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.
• Collaborate on mathematical subjects
• Present mathematical results orally and in a structured manner
• Develop an effective slideshow to support an oral presentation
• 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

At the end of the instruction, the students will be able to use elementary notions of topology and mathematical logic (naïve set theory and cardinals; Zermelo-Fraenkel set theory, choice axiom, Zorn Lemma, cardinals, ordinals... ) in subsequent courses. They will be able to follow an advanced course of topology and mathematical logic and to communicate in front of their student fellows through lectures they will give on these subjects.

UE Content: description and pedagogical relevance

First notions of mathematical logic : connectives, quantifications, formulas, languages, models, cardinality, ...
Exposition of the role of mathematical logic in mathematics through examples ; first approach to some famous problems (continuum hypothesis, ...); first notions of topology (open and clsed sets, neighborhood, product topology...)
Introduction to the course of mathematical logic of 3rd year of bachelor degree.
To learn to communicate : the examination consists in a 1h course to be given in front
of the class (one or three students prepared and work together on a given thema).

Prior Experience

Basic notions of naïve set theory (functions, relations, equivalence relations); basic notions of group theory and linear algebra.

Type(s) and mode(s) of Q1 UE assessment

• Written examination - Face-to-face

Q1 UE Assessment Comments

Written exam on simple application of the theory.

Method of calculating the overall mark for the Q1 UE assessment

None

Type(s) and mode(s) of Q1 UE resit assessment (BAB1)

• Written examination - Face-to-face

Q1 UE Resit Assessment Comments (BAB1)

not applicable

Method of calculating the overall mark for the Q1 UE resit assessment

not applicable

Type(s) and mode(s) of Q2 UE assessment

• Oral presentation - Face-to-face

Q2 UE Assessment Comments

It consists in seminars given in front of their student fellows on the basis on a fixed list of topics (see https://moodle.umons.ac.be/course/view.php?id=1254). Seminars by the students take place during Term 2.

Method of calculating the overall mark for the Q2 UE assessment

Global mark based on oral presentation and joint written documents and of written exam of Q1 and tutorials

Type(s) and mode(s) of Q3 UE assessment

• Written examination - Face-to-face

Q3 UE Assessment Comments

Not applicable

Method of calculating the overall mark for the Q3 UE assessment

Not applicable