-> ๐๐๐ก๐ค๐๐จ ๐๐๐๐ค๐ง๐ฎ ๐๐ช๐ต๐ฉ ๐๐ช๐ฅ๐ฅ๐ฆ๐ฏ ๐๐ฐ๐ฏ๐ฏ๐ฆ๐ค๐ต๐ช๐ฐ๐ฏ๐ด ๐๐ค๐ณ๐ฐ๐ด๐ด ๐๐ข๐ต๐ฉ๐ฆ๐ฎ๐ข๐ต๐ช๐ค๐ด
Along this set of contents, we get ourselves started with the notion of extensions fields and Galois Theory properly. All results involving the Galois Correspondence Theorem are covered in these notes. Thus, having studied basic courses on Linear Algebra and Group Theory are definitely required to fully understand the topics we are discussing.
Later along the course, we talk through more advanced contents and applications of Galois Theory. Knowledge about Ring Theory is crucial to get confortable with such development.
๐You can find and download all available chapters of this course for free in the following list. Some chapters are still being written and will be published in a bit, but the basic course is definitely complete. Problem sets are also available and solutions are fully penned for the first four chapters.
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Normal and separable extensions
Galois Groups. The Fundamental Theorem of Galois Theory
Ring of Integers. An Introduction to Ramification Theory
$p-$adic Fields and Cyclotomic extensions. A first view of the local-global strategy
Several Applications to Number Theory
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Thank you very much for reading this course!
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