Algebra

lepl1101  2022-2023  Louvain-la-Neuve

Algebra
5.00 credits
30.0 h + 30.0 h
Q1
Teacher(s)
. SOMEBODY; Glineur François; Jungers Raphaël; Remacle Jean-François; Verleysen Michel (coordinator); Wertz Vincent (compensates Jungers Raphaël);
Language
French
Main themes
Linear algebra : linear equation systems, matrix calculus, linear applications, euclidean spaces, vector spaces on a field, linear sequences, quadratic forms. Modelling and solving of simple problems.
Learning outcomes

At the end of this learning unit, the student is able to :

1 Contribution of the course to the program objectives
Regarding the learning outcomes of the program of Bachelor in Engineering, this course contributes to the development and the acquisition of the following learning outcomes:
  • LO1.1, 1.2
  • LO 2.2, 2.3, 2.4, 2.6, 2.7
  • LO 3.1, 3.2, 3.3
  • LO 4.1, 4.4
Specific learning outcomes of the course
At the end of the course the students will be able to
  • Master the elementary notions of linear algebra ;
  • Apply the notion of euclidean space and orthogonal projection to solve approximation problems in Rn and other spaces;
  • Calculate vector spaces of a linear operator;
  • Diagonalize a linear space if possible;
  • Study the evoluation of a linear system and of a linear recurrence:
  • Determine the caracteristics of a quadratic form;
  • Understand the main mathematical proof techniques ;
  • Make a critical reading and analysis of a problem statement;
  • Find examples and counter-examples related to a mathematical statement;
  • Write short mathematical proofs with rigor;
  • Modelli of simple problems, and problem solving using the methods cited above.
 
Content
  • Systems of linear equations,
  • Matrix calculus,
  • Vector spaces,
  • Linear applications,
  • Euclidean spaces, orthogonal projection and approximation problems,
  • Linear operators, eigenvectors and diagonalization, Jordan form and matrix exponential
  • Adjoint operator, spectral theorem, quadratic forms, law of inertia,
  • Sequences and series, linear differential equations
Teaching methods
Lectures in auditorium, supervised exercise  sessions and problem based learning, possibly supplemented with writing assignments and online exercises.
Some of the above activities (lectures, exercise sessions, problem based learning) may be organised on line.
Evaluation methods
The written examination will cover the learning outcomes. Two assignments (peer-reviewed) to be carried out during the term are compulsory; these two assignments, including their evaluation, may generate up to one bonus point, valid for the January exam session only.
Online resources
Cours : LEPL1101 - Algèbre (uclouvain.be)
Bibliography
Le syllabus constitute le support de cours obligatoire.  Une référence supplémentaire intéressante à conseiller est:G. Strang, Introduction to linear algebra, 5th edition, Cambridge University Press
Teaching materials
  • syllabus (cours + exercices)
Faculty or entity
BTCI


Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Sigle
Credits
Prerequisites
Learning outcomes
Bachelor in Engineering
FSA1BA
5
Bachelor in Engineering : Architecture
ARCH1BA
5