M.Sc. (Mathematics)
–
Non

Semester
(To be offered under Distance and Continuing Education)
SCHEME OF EXAMINATIONS
First year
S.No. Paper
Hours
Marks
Passing Min.
1.1 Advanced Abstract Algebra
3
100
50
1.2 Real Analysis
1.3 Differential
Equations
1.4 Fuzzy Mathematics and Statistics
1.5 Graph Theory and Combinatorics
Second Year
1.1
Programming in C and Numerical Methods
1.2
Measure theory and Complex Analysis
1.3
Topology and Functional Analaysis
1.4
Operations Research
1.5
Mechanics
1.1
Advanced Abstract Alg
ebra
Unit I : Groups
–
A counting principle
–
Normal subgroups and quotient groups
–
homomorphism
–
isomorphism
–
Cayley’s theorem
–
permutation groups.
Unit II : Another counting principle
–
Sylow’s Theorems
Unit III :
Rings
–
homomorphism
–
Ideals and quotient rings
–
Field of quotients of
an integral domain
–
Euclidean domain
–
Polynomial rings.
Unit IV : Vector spaces
–
Linear transformation and bases
–
Algebra of linear
transformations
–
Characteristic roots
–
trian
gular form.
Unit V: Extension fields
–
roots of polynomials
–
more about roots.
Text : I.N. Herstein Topics in Algebra (Second Edition)
Chapter 2, Section 2.1 to 2.12
Chapter 3, section 3. 1 to 3.9
Chapter 4, sections 4.1 , 4.2
Chapter 5, sections 5.1.
, 5.3., 5.5
Chapter 6, sections 6.1 to 6.4
1.2
Real Analysis
Unit I : Basic topology
–
convergent sequences
–
subsequences
–
upper and lower limits
–
some special sequences
–
Unit II : Series
–
Series of non

negative terms
–
The number e
–
The root and ratio
tests
–
Power series
–
suromation by parts
–
Absolute convergence
–
Addition and
multiplication of series
–
Rearrangements.
Unit III : Continuity
–
Differentiation.
Unit IV : The Riemann
–
Steiltjes integral
–
Sequences and series of functions
–
Discussio
n of the main problem
–
Uniform convergence
–
Uniform convergence and
continuity
–
Uniform convergence and intergration.
Unit V: Uniform Convergence and differentiation
–
Equicontinuity
–
Equicontinuous
family of functions
–
Stone Weierstrass’ theorem
–
so
me special functions.
Text : Rudin
–
Principles of Mathematical Analysis (Tata McGrows Hill) Third Edition,
Chapters 2 to 8.
1.3
Differential Equations
Unit I : Second order linear equations
–
The general solution of a homogeneous
equation
–
Use of a known sol
ution to find another
–
The method of variation of
parameters
–
Power series solution
–
Series solution of a first order equation.
Unit II : Second order linear equations
–
Ordinary points
–
regular singular points
–
Legendre polynomials .
Unit III : Besse
l functions and Gamma functions
–
Linear systems
–
Homogeneous
linear systems with constant coefficients
–
The method of successive approximation
–
Piccard’s theorem.
Unit IV : Partial Differential Equations
–
Cauchy’s problem for first order equations
–
L
inear equations of first order
–
Nonlinear partial differential equations of first order
–
Cauchy’s method of characteristics
–
Compatible system of first order equations.
Unit V: Charpit’s method
–
special types of first order equations
–
Solutions
satisfying given conditions
–
Jacobi’s method
–
Linear Partial Differential Equations
with constant coefficients
–
Equation with variable coefficients.
Tests: G.F. Simmons, Differential Equations (Torta McGrow Hill )sections 14,15,
16,19 26

29, 32

35, 37,3
8,55 and 56.
I.N, Senddon, Elements of Partial Differential Equations, (Mc

Grow Hill) Chapter 2
sections 1

4, 7

13, Chapter 3 sections 1,4 and 5.
1.4
Fuzzy Mathematics and Statistics
Unit I : The concept of Fuzziness
–
Some Algebra of fuzzy sets.
Unit II: Fuz
zy quantities

