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Магистратура 2020/2021

## Введение в теорию Галуа

Статус: Курс по выбору (Математика)
Направление: 01.04.01. Математика
Когда читается: 2-й курс, 1, 2 модуль
Формат изучения: с онлайн-курсом
Охват аудитории: для всех кампусов НИУ ВШЭ
Преподаватели: Брав Кристофер Ира
Прогр. обучения: Математика
Язык: английский
Кредиты: 5

### Course Syllabus

#### Abstract

Galois theory is the study of roots of polynomials and their symmetries in terms of Galois groups. As the algebraic counterpart of the fundamental group of topology, the Galois group is an essential object in algebraic geometry and number theory.

#### Learning Objectives

• The seminar is intended to introduce the subject area to the students, and to offer them the opportunity to work through many concrete examples and applications.

#### Expected Learning Outcomes

• Successful participants will develop facility in applying ideas

#### Course Contents

• Review of polynomial rings and more general principal ideal domains.
• Extensions of fields, algebraic and transcendental
• Splitting fields of polynomials and Galois groups.
• The fundamental theorem of Galois theory
• Computing Galois groups
• Applications

#### Assessment Elements

• Midterm exam
• Final exam
The exam will be written and closely based on the example problem sheets from the seminar.
• Midterm exam
• Final exam
The exam will be written and closely based on the example problem sheets from the seminar.

#### Interim Assessment

• Interim assessment (2 module)
40% midterm; 60% final. Final mark: round percent/10 to nearest integer

#### Recommended Core Bibliography

• Instructor Luís Finotti, Textbook D. Dummit, R. Foote, & Abstract Algebra. (n.d.). Math 551: Modern Algebra I – Fall 2007. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.1CEBE666

#### Recommended Additional Bibliography

• Emil Artin. (2007). Algebra with Galois Theory. [N.p.]: AMS. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1495050