Galois Theory: Textbook recommendations?

In summary: L. GriffithsIn summary, a reader has been studying "A book of Abstract Algebra" by Charles C. Pinter for two years, and is now looking for a book on Galois theory for their next project. They have received a recommendation for "Galois Theory (Second Edition)" by David Cox.
  • #1
Kiwi1
108
0
I have been working my way through the book "A book of Abstract Algebra" by Charles C. Pinter. By the time I get to the end it will have taken me 2 years of self study, solving every exercise during my daily commute. A great little book!

The last two chapters are titled:

Chapter 32: Galois Theory: The heart of the matter
Chapter 33: Solving equations by radicals

Can anyone recommend a book on Galois theory for me to choose as my next "project"? If you happen to know Pinter's book even better because it really suits my style and is at a good level for me.
 
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  • #2
Hi Kiwi,

You might enjoy "Galois Theory" by Emil Artin and "Galois Theory for Beginners: A Historical Perspective" by Jorg Bewersdorff.
 
  • #3
Kiwi said:
I have been working my way through the book "A book of Abstract Algebra" by Charles C. Pinter. By the time I get to the end it will have taken me 2 years of self study, solving every exercise during my daily commute. A great little book!

The last two chapters are titled:

Chapter 32: Galois Theory: The heart of the matter
Chapter 33: Solving equations by radicals

Can anyone recommend a book on Galois theory for me to choose as my next "project"? If you happen to know Pinter's book even better because it really suits my style and is at a good level for me.
Hi Kiwi ...A possible text would be ...Galois Theory (Second Edition) by David Cox (Wiley 2012)I have only just purchased the book ... but at first glance it looks pretty good ...Peter
 

1. What is Galois Theory and why is it important?

Galois Theory is a branch of mathematics that studies field extensions, which are algebraic structures that generalize the concept of numbers. It is important because it provides a powerful tool for understanding and solving polynomial equations, which have applications in various fields such as cryptography, coding theory, and physics.

2. What are some recommended textbooks for learning Galois Theory?

Some popular textbooks for learning Galois Theory include "Galois Theory" by Emil Artin, "Field and Galois Theory" by Patrick Morandi, and "Galois Theory" by David Cox. It is also recommended to have a strong foundation in abstract algebra before diving into Galois Theory.

3. Are there any online resources for learning Galois Theory?

Yes, there are many online resources available for learning Galois Theory. Some popular ones include lectures and videos on YouTube, online courses on platforms like Coursera and edX, and lecture notes and exercises on university websites.

4. Is Galois Theory difficult to understand?

Galois Theory can be challenging for beginners, but with patience and a strong foundation in abstract algebra, it can be comprehensible. It is a highly abstract and theoretical topic, so it is important to have a good understanding of the underlying concepts and definitions.

5. What are some real-world applications of Galois Theory?

Galois Theory has various applications in cryptography, coding theory, and algebraic geometry. It is also used in the study of finite fields, which have applications in computer science and engineering. Additionally, Galois Theory has connections to other branches of mathematics such as number theory and group theory.

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