Бакалавриат
2020/2021
Введение в теорию Галуа
Лучший по критерию «Полезность курса для расширения кругозора и разностороннего развития»
Статус:
Курс по выбору (Совместный бакалавриат НИУ ВШЭ и ЦПМ)
Направление:
01.03.01. Математика
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
4-й курс, 1, 2 модуль
Формат изучения:
с онлайн-курсом
Преподаватели:
Брав Кристофер Ира
Язык:
английский
Кредиты:
5
Контактные часы:
60
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.
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 examThe exam will be written and closely based on the example problem sheets from the seminar.
- Midterm exam
- Final examThe 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
Bibliography
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