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Course11110614549 lectures

Introduction to Galois Theory

Prof. Krishna Hanumanthu · Chennai Mathematical Institute

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Motivation and overview of the course Video
  2. Review of group theory Video
  3. Review of ring theory I Video
  4. Review of ring theory II Video
  5. Review of field theory I Video
  6. Review of field theory II Video
  7. Review of field theory III Video

Week 2

  1. Problem Session 1 Video
  2. Problem Session 2 Video
  3. Beginning of Galois theory Video
  4. Fixed fields Video
  5. Theorem I on fixed fields Video
  6. Theorem II on fixed fields Video

Week 3

  1. Galois extensions, Galois groups Video
  2. Normal extensions Video
  3. Problem Session - Part 3 Video
  4. Problem Session - Part 4 Video
  5. Separable extension - Part 1 Video
  6. Separable extension - Part 2 Video

Week 4

  1. Characterization of Galois extensions - Part 1 Video
  2. Characterization of Galois extensions - Part 2 Video
  3. Examples of Galois extensions Video
  4. Motivating the main theorem of Galois theory Video
  5. Main theorem of Galois theory - Part 1 Video
  6. Main theorem of Galois theory - Part 2 Video
  7. Fundamental theorem of algebra Video

Week 5

  1. Problem Session - Part 5 Video
  2. Problem Session - Part 6 Video
  3. Problem Session - Part 7 Video
  4. Problem Session - Part 8 Video
  5. Problem Session - Part 9 Video
  6. Kummer extensions - Part 1 Video

Week 6

  1. Kummer extensions - Part 2 Video
  2. Kummer extensions - Part 3 Video
  3. Cyclotomic extensions - Part 1 Video
  4. Cyclotomic extensions - Part 2 Video
  5. Solvability by radicals Video
  6. Characterizations of solvability - Part 1 Video

Week 7

  1. Characterizations of solvability - Part 2 Video
  2. Discriminants, Galois groups of polynomials Video
  3. Quartics are solvable Video
  4. Solvable groups - Part 1 Video
  5. Solvable groups - Part 2 Video
  6. Solvable groups - Part 3 Video

Week 8

  1. Insolvability of quintics Video
  2. Problem Session - Part 10 Video
  3. Problem Session - Part 11 Video
  4. Problem Session - Part 12 Video
  5. Problem Session - Part 13 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
Chennai Mathematical Institute
Department
Mathematics
Teacher
Prof. Krishna Hanumanthu
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
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