Public University of Navarre

CastellanoEuskara | Academic year: 2024/2025 | Previous academic years:  2023/2024  |  2022/2023 
Bachelor's degree in Computer Science at the Universidad Pública de Navarra
Course code: 240101 Subject title: MATHEMATICS I
Credits: 6 Type of subject: Basic Year: 1 Period: 1º S
Department: Estadística, Informática y Matemáticas
ASIAIN OLLO, MARÍA JOSÉ (Resp)   [Mentoring ] MILLOR MURUZABAL, NORA   [Mentoring ]

Partes de este texto:


Module/Subject matter

Module: Basic training

Subject matter: Mathematics



Vector spaces

Linear applications

Matrices and systems of linear equations

Diagonalization of square matrices

Euclidean vector space

Diagonalization of symmetric matrices

Aproximate solutions

Decompositions based of eigenvalues


General proficiencies

  • G8 Knowledge of basic and tecnological subjects to have the ability to learn new methods and theories, and versatility to adapt to new situations
  • G9 Problem solving proficiency with personal initiative, decision making, creativity and critical reasoning. Ability to elaborate and communicate knowledge, abilities and skills in computer engineering
  • T1 Analysis and synthesis ability
  • T3 Oral and written communication
  • T4 Problem solving
  • T8 Self-learning


Specific proficiencies

  • FB1 Ability to solve mathematical problems in engineering. Ability to apply theoretical knowledge on linear algebra, differential and integral calculus, numerical methods, numerical algorithms, statistics and optimization
  • FB3 Ability to understand and master the basic concepts of discrete matemathics, logic, algorithmics and computational complexity, and their applications to problem solving in engineering


Learning outcomes

  • RA1 - Solve systems of linear equations using different methods based on Matrix decompositions (LU, QR, generalized inverse).
  • RA2 - Make matrix representations of plane and space transformations, proyections, and orthogonal proyections onto subspaces
  • RA3 - Diagonalize matrices through fundamental subspaces.
  • RA4 - Use matrix diagonalization to study stochastic processes (Markov chains).
  • RA5 - Find the singular value descomposition of a given matrix and use it to approximate systems of linear equations by the pseudo-inverse matrix.
  • RA6 - Find the least-squares polynomial approximation to a function.
  • RA7 - Use some symbolic computation software such as Matlab or Mathematica.



Methodology - Activity Attendance  Self-study
A-1 Lectures 46  
A-2 Practical clases 14  
A-3 Self-study    75
A-4 Exam, evaluation tests 5  
A-5 Office hours 10  
Total 75 75




Weight (%) It allows
test resit
required grade
RA1 - RA7 Theoretical and practical exam concepts of vectorial space, linear application, matrices and systems of equations 55 Yes  
RA1 - RA7 Theoretical and practical exam concepts of values and eigenvectors, diagonalization and approximation of solutions 35 Yes  
RA1 - RA7 Tests at home and class 10 Yes  




Lesson 1.- Sets, applications and relationships. Operations. Consistencies. Definitions of ring and body.


Lesson 2.- Vector spaces. Linear combinations. Linear dependence and independence. Vector subspaces. Bases and dimensions.


Lesson 3.- Linear applications. Core and image. Construction of linear applications.  


Lesson 4.- Matrices. Elemental operations, range and form of Hermite. Matrix equivalence.  Systems of linear equations: Rouché-Frobenius theorem. Generalized inverse.


Lesson 5.- Eigenvalues and eigenvectors. Diagonalization of square matrices.


Lesson 6.- Scalar product. Norm of a vector. Angle between two vectors. Euclidean vector space.  Orthogonal and orthonormed bases. Orthogonal projection. Orthogonal matrices. Diagonalization of symmetric matrices.


Lesson 7.- Approximate solutions of a system of equations. Applications.




Access the bibliography that your professor has requested from the Library.

  • J. Hefferon, Linear Algebra, Virginia Commonwealth University Mathematics 2009
  • D. C. Lay, Linear Algebra and its applications, Pearson Education 2006
  • D. J. S. Robinson, A course in Linear Algebra with applications, World Scientific
  • R. A. Adams: Calculus. A complete course. Addison Wesley
  • Larson, Calculus of a Single Variable, 10th Edition, Brooks/Cole, Cengage Learning 2014
  • S.L. Salas, E. Hille and Etgen, Calculus, Reverté



English, Spanish and Basque.



Arrosadia campus