eduardo.eyras [at] upf.edu

- 0. Description of the course (Slides)
**Linear Algebra**

- 1. Vector spaces, basis and dimension.
Slides.
Notes, Exercises and R practical.

- 2. Projections and Subspaces
Slides
Notes, Exercises and R practical

- 3. Matrices (determinants, rank, inverse)
(Slides)
(Notes, Exercises and R practical)

- 4. Matrices, Linear maps and change of basis
(Slides)
(Notes, Exercises and R practical).

- 5. Matrix diagonalization.
(Slides)
Notes, Exercises and R practical)

- 6. Matrix decomposition.
(Slides)
(Notes, Exercises and R practical)

**Optimization**

- 7. Many-valued functions and optimization.
(Slides)

- 8. Optimization with constraints.
(Slides)
(
Notes and Exercises for units 7 and 8)

- 9. Gradient, level surfaces and tangent hyperplanes. (Slides) ( Notes and Exercises)
- 10. Applications.
(SVM slides)
(
Notes (PCA, MDS, Least Squares, SVMs) and R practical.

Homework: (Homework)

**
December 17th, 11:00-13:00 (aula 61.226)**

Exams from previous years

- Elements of Mathematics Lecture Notes by J. Villa and P. Rue
- Linear Algebra Lectures from previous years
- Geometry lectures from previous years
- Optimization lectures from previous years
- Course on Linear Algebra. Jim Hefferon. Saint Michael's College. USA 2014.
- Calculus For Biologists: A Beginning – Getting Ready For Models and Analyzing Models. James Peterson. Gneural Gnome Press 2008.
- More Calculus For Biologists: Partial Differential Equations and Control Theory. James Peterson. Gneural Gnome Press 2009.
- Mathematics for Biologists. Kirsten ten Tusscher and Alexander Panfilov. Theoretical Biology & Bioinformatics. Utrecht University 2011.
- Chance in Biology: Using Probability to Explore Nature Mark Denny & Steven Gaines. Princeton University Press 2002. (a good basic introduction to probability and statistics in biology).
- Some notes on SVMs: Support Vector Machines Explained, Stanford Computer Science Notes.