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Обычная версия сайта
2017/2018

Научно-исследовательский семинар "Выпуклая и алгебраическая геометрия 1"

Лучший по критерию «Полезность курса для расширения кругозора и разностороннего развития»
Статус: Дисциплина общефакультетского пула
Когда читается: 1, 2 модуль
Язык: английский
Кредиты: 3

Course Syllabus

Abstract

This course is aimed as an introduction to a variety of mathematical fields, which all have a common theme – convex geometry. The classes consist of either a lecture or a talk by one of the students. The students are encourage to take one of the topics from the course as a research project.
Learning Objectives

Learning Objectives

  • Acquaintance with the basic notions, methods, and problems of convex geometry.
  • Acquiring an idea of the role of convex geometry in other areas of mathematics (algebra, geometry, analysis, etc.)
  • Acquiring the skills of applying methods and constructions of convex geometry to scientific research in various areas of mathematics.
  • Acquiring the ability for independent study of topical mathematical literature.
Expected Learning Outcomes

Expected Learning Outcomes

  • Knowledge of the basic notions, methods and problems of convex geometry.
  • Skills of applying methods and construction of convex geometry in other areas of mathematics.
  • Experience in independent study of topical mathematical literature
Course Contents

Course Contents

  • Convexity and lattices
  • Smooth convex bodies
  • Convex polyhedra
  • Mixed volumes
  • Convex inequalities
  • Ehrhart polynomials
Assessment Elements

Assessment Elements

  • non-blocking Cumulative grade
  • non-blocking Final exam
    Midterm
Interim Assessment

Interim Assessment

  • Interim assessment (2 module)
    O_{current} = O_{homework}*0.8 + O_{independent works}*0.2 O_{midterm/final} = O_{current}*0.2 + O_{final exam}*0.8
Bibliography

Bibliography

Recommended Core Bibliography

  • Günter M. Ziegler. (2007). Lectures on Polytopes: Updates, Corrections, and More. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.2D793EFE
  • John R. Harper, & Richard Mandelbaum. (2011). Combinatorial Methods in Topology and Algebraic Geometry. [N.p.]: AMS. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=776570
  • Tao, T. (2013). Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1310.6482

Recommended Additional Bibliography

  • Dolgachev, I. (2012). Classical Algebraic Geometry : A Modern View. Cambridge: Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=473170