TEW Rings and Fields, Complex Analysis, Geometry of Curves (2016) - Speakers and Syllabus

Brief description about the Workshop

Three minicourses will be held on the following topics. Apart from this, there will be expository talks on some special topics.

  • Mini-course in Algebra (Rings and Fields) - 6 lectures
  • Mini-course in Complex analysis - 6 lectures
  • Mini-course in Geometry of curves - 6 lectures

Total number of lectures - 18
Duration of each lecture - 1 hour and 15 minutes.
Tutorial session will be conducted everyday. The aim is to prepare the participants for teaching similar courses in their college curriculum.

Names of resource persons:

1. Samik Basu, Ramkrishna Vivekananda University, Belur

2. Somnath Basu, Ramkrishna Vivekananda University, Belur

3. Subrata Shyam Roy, Indian Institute of Science Education and Research, Kalyani

4. Shibananda Biswas, Indian Institute of Science Education and Research, Kalyani

5. Mrinal kanti Das, Indian Statistical Institute, Kolkata

6. Soumi Tikader, Indian Statistical Institute, Kolkata

 Syllabus and Time-table

1. Algebra (Rings and Fields) Mon-Sat (4-9 January, 2016): 10:00 - 11:15 am.

  • Main speaker: Mrinal kanti Das, ISI, Kolkata - (6 lectures)Definitions of rings and fields; ideals and quotient ring; ring homomorphisms and isomorphism theorems for rings; prime and maximal ideals; integral domains; characteristic; field of fractions; Euclidean domains; unique factorisation domains; principal ideal domains; polynomial rings. Field extensions, splitting fields, algebraic closure, separability, normal extensions. Finite fields: structure of finite fields; existence and uniqueness theorems; primitive elements; minimal polynomials of elements; irreducible and primitive polynomials.
  • Tutorial : Tuesday and Friday 3:45 - 5:00 PM
  • Tutor: Soumi Tikader, ISI, Kolkata.

2. Complex analysis Mon-Sat (4-9 January, 2016): 11:45 AM - 1:00 PM.

  • Main speakers: Subrata Shyam Roy and Shibananda Biswas, IISER, Kalyani(6 lectures)Holomorphic functions and the Cauchy-Riemann equations, Power series, Functions defined by power series as holomorphic functions, Complex line integrals and Cauchy’s theorem, Cauchy’s integral formula. Representations of holomorphic functions in terms of power series. Liouville’s theorem, Zeros of analytic functions, The fundamental theorem of algebra.
  • Tutorial : Monday and Thursday 3:45 - 5:00 PM
  • The speakers will conduct the tutorial classes without any tutor.

3. Geometry of curves Mon-Sat (4-9 January, 2016): 2:00 - 3:15 PM

  • Main speakers: Somnath Basu and Samik Basu, Ramkrishna Vivekananda University, Belur (6 lectures)Parametrized curves, re-parametrization. Regular and singular points of a parametrized curve. Curvature and torsion for space curves. Serret-Frenet formula for space curves.Existence theorem for space curves with prescribed curvature and torsion. Isoperimetric inequality; Four Vertex Theorem.
  • Tutorial : Wednesday and Saturday 3:45 - 5:00 PM
  • The speakers will conduct the tutorial classes without any tutor.