SIGTACS Lecture Series
Title: Galois Theory.
Speaker: Himanshu Shukla
Time: Wednesday 4-5 pm, Friday 5-6 pm
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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