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#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 46 hours to complete

Suggested: 9 weeks of study, 4-8 hours/week...

#### English

Subtitles: English

#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 46 hours to complete

Suggested: 9 weeks of study, 4-8 hours/week...

#### English

Subtitles: English

### Syllabus - What you will learn from this course

Week
1
1 hour to complete

## Introduction

1 video (Total 3 min), 2 readings
1 video
Introduction/Manual10m
References10m
2 hours to complete

## Week 1

6 videos (Total 84 min), 1 quiz
6 videos
1.2 Algebraic elements. Minimal polynomial.12m
1.3 Algebraic elements. Algebraic extensions.14m
1.4 Finite extensions. Algebraicity and finiteness.14m
1.5 Algebraicity in towers. An example.14m
1.6. A digression: Gauss lemma, Eisenstein criterion.13m
1 practice exercise
Quiz 140m
Week
2
2 hours to complete

## Week 2

5 videos (Total 67 min), 1 quiz
5 videos
2.2 Splitting field.11m
2.3 An example. Algebraic closure.14m
2.4 Algebraic closure (continued).15m
2.5 Extension of homomorphisms. Uniqueness of algebraic closure.11m
1 practice exercise
QUIZ 240m
Week
3
4 hours to complete

## Week 3

6 videos (Total 82 min), 1 reading, 1 quiz
6 videos
3.2 Properties of finite fields.14m
3.3 Multiplicative group and automorphism group of a finite field.15m
3.4 Separable elements.15m
3.5. Separable degree, separable extensions.15m
3.6 Perfect fields.9m
1 practice exercise
QUIZ 340m
Week
4
2 hours to complete

## Week 4

6 videos (Total 91 min), 1 quiz
6 videos
4.2 Tensor product of modules14m
4.3 Base change14m
4.4 Examples. Tensor product of algebras.15m
4.5 Relatively prime ideals. Chinese remainder theorem.14m
4.6 Structure of finite algebras over a field. Examples.16m
1 practice exercise
QUIZ 440m
4.3
29 Reviews

### Top reviews from Introduction to Galois Theory

By CLJun 16th 2016

Outstanding course so far - a great refresher for me on Galois theory. It's nice to see more advanced mathematics classes on Coursera.

## Instructor

### Ekaterina Amerik

Professor
Department of Mathematics

## About National Research University Higher School of Economics

National Research University - Higher School of Economics (HSE) is one of the top research universities in Russia. Established in 1992 to promote new research and teaching in economics and related disciplines, it now offers programs at all levels of university education across an extraordinary range of fields of study including business, sociology, cultural studies, philosophy, political science, international relations, law, Asian studies, media and communicamathematics, engineering, and more. Learn more on www.hse.ru...