Research Seminar "Number Theoretic and Algebraic Methods in Data Analysis"

2024/2025

Academic Year

ENG

Instruction in English

6

ECTS credits

Delivered at:

School of Data Analysis and Artificial Intelligence

Course type:

Compulsory course

When:

1 year, 3, 4 module

Instructor

Frolenkov, Dmitry

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

Course Contents

• The basics of arithmetic
• Cryptography basics
• Cryptography

Assessment Elements

• Test1
• Экамен
• Presentation
• Discussion
• Written Report

Interim Assessment

• 2024/2025 4th module
  0.5 * Test1 + 0.5 * Экамен
• 2025/2026 2nd module
  Presentation*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

Authors

• FROLENKOV DMITRIY ANDREEVICH
• Антропова Лариса Ивановна