Galois Theory

Learn and develop an advanced understanding of Galois Theory with this course

IIT Bombay and NPTEL

About the Course

This 12-week comprehensive course covers Galois Theory, unifying various branches of mathematics and solving historically significant problems. It is designed for undergraduates, graduates, and researchers, starting with the quadratic formula and progressing to polynomials of degrees 3 and 4. Galois Theory, developed to explain the lack of formulas for polynomials of degree ≥ 5, is presented with historical insights. Classical results by Abel, Gauss, and Galois lead to a modern treatment, focusing on the solvability of polynomials. Basic knowledge of linear algebra is expected, but the course is self-contained, covering necessary fields, polynomials, and group theory. Topics include Galois extensions, finite fields, cyclic groups, and the inverse Galois problem.

Table Of Content

1.What You Will Learn?

2.Who Should Go For It?

3.Points to Note

4.Summary

What You Will Learn?

The course provides a comprehensive curriculum to dive into various aspects of Galois Theory. Here's a glimpse of the key topics covered:

Prime Factorisation in Polynomial Rings

Gauss’s Theorem

Algebraic Extensions

Group Actions

Galois Extensions

Finite Fields, Cyclic Groups

Splitting Fields

Normal and Separable Extensions

Norms and Trace

Fundamental Theorem on Symmetric

Orbits of the action of Galois group

Inverse Galois Problem

Who Should Go For It?

It is designed for individuals with a foundation in specific areas to ensure they can grasp the concepts effectively and will be an ideal choice for those undergraduate students who wish to understand and apply their knowledge of:

Undergraduate students

Graduate students

Researchers

Points To Note

The course is free of charge, making it a fantastic opportunity to gain valuable knowledge in Galois Theory

It positions mathematics enthusiasts for some of the upgraded exciting career opportunities.

Provides high-quality video lectures to enhance the learning experience thoroughly

There are four categories of certificates- Gold, Silver, Elite or Completed that a student will receive depending on his/her final score

Summary

Field of Study:	Galois Theory
Type:	Free Course
Duration:	12 Weeks
Mode of Learning:	Online
Average Salary Offered:	The average salary offered in this field ranges from ₹ 6 LPA to ₹ 25 LPA depending upon your skills, experience, and level of knowledge.
Employment Roles:	Mathematician Cryptographer Research Scientist Data Analyst Algorithm Developer

The intend of Learning Routes is to provide unbiased, precise information & comparative guidance on Universities and its Programmes of Study to the Admission Aspirants. The contents of the Learning Routes Site, such as Texts, Graphics, Images, Blogs, Videos University Logos, and other materials (collectively, 'Content') are for information purpose only. The content is not intended to be a substitute for in any form on offerings of its academia partners. Infringing on intellectual property or associated rights is not intended or deliberately acted upon. The information provided by Learning Routes on www.learningroutes.in is for general information purposes only. All information on the site is provided in good faith with accuracy and to the best of our knowledge, however, we make no representation or warranty of any kind, express or implied, regarding the accuracy, adequacy, validity, reliability, or completeness of any information on the Site. Learning Routes & its fraternity will not be liable for any errors, omissions, damages, or losses resultant, if any, from the usage of fit information.

[email protected]

Get Free Counselling

+91-9228122474