Master 2024/2025

Research seminar "Introduction to the theory of knots"

Type: Compulsory course (Mathematics)

Area of studies: Mathematics

Delivered by: Department of Fundamental Mathematics

Where: Faculty of Informatics, Mathematics, and Computer Science (HSE Nizhny Novgorod)

When: 2 year, 1, 2 module

Mode of studies: offline

Open to: students of all HSE University campuses

Instructors: Elena Gurevich

Master’s programme: Mathematics

Language: English

ECTS credits: 6

Course Syllabus

Abstract

The discipline is taught in the second year of the master's degree. It is aimed at an introduction to the theory of knots.

Learning Objectives

• The aim of the course is to introduce the notion of a knot and its properties, as well as to dive into some important aspects of homotopy theory with the help of this notion.

Expected Learning Outcomes

• solve typical problems and able to explain the solution

Course Contents

• Inavriants of knots and links in S^3
• Knots in R^4
• Knots in dynamics

Assessment Elements

• доклад
• контрольная работа

Interim Assessment

• 2024/2025 2nd module
  0.1 * доклад + 0.7 * доклад + 0.2 * контрольная работа

Bibliography

Recommended Core Bibliography

• A combinatorial introduction to topology, Henle, M., 1994
• Dynamical Systems on 2- and 3-Manifolds, XXVI, 295 p., Grines, V. Z., Medvedev, T. V., Pochinka, O. V., 2016
• The geometry and physics of knots, Atiyah, M., 2004
• Topology, Munkres, J. R., 2000

Recommended Additional Bibliography

• Differential topology, Hirsch, M. W., 1976

Authors

• POCHINKA OLGA VITALEVNA
• GUREVICH ELENA YAKOVLEVNA
• NOZDRINOVA ELENA VYACHESLAVOVNA