eduardo.eyras [at] upf.edu

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

- 1. Vector spaces, basis and dimension.
(Exercises).

- 2. Linear maps
(Exercises)

- 3. Linear maps and matrices.
(Exercises)

- 4. Projections and Subspaces
(Exercises)

- 5. Matrices, determinants, eigenvalues and diagonalization.
(Exercises)

- 6. Singular Value Decomposition (SVD) and Principal Components Analysis (PCA).

**Optimization**

- 7. Many-valued functions and optimization.
- 8. Gradient, level surfaces and tangent hyperplanes.
- 9. Optimization with constraints.
- 10. Linear decision hyperplanes and Support Vector Machines.

Homework (to be delivered by Monday, December 5h) (Homework)

**December 14th, 11am-1pm (aula 61.325-61.327)**

- 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).