Galois Theory Reading Group
Book: "Field and Galois Theory" by Patrick Morandi
Download link:
>https://www.medellin.unal.edu.co/~mmtoro/doc/campos/Morandi.pdf
>http://gen.lib.rus.ec/search.php?req=morandi+galois&lg_topic=libgen&open=0&view=simple&res=25&phrase=1&column=def
Errata:
>https://wordpress.nmsu.edu/pamorand/files/2018/10/Errata.pdf
This thread is dedicated to the study of Galois theory as a group. The idea is to discuss the subject with other anons as you work through the book, whether it be doing the exercises, helping each other through tough theorems and proofs, or asking interesting questions about the material itself.
I've opted for this book since it assumes very little, and has an appendix with most of the results one needs that are perhaps more complicated. It is also crystal clear in its explanations, and the exercises are fair.
>What you will get out of this
Good knowledge of the basics of field and Galois theory that are pretty much a prerequisite for any sort of algebraic number theory, arithmetic or algebraic geometry, and perhaps some use for other fields, such as algebraic topology.
>Minimal prerequisites
1. Basic ring theory: first isomorphism theorem, ideal correspondence, prime and maximal ideals, basics of UFDs, PIDs and polynomial rings.
2. Basic group theory: cosets, normal subgroups and quotients, Lagrange's theorem, actions.
3. Basic linear algebra / vector spaces over a field: bases, dimension, rank-nullity, determinants.
Most of the above prerequisites are briefly looked at in the appendix, so might be worth to read over it first.
>Minimal objectives
Chapter 1, sections 1-5 cover all the basics of field theory and the fundamental theorem of Galois theory ~ 60 pages. Can skip the sections on purely inseparable extensions and the fundamental theorem of algebra. You should at least try to complete section 5 to get the most out of the preceding 4 chapters.
Book: "Field and Galois Theory" by Patrick Morandi
Download link:
>https://www.medellin.unal.edu.co/~mmtoro/doc/campos/Morandi.pdf
>http://gen.lib.rus.ec/search.php?req=morandi+galois&lg_topic=libgen&open=0&view=simple&res=25&phrase=1&column=def
Errata:
>https://wordpress.nmsu.edu/pamorand/files/2018/10/Errata.pdf
This thread is dedicated to the study of Galois theory as a group. The idea is to discuss the subject with other anons as you work through the book, whether it be doing the exercises, helping each other through tough theorems and proofs, or asking interesting questions about the material itself.
I've opted for this book since it assumes very little, and has an appendix with most of the results one needs that are perhaps more complicated. It is also crystal clear in its explanations, and the exercises are fair.
>What you will get out of this
Good knowledge of the basics of field and Galois theory that are pretty much a prerequisite for any sort of algebraic number theory, arithmetic or algebraic geometry, and perhaps some use for other fields, such as algebraic topology.
>Minimal prerequisites
1. Basic ring theory: first isomorphism theorem, ideal correspondence, prime and maximal ideals, basics of UFDs, PIDs and polynomial rings.
2. Basic group theory: cosets, normal subgroups and quotients, Lagrange's theorem, actions.
3. Basic linear algebra / vector spaces over a field: bases, dimension, rank-nullity, determinants.
Most of the above prerequisites are briefly looked at in the appendix, so might be worth to read over it first.
>Minimal objectives
Chapter 1, sections 1-5 cover all the basics of field theory and the fundamental theorem of Galois theory ~ 60 pages. Can skip the sections on purely inseparable extensions and the fundamental theorem of algebra. You should at least try to complete section 5 to get the most out of the preceding 4 chapters.
