MTAT.05.008 Fou Math
Mathematical Foundations for Computer Science
Role of the course
Students who want to specialize in Quantum Computer Science occasionally lack some of the math background. That is particularly true for those who want to specialize in Quantum Computer Science (quantum computing, quantum crypto), where advanced linear algebra is needed. This course is meant to fill in math background for 1st semester MSc students who want to specialize in Quantum Computing, Quantum Computer Science.
The biggest hurdle here is Linear Algebra: Outside of quantum computer science, here seems to be no other reason for a computer science student to know, e.g., complex numbers or even spectral theory (crazy, right?), so CS students' background there is often too weak for quantum stuff. Even math undergrads have learned less about tensor products of Hilbert spaces than what is needed for quantum computer science (but, of course, they can catch on quickly).
Syllabus
This is the fourth run of the course. Again, we have learned from the feedback of the students, and made changes. The choice of content is now more focused, the homework load has been reduced. With the possibility to point interested students to future Q𝚽4QCS courses, in Fou Math, quantum mechanics appears only where it motivates the math.
The content:
- Complex numbers
- Exponential function, and more complex numbers
- Real and complex Hilbert spaces, ONBs, tensor products
- Operator concept, adjoint, matrices & operators, basis change
- Commuting operators, spectral theorem and applications
- 🆕 Basics of infinite dimensional Hilbert space
Organization
PARTICIPATION
- All sessions will be streamed online, presence in the lecture hall is not required
- Everybody who is present in the lecture hall must wear a mask (except when speaking)
SPACETIME
- Class times: Mon 12:15-14:00, Thu 10:15-12:00
- Online class meetings: We will share a video conference link by email
- First class meeting: Thu, Sep 2
ONLINE
- Slides and homework assignments:
- When you have a question:
- For time-sensitive stuff (Zoom links, presentation links, ...) we use GitHub Discussions
Instructor team
- Assoc. Prof. Dirk Oliver Theis
- Evgenii Dolzhkov