## MTAT.05.008 Fou Math: Mathematical Foundations for Computer Science

This is the second run of the course: We have learned a lot from last year's run, and made changes to improve the learning experience.

## Content

- This course is compulsory requirement for all quantum computing courses.
- All students who specialize in Theoretical Informatics are recommended to take this course in their first graduate semester to acquire a healthy background in math.

A course giving all the mathematics that is desperately required for (theoretical and quantum) computer science (based on the U-Tartu CS bachelor curriculum) would have a work-load of 40 ECTS (estimated). The content selection in Fou Math centers on the topics which are least represented in the average (Tartu) CS master's student: Linear algebra.

I. General Theory of Vector Spaces

- Vector spaces
- Bases
- Linear mappings
- Determinants
- Eigenvalues, triangular matrices, diagonalization

II. Vector Spaces Over The Real, Complex Numbers

- Inner product spaces, norms, projectors
- Orthonormal bases and Gram-Schmidt
- Commuting operators and the spectral theorem
- Hermitian, normal, unitary, ... operators / matrices
- Positive (semidefinite) operators / matrices
- Singular value decomposition

## Organization

There will be two lecture session per week to allow for a leisurely pace with opportunity to review the missing background. Students will be required to review the material at home (if you don't spend 2h reviewing for every 90min class, you won't understand what's going on). Students will also need to read at least one of the following textbooks:

- Carl Meyer
*Matrix Analysis and Applied Linear Algebra*from Chapter 3. - Axler
*Linear Algebra Done Right* *Schaum's Outline of Linear Algebra*

Grades are given based on weekly in-class quizzes.

## Contact

- Assoc. Prof. Dirk Oliver Theis
`d o t h e i s [at] u t [dot] e e`

- TA Javier Gil Vidal
`f r a n c i s c o [dot] j a v i e r [dot] g i l [dot] v i d a l @ u t . e e`