Paper Code

Paper Title

Course outcome

MATH101TH
CORE COURSE1

Differential calculus

· Use
of e  δ definition to find the limits and continuity of functions.
· Study
relationship between continuation and differentiation.
· Able
to understand the idea of limits of functions by L hospitals rule
· Learn
the proofs of general theorem and their geometrical consequences.
· Learns
the notation of concavity convexity asymptotes.
· Are
able to trace the curves in polar and rectangular coordinates.
· Understands
the concepts of limit and continuity of functions of several variables.
· Are
able to convert Cartesian to polar coordinates and vice versa.
· Learn
the proof and applications of Euler’s theorem on homogeneous functions
· Are
able to calculate Jacobeans’.

Ability Enhancement
Compulsory Course I

English/Hindi(Communication)/Environmental Science

These courses are the courses based upon the content that leads to Knowledge enhancement.
And are valuebased and/or skillbased and are aimed at providing handsontraining,
competencies, skills etc. in English and/Hindi and Environment science.

MATH201TH
CORE COURSE 2

Differential equations

· Understands
basic definitions and terminology associated with ordinary differential equations.
· Learn
rules to find integrating factors.
· Distinguish
between linear and non linear, ordinary and partial differential equations.
· Recognize
and solve homogeneous and non homogeneous equations by different methods
· Students
are able to apply the methods of variation of parameters and reduction of order.
· Use
working to determine linear dependence and linear independent of functions.
· Learns
to solve Cauchy Euler’s equations.
· Learn
the concepts of total differential equations.
· Can
form partial differential equations of first order and use Langrange’s methods to
solve partial differential equations.
· Are
able to find solutions of partial differential equations by Charpit’s method.
· Learn
to classify second order partial differential equation through lustration only.

Ability Enhancement
Compulsory Course II

English/Hindi(Communication)/Environmental Science

These courses are the courses based upon the content that leads to Knowledge enhancement.
And are valuebased and/or skillbased and are aimed at providing handsontraining,
competencies, skills etc. in English and/Hindi and Environment science.

MATH301TH CORE COURSE 3

REAL ANALYSIS

· Define
and recognize sequence and series of real numbers and their conversions and uniform
conversions
· Recognize
the difference between point wise conversions and uniform conversions of sequence
of function.
· Use
comparison, condensation, ratio, root condensation and Leibnitz’s test for conversion
of series.
· Construct
mathematical proofs of basic results in real analysis
· are
able to comprehend bounded sets ,Archimedean properties and BolzanoWeierstrass
theorem
· Students
can produce proofs of results of real analysis.

Skill Enhancement Course1
MATH302TH
OR
MATH303T
OR
MATH304TH

Analytical Geometry
OR
Integral Calculus

Integral Calculus, (MATH304TH)
·
Learns integration by partial functions and properties of the definite
integrals
·
Establish various reduction formulae
·
Are able to connect to integrals (smaller index+1)
·
Learn to find area and length of curves in planes.
· Evaluate
double and triple integrals.;

MATH401TH CORE COURSE4

Algebra

· Study
the definition of groups rings and fields.
· Are
able to understand concept if subgroups, normal subgroups and quotient groups.
· Use
concepts of homomorphism isomorphism and endomorphism for group sand rings.
· Use
canonical types of groups like cyclic groups ,permutation groups and rings such
as polynomial rings and quotient rings
· Are
able to find cossets and related theorem.
· Produce
groups of theorem on algebra.

Skill Enhancement Course2
MATH402TH
OR
MATH403TH

Vector Calculus
OR
Theory of Equations
OR
Number Theory

VECTOR CALCULUS(MATH402TH
· Study
differentiation & partial differentiation of a vector sum.
· Learn
the concept of the dot product.
· To
study to find gradient, divergence and curl of vectors.
(Theory of Equations MATH403TH)
· Students
will be familiar with general properties of polynomials and their graphical representation.
· Will
be able to compute maximum and minimum values of polynomials.
· Will
gain the ability to use Descartes role of science for positive and negative roots.
· Will
come to know about the concept of symmetric functions.
· Will
use transformation of equations and will be able to find solutions of binomial and
reciprocal equations.
· Students
will gain the ability to find algebraic solutions of cubic and biquadrate’s.

DSECourse1
MATH501TH
OR
MATH502TH
OR
MATH503TH

Matrices
OR
Mechanics
OR
Linear Algebra

Linear Algebra(MATH503TH)
·
Analysis vectors in R^{n} algebraically
·
Learn the concepts of linear independence and dependence, linear span
basis and dimensions.
·
Study vector spaces and subspaces.
·
Use matrix algebra and relate matrices to linear transformations.
·
Study inner product spaces and Cauchy Schwarz’s in equality.

Skill Enhancement Course 3
MATH504TH
OR
MATH505TH
OR
MATH506TH

Probability and Statistics
OR
Mathematical Finance
OR
Mathematical Modeling


DSE Course 2
MATH601TH
OR
MATH602TH
OR
MATH603TH

Numerical analysis
OR
Complex methods
OR
Analysis
Linear programming

Numerical Analysis,(MATH601th)
·
Study to find the approximate rules of non linear equation s by using
different methods such as bisection, secant and Newton Repson method.
·
How to find missing numbers from the available data and the estimate
value of known quantity between the two known quantities.
·
To find the value of definite integral from set of tabulated values
of the integrand by using trapezoidal and Simpsons rule.
Complex Methods (MATH602TH)
·
Define functions in their complex domains
·
Study relation between points in Cartesian plane and complex planes
·
Study the complex integration of functions, limit and continuity of
complex functions, Cauchy Riemann equation harmonic functions.

Skill Enhancement CourseIV
MATH604TH
Or
MATH605TH
Or
MATH606TH

Boolean Algebra
Or
Transportation And
Game Theory
Or
Graph Theory

Boolean algebra (MATH604TH)
·
Study the definition, examples of ordered sets, maps between
the ordered sets, maximal and minimal elements,l attices, sublattices and homomorphisms.
·
Definition and properties of modular and distributive lattices,
boolian polynomials , minimal form of boolian polynomials.
