Tools
AA | Recommended Learning Resources/Tools |
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S-MATH-705 | http://math.umons.ac.be/logic/etudiants.htm https://moodle.umons.ac.be/course/view.php?id=121 |
S-MATH-706 | http://math.umons.ac.be/logic/etudiants.htm https://moodle.umons.ac.be/course/view.php?id=121 |
S-MATH-707 | Same list as for Part A |
S-MATH-708 | Same list as for Part A |
S-MATH-666 | Not applicable |
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 | Same as for Part A |
S-MATH-708 | As for Part A |
S-MATH-666 | https://link.springer.com/book/10.1007/978-0-8176-8415-0 |