Teaching

I like teaching, and I really enjoy the moments when I am able to convey not only the technical results or algorithms per se, but get the core ideas and the underlying mathematical intuition across. Sometimes it seems even possible to convey such intuition assuming remarkably limited prerequisites — such as in our (mini-)courses aimed at high-school students interested in STEM. Admittedly, it is not easy to get such a group together physically, hence my special interest towards remote studies.

This page contains notes related to my teaching experience, which happens to span, roughly, undergraduate and graduate university- (including continued education), and partly high-school levels.

University-level courses

“Mathematics of Quantum Computing”

Together with Dr. Schöbel, we taught a one-semester (14 weeks) course MAT-59-15-V-7 at RPTU aimed at BSc and MSc students, where I was responsible for a half-semester worth of material (second part) called “Quantum Algorithms”, with a special emphasis on quantum optimization.

“Mathematical Foundations of Quantum Technology”

In the framework of QuanTUK project funded by BMFTR, we developed an MSc program “Quantum Technologies” for our (awesome!) Distance and Independent Studies Center (DISC). I authored two courses in the program, the second one in co-authorship with Dr. Schöbel.

The first one covered the mathematical foundations of quantum computing, including a few remarks about complex numbers, an introduction to linear algebra in the context of quantum computing, and a few further ideas specific to quantum algorithms (such as quantum teleportation, entanglement and oracle-based algorithms).

Quantum Algorithms and Quantum Optimization

The second course developed in the QuanTUK project, called “Quantum Computing Part I” in the program, zoomed in on the topics of quantum algorithms in general, and those relevant for quantum optimization in particular (including the exposition related to Adiabatic theorem, annealing, and QAOA).

Mini-courses aimed at high-school students

I have designed from scratch and delivered three mini-courses for School for Molecular and Theoretical Biology (SMTB) and Puschino Winter School. Both were aimed at (gifted) high school students and undergrads. They had nothing to do with the high school program, but I obviously needed to exercise some care with respect to prerequisites. Each course comprised four 50-minutes sessions.

“A glimpse into Algorithms.”

Summary: Introducing and illustrating some key concepts from CS using simple numerical experiments in Python. A crash-course-intro to algorithms and data structures from the computational perspective. E.g., discussing correctness starting from unit tests; asymptotic, best/worst case, and other concepts related to runtime — with measuring actual runtime in seconds using Python’s time module, etc. The purpose was to mention the key ideas, demonstrate that they are (1) not “scary”, and (2) pretty relevant to the practice, even if you are not an (aspiring) computer scientist or a programmer. (This aspect was especially relevant since majority of the students had a background in biology, but was interested in computational aspects as well.)

More details: for syllabus, a few methodological notes, and links to actual teaching materials (slides / jupyter notebooks) see 👉 here.

“Practical Introduction to Probability Theory.”

Summary: This is a theoretical course, i.e., aimed in first place to introduce and discuss the concepts of probability space, random events, independence, random variables, and some others. However, it is presented kind of “backwards”: starting from numerical experiments and trying to “reverse-engineer” the logic behind the math that we actually have in Probability theory. The ultimate goal was to build (together with the students) a usable, practical, but consistent mathematical model of random events.

More details: for syllabus, a few methodological notes, and links to actual teaching materials (slides / jupyter notebooks) see 👉 here.

“How to teach machines: simple examples on ML.”

Summary: The idea was to provide a glimpse into ML by discussing three fundamental model types: predicting a number (linear regression), predicting a yes-or-no answer (logistic regression), and predicting… whatever (neural network). Each topic included a simple numerical illustration (such as this three-node network above), and a simple-but-practically-reasonable exercise (such as handwritten number recognition with MNIST dataset, using the same logic, but more neurons and layers.)

More details: syllabus and methodological notes (including teaching materials / jupyter notebooks) are 👉 here.

Full index of other “teaching” notes

Below is a complete list of my other notes and materials related to teaching. Any feedback / suggestions / corrections are very welcome!