Course: 2024/2025

Mathematics for data analysis

(17228)

Requirements (Subjects that are assumed to be known)

Proficiency in undergraduate mathematics (Linear Algebra, in particular)

- 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

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

- Marc Peter Deisenroth, A Aldo Faisal, and Cheng Soon Ong · Mathematics for Machine Learning : https://mml-book.github.io/

Additional Bibliography

- Carl D. Meyer. Matrix Analysis and Applied Linear Algebra. SIAM. 2010
- Cleve Moler. Numerical Methods with Matlab. SIAM. 2004
- David Watkins. Fundamentals of Matrix Computations, 3rd Ed. Wiley. 2010
- James W. Demmel. Applied Numerical Linear Algebra. SIAM. 1997

(*) Access to some electronic resources may be restricted to members of the university community and require validation through Campus Global. If you try to connect from outside of the University you will need to set up a VPN

The course syllabus may change due academic events or other reasons.