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Regular version of the site
2021/2022

Research Seminar "Topology I"

Category 'Best Course for Career Development'
Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'
Category 'Best Course for New Knowledge and Skills'
Type: Optional course (faculty)
When: 1, 2 module
Open to: students of one campus
Instructors: Christopher Ira Brav
Language: English
ECTS credits: 6
Contact hours: 60

Course Syllabus

Abstract

Topology studies a fairly general notion of space equipped with a notion of closeness. It is of importance in geometry and analysis. The course covers basic point-set topology, the classification of surfaces, and the theory of fundamental groups and covering spaces.
Learning Objectives

Learning Objectives

  • The lectures cover basis material and examples, while the seminars allow students to more deeply explore the theory and examples.
Expected Learning Outcomes

Expected Learning Outcomes

  • Students will become fluent in the basic notions of topology and will gain experience in the oral and written presentation of mathematics.
Course Contents

Course Contents

  • Basic point-set topology
  • Properties of topological spaces
  • Constructions of topological spaces
  • Fundamental groups and covering spaces
  • Classification of surfaces
Assessment Elements

Assessment Elements

  • non-blocking Midterm exam
  • non-blocking Final Exam
  • non-blocking Seminar participation
Interim Assessment

Interim Assessment

  • 2021/2022 2nd module
    0.2 * Seminar participation + 0.4 * Final Exam + 0.4 * Midterm exam
Bibliography

Bibliography

Recommended Core Bibliography

  • Наглядная топология, Прасолов, В. В., 2006

Recommended Additional Bibliography

  • Brown, R. (2006). Chapter 9: Computation of the fundamental groupoid: 9.1 The Van Kampen theorem for adjunction spaces. In Topology & Groupoids (pp. 339–352). Ronald Brown.