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Introduction to Galois Theory(으)로 돌아가기

HSE 대학의 Introduction to Galois Theory 학습자 리뷰 및 피드백

4.3
별점
121개의 평가
38개의 리뷰

강좌 소개

A very beautiful classical theory on field extensions of a certain type (Galois extensions) initiated by Galois in the 19th century. Explains, in particular, why it is not possible to solve an equation of degree 5 or more in the same way as we solve quadratic or cubic equations. The students shall learn to compute Galois groups and study the properties of various field extensions. We first shall survey the basic notions and properties of field extensions: algebraic, transcendental, finite field extensions, degree of an extension, algebraic closure, decomposition field of a polynomial. Then we shall do a bit of commutative algebra (finite algebras over a field, base change via tensor product) and apply this to study the notion of separability in some detail. After that we shall discuss Galois extensions and Galois correspondence and give many examples (cyclotomic extensions, finite fields, Kummer extensions, Artin-Schreier extensions, etc.). We shall address the question of solvability of equations by radicals (Abel theorem). We shall also try to explain the relation to representations and to topological coverings. Finally, we shall briefly discuss extensions of rings (integral elemets, norms, traces, etc.) and explain how to use the reduction modulo primes to compute Galois groups. A weekly test and two more serious exams in the middle and in the end of the course. For the final result, tests count 40%, first (shorter) exam 20%, final exam 40%. Do you have technical problems? Write to us: coursera@hse.ru...

최상위 리뷰

MP
2020년 7월 30일

A difficult course for me, personally, but that makes it all the more worth it! Taking this course has helped me learn more I thought I would. Definitely recommended.

F
2021년 9월 11일

Thank You Prof Ekaterina Amerik for this course. I understand with your explaination. Maybe i must study again and again for understand this material.

필터링 기준:

Introduction to Galois Theory의 38개 리뷰 중 26~38

교육 기관: petya

2018년 8월 20일

perfect

교육 기관: Hangfeng G

2020년 3월 16일

the content is rich, though a little advanced. I strongly recommend this course to others, because I personally learned a lot from it.

교육 기관: Troy W

2018년 3월 12일

The teacher is good at explaining things.

It is best you take an algebra course for prerequisite.

교육 기관: TH

2016년 3월 23일

Actually rigorous and non-trivial maths.

교육 기관: Vineet G

2016년 5월 30일

The material is very interesting, but the course goes very fast, and the presentation is dry.

교육 기관: 李宗桓

2016년 4월 24일

我对此评分不高的主要原因是因为授课太难,另外中间tensor product of modules很难又很偏。

교육 기관: Jim M

2021년 12월 27일

I would not recommend this course to anyone. Perhaps the higher ratings are from when the course was run live. As it stands as a self-paced course, the lectures are insufficient to prepare for the quizzes. There are no notes, nor are there suggested supplemental readings for each lecture. The transcripts of the videos that are provided do not capture the mathematical symbols and concepts. The quizzes have multi-selection questions that are scored all or nothing with no feedback as to which parts you got correct. I am very disappointed.

교육 기관: Musa J

2018년 1월 28일

Please show visual examples, diagrams to start with; -Class notes should be ready before class starts; first motivational examples then definitions please. https://www.youtube.com/watch?v=8qkfW35AqrQ Visual Group Theory, Lecture 6.6: The fundamental theorem of Galois theory. For now pls unenroll me from this course.

교육 기관: Corey Z

2018년 1월 25일

Very Hard to follow. She is constantly writing things while teaching. She could have written down everthing before class.

교육 기관: Ryan B

2017년 9월 11일

Not a very good or interesting course and does not use standard notation for the subject.

교육 기관: Rod B

2016년 4월 18일

Hopeless ! Less clear and understandable than simply reading a textbook.

A waste of time.

교육 기관: Maneesh N

2019년 10월 29일

Instructor is monotonous.