Week 0

This course produces student research papers. It gathers research teams. Each team combines a student, a consultant, and an expert. The student is a project driver who wants to plunge into scientific research activities. The graduate student consultant conducts the research and helps the student. The expert, a professor, states the problem and enlightens the road to the goal.

• A student is willing to learn to formally state research problems, find adequate references, and generate novel and significant problem-solving ideas.
• An advisor helps the student with technical issues, consults on machine learning topics, promptly reacts to arising problems, and performs evaluations and grading. Each advisor is supposed to possess sufficient publishing experience. Ideally, the advisor is writing a paper on the adjacent topic. Organizing the weekly reviewing process is recommended so that a student can input the corrections himself.
• An expert guarantees the novelty and importance of the paper, suggests the problems, and provides data.

Resources

1. Introduction video, 2024
2. Introduction update 2024
3. Youtube video
4. Motivation for students
5. Introduction for colleagues
6. Introduction for the committee

Student prerequisites

Briefly: it is for 3rd year BS students.

1. Discrete Analysis and Set Theory
2. Calculus and Mathematical Analysis
3. Probability and Statistics
4. Algebra, Group theory is welcome
5. Functional Analysis is welcome
6. General Physics is highly welcome

References to catch-up

1. Graph Theory by Reinhard Diestel, 2017
2. Lectures on Discrete Geometry by Jiří Matoušek, 2002
3. Thomas’ Calculus, based on the original work by George B. Thomas, Jr, 2010
4. Linear algebra by Jörg Liesen, Volker Mehrmann, 2015
5. Linear algebra by Jim Hefferon, 2017
6. Lie Groups, Lie Algebras, and Representations: An Elementary Introduction by Brian Hall, 2015
7. Mathematics for Physicists: Introductory Concepts and Methods by Alexander Altland and Jan von Delft, 2014
8. Mathematical Methods for Physicists by Danilo Babusci, Giuseppe Dattoli, Silvia Licciardi and Elio Sabia, 2020
9. A First Course in Probability by Sheldon Ross, 2019
10. Probability Theory by Alexandr A. Borovkov, 2009
11. Lectures on Probability Theory and Mathematical Statistics by Marco Taboga, 2012
12. Lectures on Probability Theory and Statistics by Boris Tsirelson and Wendelin Werner, 2002
13. Elements of Information Theory by Thomas M. Cover and Joy A. Thomas, 2006

Teaching materials

1. Set up this year's folder, project list template, and group table template.
2. Invite experts to put their project descriptions on the page or collect them by mail.
3. Introduce the experts and the consultants if needed (check if each project has its proper consultant).
4. Revise all project descriptions and assess feasibility and impactfulness. Does each project fit this course?