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MATH-S1012

Mathématique générale : compléments d’analyse et algèbre linéaire

academic year
2025-2026
2026-2027

Course teacher(s)

Luca Paolo MERLINO (Coordinator)

ECTS credits

5

Language(s) of instruction

french

Course content

  • Convexity
  • Real matrices (matrix addition and multiplication, trace, transpose, special matrices, elementary matrices, invertibility of square matrices, rank of a matrix)
  • Linear systems (matrix form, Cramer's systems, general linear systems)
  • Determinants (properties, relationship between determinants and matrix invertibility, computation of the inverse using determinants)
  • Vector spaces (vector subspaces, linear dependence and independence, bases, change of basis, linear transformations, eigenvectors and eigenvalues, symmetric bilinear forms, inner products, quadratic forms)
  • Complex numbers (addition and multiplication, De Moivre's formula, roots of polynomials, n-th roots)

Objectives (and/or specific learning outcomes)

LG2. Academic mindset
LO 2.2  Display critical thinking, logical and abstract reasoning and develop an independent approach to learning

LG3. Quantitative skills
LO 3.1  Solve standard mathematical problems
LO 3.3  Assess the quality of the a quantitative analysis of an economic problem

Teaching methods and learning activities

Theory: ex-cathedra course.

Notes for the theoretical part: slides that are projected (and commented!) during the course.

Exercises: students are divided into groups for exercise sessions.

Exercise booklet divided into 12 lessons, each of which starts by a short reminder of the corresponding theory followed by some solved exercises, plus some proposed exercises (final answers (at least) are provided).
Some solved exams from previous years are available on the "université virtuelle".

During the academic year, guidance sessions and assistance are organized.

References, bibliography, and recommended reading

Mathématiques pour l'économie, 2023, Knut Sydsæter, Peter Hammond, Arne Strøm, Andrés Carvajal, 6e édition, Pearson France.

Course notes

  • Syllabus
  • Université virtuelle

Other information

Contacts

luca.paolo.merlino@ulb.be

Campus

Solbosch

Evaluation

Method(s) of evaluation

  • written examination

written examination

  • Open question with short answer
  • Closed question with multiple choices (MCQ)
  • Closed question with Multiple Answers (MAQ)
  • Open question with fill-in the blanks text
  • Open question with developed answer

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

Mark calculation method (including weighting of intermediary marks)

100% written exam.

Language(s) of evaluation

  • french

Programmes