Objectives of Programme's Learning Outcomes

• Understand "elementary" mathematics profoundly
• 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.
• Collaborate on mathematical subjects
• 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

Learning Outcomes of UE

<em>At the end of this course, students will be able to </em>:
- 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

• Quoted exercices

Q1 UE Assessment Comments

Term 1 evaluation is based on a written open-book test (not compulsory). 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. 

Type of Assessment for UE in Q2

• Written examination
• Quoted exercices

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 open-book test.
 

Type of Assessment for UE in Q3

• Written examination

Q3 UE Assessment Comments

The examination covers all of the material and consists of exercises. It is an open-book test.

Type of Resit Assessment for UE in Q1 (BAB1)

• Written examination

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 an open-book test.