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Effectively write abstract mathematical proofs in a clear and logical manner.
Locate and use theorems to solve problems in number theory and theory of polynomials over a field.
Demonstrate ability to think critically by interpreting theorems and relating results to problems in other mathematical disciplines.
MODULE – I (6hr+0hr+2hr)
Another Counting Principle, Sylow’s Theorems.
Project 1 : A Notes on the Proof of the Sylow Theorem
MODULE – II (6hr+0hr+2hr)
Introduction to Ring, Some special classes of ring, Ring homomorphisms.
Project 2: A study on ring theory and it’s property
MODULE – III (3hr+0hr+2hr)
More Ideals and Quotient Rings, The Field of Quotients of an Integral Domain.
Project 3: The Quotient Field of an Intersection of Integral Domains
MODULE – IV (4hr+0hr+2hr)
Euclidean Rings, A Particular Euclidean Ring, Polynomial Rings.
Project 4: On the Existence of a Euclidean Algorithm in Number Rings with Infinitely Many Units
MODULE – V (4hr+0hr+0hr)
Polynomial Rings over the Rational Field, Polynomial Rings over Commutative Rings.
MODULE – VI (3hr+0hr+2hr)
Extension Fields, Roots of polynomials
Project 5: A study on Structure of a Finite Field
MODULE – VII (4hr+0hr+2hr)
Elementary Basic Concepts of Vector Space, Linear Independence and Basis, Dual Spaces, Inner Product Spaces
Project 6: Notes on dual spaces
Topics in Algebra – I. N. Herstein (John Wiley and Sons or Vikas Publication), 2nd Edition
Chapters: 2 (2.11 to 2.12), 3 (3.1 to 3.11), 4 (4.1 to 4.4), 5(5.1 and 5.3)
BOOKS FOR REFERENCE
Mr. Satyabrata Sadangi has received his M.Sc. (Mathematics) from National Institute of Technology(NIT) Rourkela, Orissa, India and B.Ed. from PRSU University, C.G, India. Mr. Sadangi has more than ten years of teaching experience in different educational institutes. Presently he is working as an Assistant Professor, Department of Mathematics, School of Applied Sciences, Centurion University of […]