Curriculum | GROUPS AND RINGS (Code-09050502)

GROUPS AND RINGS (Code-09050502)

S.No. Content of the topics Learning       Objectives Teaching Guidelines Methodology Time                         (Hours)
1 1.Definition of a group with example and simple properties of groups Student will be able to understand the concept groups, subgroups and normal groups Lecture should be effective so that student will be able to grasp the topics easily Assignments/Seminars/ Class Tests/ Presentations 10
2.Subgroups and subgroup criteria
Generation of groups, cyclic groups
3.Cosets, Left and right cosets
4.Index of a sub-group, Coset decomposition
5.Lagrange’s theorem and its consequences
6.Normal subgroups, Quotient groups
2 1.Homomorphisms, isomorphisms Student will be able to understand homomorphism Lecture should be effective so that student will be able to grasp the topics easily Assignments/Seminars/ Class Tests/ Presentations 15
2.Automorphisms and inner automorphisms of a group
3.Automorphisms of cyclic groups
4.Permutations groups, even and odd permutations
5.Alternating groups
6.Cayley’s theorem
7.Centre of a group and derived group of a group
3 1.Introduction to rings, subrings Student will be able to understand study of rings and ideals Lecture should be effective so that student will be able to grasp the topics easily Assignments/Seminars/ Class Tests/ Presentations 15
2.Integral domains and fields
3.Characteristics of a ring, Ring homomorphisms
4.Ideals(principle, prime and Maximal) and Quotient rings
5.Field of quotients of an integral domain
4 1.Euclidean rings Student will study about the  polynomial rings                                                         Lecture should be effective so that student will be able to grasp the topics easily Assignments/Seminars/ Class Tests/ Presentations 12
2.Polynomial rings
3.Polynomials over the rational field
4.The Einstein’s criterion
5.Polynomial rings over commutative rings
6.Unique factorization domain
7.R unique factorization domain implies so is R[X1,X2,…XN]
Admission Open- 2018