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Regular version of the site
Master 2023/2024

Research seminar "Introduction to the theory of knots"

Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'
Category 'Best Course for New Knowledge and Skills'
Type: Compulsory course (Mathematics)
Area of studies: Mathematics
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
Contact hours: 42

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

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

Expected Learning Outcomes

  • solve typical problems and able to explain the solution
Course Contents

Course Contents

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

Assessment Elements

  • non-blocking доклад
  • non-blocking In-class assignment
Interim Assessment

Interim Assessment

  • 2023/2024 2nd module
    0.2 * In-class assignment + 0.4 * доклад + 0.4 * доклад
Bibliography

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