Master
2024/2025
Research Seminar "Number Theoretic and Algebraic Methods in Data Analysis"
Type:
Compulsory course (Data Science)
Area of studies:
Applied Mathematics and Informatics
Delivered by:
School of Data Analysis and Artificial Intelligence
Where:
Faculty of Computer Science
When:
1 year, 3, 4 module
Mode of studies:
offline
Open to:
students of one campus
Instructors:
Dmitry Frolenkov
Master’s programme:
Data Science
Language:
English
ECTS credits:
6
Course Syllabus
Abstract
The discipline goal is to develop students' professional skills in applied fields of the computer science. The course is devoted to the study of number theory and its applications in computer science, mainly in cryptography.The course is aimed at the formation and development of theoretical-numerical thinking, as well as the understanding of the fundamental concepts of number theory and the ways in which they can be used in cryptography.
Learning Objectives
- The discipline goal is to develop students' professional skills in number theory and cryptography.
Expected Learning Outcomes
- Students will develop skills in formalizing and solving applied problems using the methods of Discrete Mathematics.
- Students will gain an understanding of Linear congruences and Diophantine equations.
- Students will gain an understanding of Modular arithmetic.
- Students will gain an understanding of several major theorems in discrete mathematics (Euler's theorem, Fermat's little theorem, Chinese remainder theorem).
- Students will gain an understanding of the Euclidean algorithm.
- Students will gain an understanding of the Fundamental theorem of arithmetics.
- Students will gain an understanding of the Induction principle.
- Students will master basic concepts and methods of Discrete Mathematics as far as these are necessary for studying more advanced courses and for the future professional life.
- A student is able to explain the main concept of cryptographic methods of information security
Interim Assessment
- 2024/2025 4th module0.5 * Test1 + 0.5 * Test1 + 0.5 * Экамен + 0.5 * Экамен
- 2025/2026 2nd modulePresentation*0.4 + Discussion*0.5 + Written Report *0.1
Bibliography
Recommended Core Bibliography
- Discrete mathematics, Biggs, N. L., 2004
- Introduction to cryptography, Buchmann, J., 2004
- J.H. Silverman, Jill Pipher, Jeffrey Hoffstein. An Introduction to Mathematical Cryptography. Springer-Verlag New York 2008
Recommended Additional Bibliography
- Lovász, L., Pelikán, J., & Vsztergombi, K. (2003). Discrete Mathematics : Elementary and Beyond. New York: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=108108