1) Going up theorem, Going down theorem and related topics ; 2) Euclidean domain, Principle ideal domain, Unique factorization domain and related topics ; 3) Cauchy theorem and integral formula, power series representation, classification of singularities and related topics ; 4) Open mapping theorem, Principle of Uniform Boundedness and related topics. ; 5) Tychonoff’s theorem and related topics ; 6) Bilinear form, Hermitian form, Quadratic form and related topics ; 7) Radical Extension and related topics (Guest Lecture Series for M.Sc.Mathematics Students)
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