Study programme 20202021  Français  
Algebra I  
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 Covid19 assessment methods are possibly planned for the end of Q3 

Code  Type  Head of UE  Department’s contact details  Teacher(s) 

USB1SCMATH002M  Compulsory UE  MICHAUX Christian  S838  Logique mathématique 

Language of instruction  Language of assessment  HT(*)  HTPE(*)  HTPS(*)  HR(*)  HD(*)  Credits  Weighting  Term 

 Français  30  69  16  0  0  9  9.00  1st term 
AA Code  Teaching Activity (AA)  HT(*)  HTPE(*)  HTPS(*)  HR(*)  HD(*)  Term  Weighting 

SMATH705  Algebra I (part A)  15  20  0  0  0  Q1  
SMATH706  Algebra Tutorials (part A)  0  0  7  0  0  Q1  
SMATH707  Algebra I (part B)  15  35  0  0  0  Q2  
SMATH708  Algebra Tutorials (part B)  0  0  7  0  0  Q2  
SMATH666  Complex numbers  0  14  2  0  0  Q1 
Programme component 

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;
 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.
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 (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 of Assessment for UE in Q1
Q1 UE Assessment Comments
Term 1 evaluation is based on a test on complex numbers and on a written openbook 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.
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 partial test gives waiver for the same part of the written examination. The written examination consists of exercises on the three parts (groups, groups of permutations and polynomial rings. All tests and examinations are openbook test.
Type of Assessment for UE in Q3
Q3 UE Assessment Comments
The examination covers all of the material and consists of exercises. It is an openbook test.
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 (complex numbers).
Type of Teaching Activity/Activities
AA  Type of Teaching Activity/Activities 

SMATH705 

SMATH706 

SMATH707 

SMATH708 

SMATH666 

Mode of delivery
AA  Mode of delivery 

SMATH705 

SMATH706 

SMATH707 

SMATH708 

SMATH666 

Required Reading
AA  

SMATH705  
SMATH706  
SMATH707  
SMATH708  
SMATH666 
Required Learning Resources/Tools
AA  Required Learning Resources/Tools 

SMATH705  Not applicable 
SMATH706  Not applicable 
SMATH707  The syllabus of Part A is valid for Part B. 
SMATH708  The syllabus of Part A is valid for Part B. 
SMATH666  Website of "elementary mathematics": http://math.umons.ac.be/anum/fr/enseignement/mathelem/ 
Recommended Reading
AA  

SMATH705  
SMATH706  
SMATH707  
SMATH708  
SMATH666 
Recommended Learning Resources/Tools
AA  Recommended Learning Resources/Tools 

SMATH705  http://math.umons.ac.be/logic/etudiants.htm https://moodle.umons.ac.be/course/view.php?id=121 
SMATH706  http://math.umons.ac.be/logic/etudiants.htm https://moodle.umons.ac.be/course/view.php?id=121 
SMATH707  Same list as for Part A 
SMATH708  Same list as for Part A 
SMATH666  Not applicable 
Other Recommended Reading
AA  Other Recommended Reading 

SMATH705  S. Lang, Structures algébriques, InterEditions, Paris. I.N. Herstein, Topics in algebra, John Wiley & Sons, London. 
SMATH706  S. Lang, Structures algébriques, InterEditions, Paris. I.N. Herstein, Topics in algebra, John Wiley & Sons, London. 
SMATH707  Same as for Part A 
SMATH708  As for Part A 
SMATH666  https://link.springer.com/book/10.1007/9780817684150 