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Обычная версия сайта
2018/2019

Научно-исследовательский семинар "Геометрия и топология"

Статус: Дисциплина общефакультетского пула
Когда читается: 3, 4 модуль
Язык: английский
Кредиты: 5
Контактные часы: 76

Course Syllabus

Abstract

The course covers basic notions of topology such as metric spaces, smooth manifolds and fundamental group. The main focus is on concrete examples such as Riemann surfaces, projective spaces, Grassmannians. The course can serve as an introduction to more advanced geometry and topology courses.
Learning Objectives

Learning Objectives

  • The seminar is intended to give a background on contemporary geometry and topology.
Expected Learning Outcomes

Expected Learning Outcomes

  • Successful participants will be able to rigorously justify geometric heuristics, to apply methods of topology to various problems in mathematics.
Course Contents

Course Contents

  • Reminder on set theory: countable and uncountable sets, Cantor set, axiom of choice, non-measurable set.
  • Point-set topology: topological spaces, open and closed subsets, continuous functions, homeomorphism and homotopy equivalence.
  • Metric spaces, compactness, manifolds. Peano curve and Cantor staircase function.
  • Fundamental group and covering spaces, Riemann surfaces.
  • Projective spaces and Grassmannians.
Assessment Elements

Assessment Elements

  • non-blocking Cumulative grade
    cumulative grade is proportional to number of tasks solved.
  • non-blocking Final exam
Interim Assessment

Interim Assessment

  • Interim assessment (4 module)
    0.3 * Cumulative grade + 0.7 * Final exam
Bibliography

Bibliography

Recommended Core Bibliography

  • Ash, R. B. (2009). Real Variables with Basic Metric Space Topology (Vol. Dover edition). Mineola, N.Y.: Dover Publications. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1150123

Recommended Additional Bibliography

  • Allen Hatcher. (2002). Algebraic topology. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.87FE219C