Public University of Navarre



Academic year: 2021/2022 | Previous academic years:  2020/2021  |  2019/2020  |  2018/2019  |  2017/2018 
Bachelor's degree in Computer Science at the Universidad Pública de Navarra
Course code: 250101 Subject title: MATHEMATICS I
Credits: 6 Type of subject: Basic Year: 1 Period: 1º S
Department: Estadística, Informática y Matemáticas
Lecturers:
ASIAIN OLLO, MARÍA JOSÉ (Resp)   [Mentoring ] MILLOR MURUZABAL, NORA   [Mentoring ]

Partes de este texto:

 

Module/Subject matter

Module: Basic training

Subject matter: Mathematics

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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

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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

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Learning outcomes

At the end of this course students will be able to

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

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Methodology

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

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Relationship between formative activities and proficiencies/learning outcomes

Proficiency Activities
G8 A-1, A-2, A-3, A-5
G9 A-1, A-2, A-3, A-5
FB1 A-1, A-2, A-3, A-4, A-5
FB3 A-1, A-2, A-3, A-5
T1 A-1, A-2, A-3, A-5
T3   A-1, A-2, A-4
T4   A-2, A-4, A-5
T8 A-2, A-3

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Languages

English

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Evaluation

Learning outcome Evaluation procedure Weight (%) Recoverable
All  in-class work  20  Yes
All  exams  80  Yes

 

 

Contents Criteria Evaluation procedures Weight (%)
Theoretical and practical contents Key concepts identification and understanding of theoretical and operational knowledge of the subject.  Theoretical-practical exams 80% 
Competence for analysis and synthesis. 
Practical application of knowledge. 
Proper response in time, form and content suitability.
Theoretical-practical exams Practical application of knowledge. Individual tests performed during the course  20%
Creativity, ability to analyse and synthesise

 

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Contents

Vector Spaces
Bases and dimension.
Linear Transformations. Matrix associated to a linear transformation.
Diagonalization of matrices.
Orthogonal matrices.

Functions of a real variable.
Approximation of functions by polynomials.

Integration of functions of one real variable.
Applications.

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Agenda

Unit 1.- Sets, applications and relationships. Operations. Congruences. Definition of ring and body.

Unit 2.- Vector spaces. Linear combinations. Linear dependence and freedom. Vector subspaces. Supports and dimensions.

Unit 3.- Linear applications. Kernel and image. Construction of linear applications.

Unit 4. Subject- Matrices. Hermit basic operations, rank and form. Matrix equivalence. Systems of linear equations: Rouché-Frobenius theorem. Generalized reverse.

Unit 5.- Eigenvalues and vectors. Diagonalization of square matrices.

Unit 6.- Scalar product. Vector norm. The angle between two vectors. Euclidean vector space. Orthogonal and orthonormal bases. Orthogonal projection. Orthogonal matrices. Symmetric matrix diagonalization.

Unit 7.- Approximate solutions of the system of equations. Applications.

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Bibliography

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


  • D. R. Guichard and others, Calculus, http://www.whitman.edu/mathematics/california_calculus/
  • J. Hefferon, Linear Algebra,http://joshua.smcvt.edu/linearalgebra
  • R. Larson and B. Edwards, Calculus of a Single Variable, Brooks/Cole Cengage Learning 2014
  • D. C. Lay, Linear Algebra and its applications, Addison Wesley 2012
  • G. Strang, Linear Algebra and its applications, Thomson 2006
  • G. Strang, Calculus, Wellesley-Cambridge Press

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