Checking date: 26/04/2024

Course: 2024/2025

Mathematics for data analysis
(17228)
Master in Big Data Analytics (Plan: 352 - Estudio: 322)
EPI

Coordinating teacher: MOLERA MOLERA, JUAN MANUEL

Department assigned to the subject: Mathematics Department

Type: Compulsory
ECTS Credits: 3.0 ECTS

Course:
Semester:

Requirements (Subjects that are assumed to be known)
Proficiency in undergraduate mathematics (Linear Algebra, in particular)
Objectives
- Use of advanced methods of Linear Algebra for analysing big data - Understanding the fundamentals of certain algorithms used in big data, in order to interpret the results, their meaning and validity Learning results: · Deep review of basic linear algebra: linear systems, vectors and matrices, including matrix diagonalization and linear transformations · Review/Learning of orthogonality concepts in linear algebra, including orthogonal matrix diagonalization and applications · Learning of the singular value decomposition (SVD) of a real matrix, including applications
Skills and learning outcomes
Description of contents: programme
1. Matrices (a) Matrix Operations (b) Change of Basis Matrix (c) Matrix of a Linear Transformation 2. Linear Systems of Equations (a) LU factorization (b) Cholesky factorization (c) Applications: Iterative Methods 3. Diagonalization (a) Diagonalization (b) Orthogonal Diagonalization (c) The Power Method (d) Markov processes 4. Least Squares Problems (a) Data fitting (b) Orthogonal projections and Least square problems (c) QR factorization (d) Constrained LSP 5. Singular Value Decomposition (a) Singular Value Decomposition (b) The pseudoinverse (c) Principal component analysis
Learning activities and methodology
This course is in FLIPPED CLASSROOM format: - The students must visualize some videos and answer a quiz about the videos before attending the class - In the class, there'll be a review of the theoretical concepts of the videos, and some problems will be solved - The students must solve extra problems as homework Tutorials are available
Assessment System
• % end-of-term-examination 40
• % of continuous assessment (assigments, laboratory, practicals...) 60

Basic Bibliography
• Timothy Sauer. Numerical Analysis 2e. Pearson. 2012
• W. Keith Nicholson. Linear Algebra with Applications. Lyryx, Open Edition. 2021
• David C. Lay, Steven R. Lay, Judi J. McDonald. Linear Algebra and Its Applications. Pearson; 5 edition. 2016
• Lloy N. Trefethen; David Bau, III. Numerical Linear Algebra. SIAM. 1997
Electronic Resources *