Galois Theory Intro Cut Short - Seeking Resources

In summary, the speaker was taking a lecture series on introductory Galois theory at their school, but the course abruptly ended after only a few lectures. They were disappointed and looking for online resources or someone to help them continue their learning. Another person suggested Mathwonk's website as a helpful resource for abstract algebra.
  • #1
Kindayr
161
0
I was taking a lecture series this summer at my school where a professor was introducing us to introductory Galois theory. It was a very 'slack' introduction, without too much rigour. However, about a month in (only 3-4, 3 hr lectures) they stopped due to outstanding circumstances.

I was a little upset due to how the course basically got my juices flowing for Galois theory and 'tougher' algebra.

I was wondering if anyone had some online resources, or was even willing to walk me through it here in this thread out of interest.

We had started from basically nothing (it was not expected to have any experience in group, ring or field theory). We had just began to discuss ideals before its abrupt end.

Anything anyone has to offer is awesome, conceptual or rigourous.

Thanks ahead :)
 
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  • #3
Whoa, that's exactly what I was looking for, perfect :)


Thanks
 

1. What is Galois Theory?

Galois Theory is a branch of mathematics that studies the symmetries and structure of solutions to polynomial equations. It explores the connections between fields, which are sets with mathematical operations like addition and multiplication, and their corresponding groups, which are sets with operations like composition and inversion.

2. Why is Galois Theory important?

Galois Theory is important because it provides a powerful framework for understanding and solving polynomial equations. It also has applications in other areas of mathematics, such as topology and number theory. Additionally, Galois Theory has connections to physics and computer science, making it a valuable tool in many fields.

3. What are some key concepts in Galois Theory?

Some key concepts in Galois Theory include fields, groups, subfields, and Galois extensions. Other important concepts include Galois groups, normal subgroups, and fixed fields. Understanding these concepts is essential for applying Galois Theory to solve problems.

4. What are some resources for learning Galois Theory?

There are many resources available for learning Galois Theory, including textbooks, online courses, and lecture notes. Some popular textbooks include "Galois Theory" by Ian Stewart and "Abstract Algebra" by David Dummit and Richard Foote. For online resources, websites such as Khan Academy and Math Stack Exchange offer free lessons and practice problems. Additionally, many universities offer courses on Galois Theory as part of their mathematics curriculum.

5. How can I apply Galois Theory to real-world problems?

Galois Theory has applications in various fields, including physics, cryptography, and coding theory. For example, Galois Theory can be used to analyze the symmetries of geometric objects in physics, to design secure encryption algorithms in cryptography, and to construct error-correcting codes in coding theory. Understanding Galois Theory can also improve problem-solving skills and critical thinking abilities, making it a valuable tool for any scientist.

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