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MATH-F121

Géométrie analytique et calcul matriciel

academic year
2025-2026
2026-2027

Course teacher(s)

Joost VERCRUYSSE (Coordinator) and William Hautekiet

ECTS credits

5

Language(s) of instruction

french

Course content

  • Complex numbers.

  • Logic, sets, relations and functions.

  • Polynomials.

  • Matrices.

  • Systems of linear equations.

  • Geometry in the real plane and three-dimensional real space.

Objectives (and/or specific learning outcomes)

The main objective is to meet the priority needs of subsequent mathematics and physics courses, particularly in the area of linear algebra. Upon completion of this course unit, students will have mastered the basic concepts and algorithms of linear algebra and elementary geometry.

Prerequisites and Corequisites

Courses requiring this course

Teaching methods and learning activities

  • Lectures and exercise sessions.

Course notes

  • Syllabus
  • Université virtuelle

Contribution to the teaching profile

Acquiring and applying knowledge

Acquire a sound understanding of fundamental mathematical concepts.

Master the basic concepts of linear algebra and geometry.

Master the principles of logical reasoning and be able to base rigorous arguments on them.

Understanding and practising the specific approach of scientific inquiry

Understand the criteria of rigour, argumentation, and proof techniques.

Understand how a concept emerges from observations and examples.

Understand the process of abstraction and its role in the development of a theory.

Understand the sometimes simplifying role of the process of generalising a theory.

Understand the value of unifying existing theories.

Identify questions that arise within a theory.

Explore the consequences of a mathematical result.

Communication

Develop and write a mathematical result or theory with rigour.

Use clear and rigorous language adapted to the target audience.

Ethics and relationship with society

Learn to critically assess the validity of an argument.

I would particularly recommend “Acquiring and applying knowledge” rather than “Acquiring and exploiting knowledge”, as the latter is a rather literal translation of exploiter and sounds unnatural in English in this academic context.

Other information

Contacts

HAUTEKIET William <william.hautekiet@ulb.be>, VERCRUYSSE Joost <joost.vercruysse@ulb.be>

Campus

Plaine

Evaluation

Method(s) of evaluation

  • written examination

written examination

A dispensatory examination will be held in October. Resit examinations will be organised in January and June. A second-session examination will be held in August.

The course coordinator reserves the right to invite any student to an additional oral examination in order to verify their personal mastery of the content of the submitted examination, particularly when inconsistencies identified in the examination prevent the course coordinator from properly assessing the student's level of mastery of the knowledge and skills targeted by the course.

Mark calculation method (including weighting of intermediary marks)

Mark on 20 for the written exam.

Language(s) of evaluation

  • french

Programmes