About this Course

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Advanced Level
Approx. 27 hours to complete
English

Instructor

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

Offered by

Placeholder

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), 4 readings
2 videos
Introduction to Galois Theory2m
4 readings
About the University10m
Rules on the academic integrity in the course10m
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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