About this Course

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Advanced Level
Approx. 27 hours to complete
English
Subtitles: English
Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Flexible deadlines
Reset deadlines in accordance to your schedule.
Advanced Level
Approx. 27 hours to complete
English
Subtitles: English

Offered by

National Research University Higher School of Economics logo

National Research University Higher School of Economics

Syllabus - What you will learn from this course

Week
1

Week 1

1 hour to complete

Introduction

1 hour to complete
2 videos (Total 4 min), 3 readings
2 videos
Introduction to Galois Theory2m
3 readings
About the University10m
Introduction/Manual10m
References10m
2 hours to complete

Week 1

2 hours to complete
6 videos (Total 84 min)
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

Week 2

2 hours to complete

Week 2

2 hours to complete
5 videos (Total 67 min)
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

Week 3

4 hours to complete

Week 3

4 hours to complete
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 reading
Ungraded assignment 12h
1 practice exercise
QUIZ 340m
Week
4

Week 4

2 hours to complete

Week 4

2 hours to complete
6 videos (Total 91 min)
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

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