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Galois Theory

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arxiv 2408.07499 v1 pith:AHNEYLCF submitted 2024-08-14 math.NT math.ACmath.RA

Tom Leinster This is my paper · ORCID
classification math.NTmath.ACmath.RA
keywords theorygaloisgroupsnotessolvablealgebraassumingbasic
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These are the notes for an undergraduate course at the University of Edinburgh, 2021-2023. Assuming basic knowledge of ring theory, group theory and linear algebra, the notes lay out the theory of field extensions and their Galois groups, up to and including the fundamental theorem of Galois theory. Also included are a section on ruler and compass constructions, a proof that solvable polynomials have solvable Galois groups, and the classification of finite fields.

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  1. An introduction to the algebra of rings and fields

    math.RA 2025-07 unverdicted novelty 2.0 of 10

    A freely licensed undergraduate textbook covering rings, modules, polynomial rings, finite fields, quadratic reciprocity, Gröbner bases, and Smith normal form, with over 200 exercises.

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