Page 82 - CatalogNEP-PS

Conjugacy and G-Sets. Normal Series, Solvable Groups, Nilpotent Groups, Direct Products,
Finitely Generated Abelian Groups, Invariants of a Finite abelian Groups, Sylow Theorems,
2
Groups of Orders , .
UNIT II (15 Hours)

Definition and Examples of Rings, Some Special Classes of Rings, Homomorphisms, Ideals and
Quotient Rings, More Ideals and Quotient Rings and The Field of Quotients of an Integral
Domain. Euclidean Rings, a Particular Euclidean Ring, Polynomial Rings, Polynomials over the
Rational Field, Polynomial Rings over Commutative Rings.

UNIT III (15 Hours)
Definition and examples, Submodules and direct sums, homomorphisms and quotient modules,
completely reducible modules, Free modules.

*TUTORIAL (15 Hours (1 Hour per week))

SUGGESTED READINGS:

nd
1. P.B. Bhattacharya, S.K. Jain & S.R. Nagpal, Basic Abstract Algebra, 2 Edition,
Cambridge University Press.
2. I.N. Herstein, Topics in Algebra, Second Edition), John Wiley & Sons, New York.
3. Kenneth Hoffman & Ray Kunze, Linear Algebra, Second Edition, Prentice-Hall of India
Private Limited, New Delhi.

Math.413 Ordinary Differential Equations 3+1*

LEARNING OBJECTIVES:

The primary objective of this course is to introduce:
 The existence and uniqueness of the solution of an initial value problem.
 The Sturm-Liouville Boundary Value Problems and to construct the orthonormal
functions.
 Investigate the nonlinear differential equations and the corresponding nonlinear
autonomous systems and their critical points which are helpful in predicting the nature of
the solution of the nonlinear differential equations.
 Understand the various theoretical concepts of homogeneous and non-homogeneous
ordinary differential equations and applications of eigen value problems.

LEARNING OUTCOMES:

On completion of the above course, the students will be able to
 Assure the existence and uniqueness of the solution of an initial value problem
 Handle the Sturm-Liouville Boundary Value Problems and to construct the orthonormal
functions which can be used to expand any function as infinite series of these functions.
 Investigate the nonlinear differential equations and the corresponding nonlinear
autonomous systems and their critical points which are helpful in predicting the nature of
the solution of the nonlinear differential equations.
 Understand the various theoretical concepts of homogeneous and non-homogeneous
ordinary differential equations and applications of eigen value problems.

THEORY (45 Hours)

UNIT I (15 Hours)

67