Algebra

linfo1112  2024-2025  Louvain-la-Neuve

Algebra
5.00 credits
30.0 h + 30.0 h
Q2
> Schedule
Teacher(s)
Craeye Christophe; Vitale Enrico;
Language
French
Prerequisites
This course assumes that the student already masters the skills of end of secondary allowing to translate a problem into a system of equations with several variables and to solve it.
Main themes
The course focuses on :
  • the understanding of mathematical tools and techniques based on a rigorous learning of concepts favored by highlighting their concrete application,
  • the rigorous manipulation of these tools and techniques in the context of concrete applications.
Matrix calculation
  • transposition,
  • operation on  matrices,
  • rank and resolution of a linear system,
  • inversion,
  • determinant
Resolution of linear equation systems
  • Matrix writing of a system of linear equations
  • Basic operations on the lines
  • Elimination of Gauss-Jordan
  • LU Factoring
  • Implementation of Linear Equation System Resolution Algorithms
Linear algebra
  • vectors, vector operations,
  • vector spaces (vector, independence, base, dimension),
  • linear applications (applications to transformations of the plan, kernel and image),
  • eigenvectors and eigenvalues (including applications)
Learning outcomes

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

1
Given the learning outcomes of the "Bachelor in Computer science" program, this course contributes to the development, acquisition and evaluation of the following learning outcomes:
  • S1.G1
  • S2.2
Students who have successfully completed this course will be able to:
  • Model concrete problems using matrices and vectors;
  • Solve concrete problems using matrix calculation techniques (in particular the resolution of linear systems);
  • Reason using correctly the mathematical notation and methods keeping in mind but exceeding a more intuitive understanding of the concepts.
 
Content
Matrix calculation
  •     transposition,
  •     matrix operation,
  •     rank, resolution of a linear system,
  •     inversion,
  •     determining
Solving Systems of Linear Equations
  •     Matrix writing of a system of linear equations
  •     Basic row operations
  •     Gauss method
  •     Orthogonality and QR factorization
  •     Implementation in Python language of algorithms for solving systems of linear equations
Linear algebra
  •     vectors, operations on vectors,
  •     vector spaces (vector, independence, basis, dimension), Euclidean space,
  •     linear applications (applications to plane, kernel and image transformations),
  •     eigenvectors and eigenvalues ​​(including linear operators)
Teaching methods
The course is given in the form of lectures and practical work sessions.
The implementation assignments are supervised by the course assistants.
A partial, optional but dispensatory questioning takes place halfway through.
Evaluation methods
Written exam and implementation assignments carried out during the semester (10% of the mark).
Other information
To review your prior knowledge, you can use the site https://www.auto-math.be
Online resources
Available on Moodle:
Course slides
Syllabus
Statements and solutions to exercises and assignments
Old exam questions, with solutions
Teaching materials
  • Syllabus
Faculty or entity
> INFO


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

Title of the programme
Sigle
Credits
Prerequisites
Learning outcomes
Bachelor in Computer Science
SINF1BA
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