DEPARTMENT OF MATHEMATICS
COURSE OUTCOMES FOR PG 2018-2019
M.Sc. MATHEMATICS
SEMESTER- I:
PAPER I - ALGEBRA PAPER
CODE: 10101
CO1: To understand the
basic concepts of G-sets and finite Abelian groups
CO2: To understand the
basic concepts of ideals and homomorphism.
CO3: To gain the knowledge
of Integrals domain and its applications
CO4: To study the basic
concepts of Modules and its applications.
SEMESTER- I:
PAPER II - REAL ANALYSIS PAPER CODE: 10102
CO1: To understand the
basic concepts of the Topological space.
C02: Students identify the difference between the
Riemann integral and Riemann Stieltjes integral.
CO3: To analyze the
arithmetic sequences and series to solve the problems.
CO4: knowledgeable students will able to solve the
proper and improper integrals
SEMESTER- I:
PAPER III – ORDINARY DIFFERENTIAL EQUATIONS
PAPER CODE: 10103
CO1: To gain the problem
solving Knowledge of Oscillating theory and boundary value problems.
CO2: To study order
equations of power series and ordinary points.
CO3: To know some special
functions of Mathematical physics
CO4: To understand the
existence, uniqueness solutions of Picard’s theorem.
SEMESTER- I:
PAPER IV - NUMERICAL METHODS AND C - PROGRAMMING
PAPER CODE: 10104
CO1: To study the concepts
of interpolation with cubic spline.
CO2: To know various
techniques of numerical solutions of ordinary differential equations.
CO3: To study the basic
concepts, definitions and over view of C
CO4: To understand the
strings, functions, structure and pointers of C-Programming.
SEMESTER- I:
PAPER V – COMPLEX ANALYSIS PAPER CODE: 10105
CO1: To understand the
basic introduction to the complex numbers and also Analytic functions
CO2: To understand the
Mobius transformation and also how to solve different types of Mobius
transformation problems.
CO3: To study the Cauchy
integral theorem and their problems in Complex integral
CO4: To understand the
solution for different types of power series problems
SEMESTER-II: PAPER VI -
DISCRETE MATHEMATICS PAPER CODE:
20101
CO1: To understand how to solve
the problems by using the mathematical logics for the statements
CO2: To study the various
methods of predicate calculus.
CO3: To understand both lattices
and Boolean algebra.
CO4: The students will be
able to apply principles and concepts of graph theory in practical situations.
SEMESTER-II: PAPER- VII -
MEASURE AND INTEGRATION PAPER CODE:
20102
CO1: Students can
understand the basic concepts of sets and relations.
CO2: The students
understand the difference between the measure and outer measure in the measure
theory
CO3: Students can identify
the Lévesque integral is extended to the Riemann Integral
CO4: To learn the
differentiation and integration.
SEMESTER-II: PAPER- VIII –
PARTIAL DIFFERENTIAL EQUATIONS
PAPER
CODE: 20103
CO1: To understand the
orthogonal trajectories and the pfaffian differential equations.
CO2: Students can learn
first order partial differential equations
CO3: To understand the
canonical forms of the second order partial differential equations
CO4: To understand the
Laplace equations and also understand the boundary value problems.
SEMESTER- II:
PAPER IX - TOPOLOGY PAPER
CODE: 20104
CO1: To know the basic
concepts of set theory and its logics.
CO2: To gain knowledge of
Topology, Basis and types of Topologies
CO3: To understand the
concepts of connectedness, compactness.
CO4: To get the basic
knowledge of countability and separation of axioms.
SEMESTER-I I:
PAPER X – ADVANCED COMPLEX ANALYSIS
PAPER CODE: 20105
CO1: To gain knowledge of
Laurent series and to solve the singular point problems.
CO2: To study residue
theorems and its applications.
CO3: To know the concepts
of Harmonic functions and conformal mapping.
CO4: To understand the
infinite product and partial fractions expansions.
