I am a graduate student.My main interest throughout my student life has been in analysis.But for competitive exams like CMI,ISI,IMSc I have to strengthen my algebra also.I have a good grasp on group theory and ring theory.But the same is not true for field theory and Galois theory.ALthough I understood field theory well,I am not good at problems on field theory and also my foundation of Galois theory is not very good.So,what I want to do is learn through solving problems and do as many examples on Galois theory as possible to get hold of the key idea.Can someone suggest me some reference or stack exchange pages where there are doable but nice conceptual problems suitable for competitive exams on Galois theory and field theory,so that I can boost my confidence by solving those problems or at least attempting to solve them.
2026-04-18 23:20:31.1776554431
Problems in field and Galois theory for competitive exam.
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For the theoretical base and some good excercises i recommend you the classical I. Stewart: Galois Theory, Chapman & Hall, 2003.
In my university i used the following: J.F. Fernando, J.M Gamboa: Ecuaciones Algebraicas. Extensiones de cuerpos y teoría de Galois. Editorial Sanz y Torres, Madrid: 2015. It's and incredible book, full of tricky problems, from one of the greatest mathematicians here in my continent, but it's in spanish and i dont think you could use it.
For a guided study with great problems i recommend you Brzeziński, J. (2018). Galois Theory Through Exercises. Springer Undergraduate Mathematics Series. Springer, Cham