Elements of Mathematics (MAT)

Welcome to the supporting website for the Elements of Mathematics course of the Master in Bioinformatics for Health Sciences.

Fall 2024-2025

• Vector spaces
• Matrices
• Gauss-Jordan elimination
• Linear maps (tutorial)
• Encoding and decoding with matrices
• Orthogonality
• Eigendecomposition
• Odds and ends, linear algebra exercises (hands-on)
• Functions in one variable
• Local approximation in one variable
• Orthogonal projections (tutorial)
• Functions in many variables
• Principal Component Analysis (tutorial)
• Local approximation in many variables
• Regression (tutorial)

Timetable

Check the official timetable for the fall 2024 term.

Content

Each session has its own page including a detailed syllabus and additional content to watch/read.

Sessions will have a duration of 2h with a break between 1st and 2nd hour. To make the most out of each session it would be beneficial that the students have a look at the web content of each session before the session takes place.

Aim

The sessions will serve several purposes:

1. Present fundamental concepts: definitions, examples and main theoretical results
2. Solving exercises
3. Q&A
4. Do hands-on tutorials

Evaluation

Evaluation will have two components:

1. Integrative work – at most 30% of the grade
2. Final test – at least 70% of the grade

Tests from previous courses

1. Final test - Fall 2023
2. Final test - Fall 2022
3. Final test - Fall 2021 - 1st round
4. Final test - Fall 2021 - 2nd round
5. Mid term deliverable - Fall 2019

Teachers

Ferran Muiños course coordinator. You can check his publications in mathematics and biology.

Paula Gomis will act as invited speaker and teaching assistant for the hands-on sessions.

References

Specific for this course

Introduction to Linear Algebra. Gilbert Strang.

3Blue1Brown YouTube Channel. Grant Sanderson.

Steve Brunton’s YouTube Channel. Steve Brunton.

Infinite Powers: How Calculus Reveals the Secrets of the Universe. Steven Strogatz. Houghton Mifflin Harcourt, 2019.

Somewhat related miscelanea

Yann LeCun’s Deep Learning Course at CDS. Yann LeCun, Alfredo Canziani.

Introduction to Linear Algebra for Applied Machine Learning with Python. Pablo Cáceres.

A friendly introduction to linear algebra for Machine Learning. Tai Danae Bradley. TensorFlow ML Tech Talks.

The Art of Linear Algebra. Kenji Hiranabe.