SEMESTER-
III: PAPER XI – COMMUTATIVE ALGEBRA
PAPER CODE: 30101
CO1: To know the basic
concepts of ideals, modules and homomorphism.
CO2: To understand the
concept of finite condition series.
CO3: To study the basic
definitions of Noetherian rings and Hilbert basis theorem
CO4: To understand the
Lasker – Noetherian decomposition theorem and applications of zero divisors,
Nil potent elements.
SEMESTER
-III: PAPER XII – FUNCTIONAL ANALYSIS
PAPER CODE: 30102
CO1: To
understand basic concepts of Vector
space and Normed linear space.
CO2: To
get Knowledge of Natural imbedding theorems and open mapping theorem.
CO3: To
understand the basic concepts of Hilbert spaces.
CO4: To
study self adjoint operators and finite dimensional spectral theory.
SEMESTER
-III: PAPER XIII - DIFFERENTIAL GEOMETRY
PAPER CODE: 30103
CO1: To Explain about the
basic concepts of space curves and different types of planes
CO2: Students can
understand the parametric equation of a surface and local intrinsic properties
of a surface.
CO3: Students can identify
the solution of local intrinsic and non intrinsic properties of a surface
CO4: To Explain about the
Geodesic equations and canonical geodesic equations.
SEMESTER-III: PAPER- XIV: NUMBER THEORY PAPER CODE: 30104
CO1: To Study the
properties of positive numbers and different types of Arithmetical functions
CO2: To Explain the
Average of Arithmetical functions.
CO3: To understand the
foundations of theory of congruence’s.
CO4: To Explain the
Quadratic residues and Quadratic non – residues and different functions of
Quadratic reciprocity laws.
SEMESTER-III: PAPER- XIV: CLASSICAL MECHANICS PAPER CODE: 30105
CO1: To analyze the
concept of Mathematical physics, D’Alembert’s principle and Lagrange’s
equations
CO2: To understand the
variation principle and Lagrange’s equations, non - halonomic system
CO3: To gain knowledge of
Hamilton equations of motion by using the Lagrange’s equations
CO4: To know the solutions
for canonical transformations problems, Poisson’s brackets and Jacobi theory.
SEMESTER-IV: PAPER XV - GALOIS
THEORY PAPER
CODE: 40101
CO1: Students can understand
the basic concepts of polynomials and ring polynomials and their properties and
the extension field.
CO2: To study the
difference between normal and separable extensions.
CO3: To learn Galois
Theory
CO4: Students can identify
the applications of Galois Theory to the classical problems.
SEMESTER-IV: PAPER XVII -
OPERATIONS RESEARCH PAPER
CODE: 40102
CO1: To Understand
different types of problems in Linear programming..
CO2: Students will know
how to run many companies to get more property by using “Scientific inventory
management”.
CO3: To solve problems by
using the dynamic programming.
CO4: To learn basics and characteristics
of Game theory.
SEMESTER- IV: PAPER XVIII – GRAPH THEORY PAPER CODE: 40103
CO1: To know basic
definitions and concept of Graphs and sub graphs.
CO2: To gain knowledge of
trees and its applications
CO3: To understand
connectivity graphs and its applications.
CO4: To understand the
Euler tour Hamiltonian cycles and its applications
SEMESTER-IV: PAPER XIX-
BANACH ALGEBRA PAPER
CODE: 40104
CO1: To identify the liner
space and Ideals and understand the spectral radius formula
CO2: To study the Gelfand
mapping and Gelfand neumark theorems,
CO3: To understand the compact
Hausdorff space and its knowledge to apply on theorems
CO4: To study the basic concepts of Boolean
algebra, Boolean rings and Picard’s
theorem.
SEMESTER- IV:
PAPER XX – MATHEMATICAL STATISTICS
PAPER CODE: 40105
CO1: To know the basic
concept and definitions of the probability set function.
CO2: To gain knowledge of
distribution of functions and sampling theory
CO3: To study various
distributions.
CO4: To gain knowledge of
point estimations, confidence intervals and relevant theorems.
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