## MTAT.05.008 Fou Math

## Mathematical Foundations for Computer Science

REMOTE PARTICIPATION This semester, the course will be organized with Covid-19-20-21 travel restrictions in mind. To make online participation as smooth and inclusive as possible, classes (with the local students present) will be life streamed, with the goal to engage remote participants on the same level as local ones with communication in both directions. Help from the local students will be necessary to make that happen.

*If you're a student admitted to the University of Tartu, and you cannot enter Estonia:*

**No problem!**### Role of the course

This course is meant to fill in math background for 1st semester MSc students who want to specialize in Quantum Computing, Quantum Cryptography or Theoretical Informatics. The biggest hurdle there turns out to be Linear Algebra: Other than quantum computer science, here seems to be no other reason for a computer science student to know, e.g., complex numbers or spectral theory, so students' background there is weak, unless they have an undergraduate degree in mathematics. However, even math undergrads have learned less about tensor products of vector spaces than what is required for quantum computer science.

Apart from Linear Algebra, the course also covers some of the math needed for Cryptology that students usually know (but there are always some exceptions): Modular arithmetic and probability.

##### Quantum Computing

For students who want to specialize in quantum computing, it is ** highly** recommended to also take the 3 ECTS course

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*LTFY.04.010 Introduction to Quantum Computing*

at the Physics Institute in this fall. There, the focus is on programming quantum computers (e.g., IBM Quantum Experience), and all required quantum mechanics background will be taught.

### Syllabus

This is the third run of the course. Again, we have learned from the feedback of the students, and changes. Students where overwhelmed with the amount of material, so we reduced it. Moreover, we changed our didactic approach: We will include programming homework which will ask students to code the many algorithmic but abstract mathematical concepts.

The content consist of three fields:

##### I. Linear Algebra

- Complex numbers & matrices
- Real and complex Hilbert spaces
- Operator concept, adjoint
- Spectral theorem and applications
- Tensor products
- Determinants and more tensor products

##### II. Probability

##### III. Modular arithmetic

The fields are taught in an "interleaved" way so that there is sufficient time for students to digest completely new material over a couple of weeks through homework problems. E.g., we start with complex numbers & matrices, and then move to probability while students continue to practice complex number arithmetic in the homework assignments.

Note: Tensor products, tensor networks, TensorFlow are three very, very different things.

### Organization

- Access to assignments & slides: Send your GitHub id to Bahman
- Class times: Mon 12:15-14:00, Thu 14:15-15:45
- Online class meetings: We will share a video conference link for every class by email
- Physical class meetings: Delta room 1022
- Repository for homework assignments & slides: dojt/Fou-Math-2020
- Online discussion forum: Issues on GitHub
~~Fou Math (MTAT.05.008a) on Piazza (which sucks)~~ - Slides: GitHub

### Instructor team

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

- Bahman Ghandchi
`b [dot] g h a n d c h i [at] g m a i l [dot] c o m`