# SIGTACS Lecture Series

**Title:** Galois Theory.

**Speaker:** Himanshu Shukla

**Time:** Wednesday 4-5 pm, Friday 5-6 pm

**Venue:** KD103

**Abstract:**

Galois theory is one of the most important theories in pure mathematics
which has found its high importance in computational number theory and
also in program analysis as per the recent researches in program analysis.
As there were people in CS203B courses who were interested in learning
higher algebra and also because I myself want to recapitulate all the
concepts that I learnt in the course MTH602A (Algebra 2), and the best way
to learn anything is to teach it. Hence, I want to take a series of
lectures on Galois theory in sigtacs. In this I want to cover up the
following:
1) Few theorems on Field theory
2) Few theorems on Ring theory involving characters, norm and trace
3) Galois correspondence theorem
4) Cyclotomic Extensions
5) Compass and Divider constructions
6) Proof of Abel Rufini theorem (only sketch, if time permits, I can go on
to prove the complete theorem)
7) Infinite Galois group (just the idea) and the failure of Galois
correspondence in this case and its importance (Proof of Fermat's last
theorem due to Prof. Andrew Wiles)

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