Logical aspects of fuzzy sets.
Unit III: Distribution of random variables.
Unit IV: Conditional Probability and stochastic independence
–
Some special
distributions
Unit V: Distributions of Functions of random variables
–
Limiting Distributi
ons.
Texts: H.T. Nguyen and E.A. Walker, A first course in Fuzzy Logic (Second Edition)
CRC Chapters 1 to 4.
R.V. Hagg and A.T. Craig, Introduction to Mathematical Statistics (fourth Edition)
Macmillan, Chapters 1 to 3, Chapter 4 (except section 4.6) and C
hapter 5.
1.5
Graph Theory and Combinatorics
Unit I : Graphs and Subgraphs
–
Trees
–
Connectivity.
Unit II : Euler Tours and Hamilton Cycles
–
Matchings
–
Edge Colorings.
Unit III : Independent sets amd cliques
–
Verter Colorings.
Unit IV: Generating Function
s
–
Recurrence relations.
Unit V: The principle of Inclusion and Exclusion
–
Polya’s theory of counting.
Texts: J.A. Bondy and U.S. R. Murty, Graph theory with Applications (Macmillan),
Chapter 1, (sections 1 to 7), chapters 2,3,4,5 and 6. (Exclusing secti
ons dealing with
Applications), Chapters 7 (Sections 1 to 3) , Chapter 8. C.L. Liu, introduction to
combinatorics (Mc. Grow Hill) chapters 2 to 5.
1.1
Programming in C and Numerical Methods
Unit I :
Overview of C
–
Constants, Variables and data types
–
Operators and
expressions
–
managing input and output operations
–
Decision making branching
and looping.
Unit II: Arrays
–
Handling of character strings
–
User defined functions
–
Structures and Union
s.
Unit III: Pointers
–
File management in C.
Unit IV : Interpolation
–
Lagrange’s interpolation formula
–
Numerical solution
of ordinary differential equations
–
Taylor series method
–
Piccard’s method
–
Euler’s method.
Unit V: Runge
–
Kuttar Fourth order
method
–
Predictor
–
Corrector methods
–
Milne’s method.
Texts: E. Balagurusamy, Programming in Ansi C (Tata Mc. Graw Hill) Chapters
1 to 12. M.K. Jain, S.R.K. Iyengar and R.K. Jain, Numerical methods for
scientific and engineering computation. (Second Ed
ition) Wiley Eastern, Sections
4.1, 4.2, 6.1, 6.2 and 6.3.
1.2
Measure Theory and complex Analysis
Unit I : Lebesgue Measure
–
Lebesgue Integral
Unit II: Measure and Integration
–
Measure and Outer Measure.
Unit III: Complex numbers
–
Analytic functions
–
Elem
entary Theory of Power
series .
Unit IV: Cauchy’s theorem
–
Cauchy’s integral formula
–
singularities.
Unit V: Taylor’s theorem
–
Maximum principle
–
The calculus of Residues .
Texts: Royden
–
Real Analysis Third Edition(PHI) Chapters 3,4,11 and 12.
Ahlfo
rs
–
Complex analysis (Tata
–
McGraw Hill) Second Edition, Chapter 1,
Chapter 2, sections 1 and 2. Chapter 4 sections 1,2,3 and 5.
1.3
Topology and Functional analysis
Unit I : Topological Spaces
–
Compactness.
Unit II: Separation
–
connectedness
Unit III: Ba
nach Spaces
Unit IV: Hilbert spaces
–
Finite dimensional spectral Theory
Unit V: General Preliminaries on Banach Algebras
–
The structure of
commutative Banach Algebra.
Text: G.F. Simmons, introduction to Topology and Modern Analysis (Mc. Graw
Hill)
Chapte
rs 3,4,5,6,9, 10, 11, 12 and 13.
1.4
Operations Research
Unit I : Linear Programming
–
Simplex method
–
Transportation and its variation
Unit II: Network Models
–
CPM
–
PERT
Unit III : Integer Programming
Unit IV: Inventory models
–
Dicision Analysis and
Games
Unit V: Queueing Models.
Text: Taha
–
Operations Research
–
An Introduction (sixth Edition) PHI,
Chapters 2,3,5,6,9,11,14 and 17.
1.5
Mechanics
Unit I: Kinematics
–
Kinetic Energy and Angular Momentum
–
Methods of
Dynamics in space.
Unit II: The simple
pendulum
–
The spherical pendulum
–
Motion of a rigid body.
Unit III: The equations of Lagrange and Hamilton
–
Hamiltonian methods.
Unit IV: Real fluids and ideal fluids
–
Velocity
–
Stream lines
–
Steady and
unsteady flows
–
velocity potential.
Unit V: Vo
rticity vector
–
Equation of continuity
–
Euler’s equation of motion
–
Bernoulli’s equation
–
some three dimensional flows.
Texts: J.L. Synge and B.A Griffith, Principles of Mechanics (Mc. Graw Hill)
Chapters 11,12 and 13 *sections 2 and 3), Chapters 14,15
, and 16 (Section 1) F.
Chorlton, Text book of Fluid Dynamics (CBs Publishers) Chapter 2, sections 2.1.
to 2.7, Chapter 3, sections 3.1 and chapter 4.
1.6
Operations Research
Unit I: Linear Programming
–
Simplex method
–
Transporation model and its
variation
Unit II: Networks Models
–
CPM
–
PERT
Unit III : Integer Programming
Unit IV: Inventory models
–
Decision Analysis and Games
B. Sc Mathematics Main (Non

Semester)
(to be offered under DD& CE)
Scheme of Examination
I Year ( 3 papers)
Paper I Calculus
Paper II Classical Algebra
Paper III Analytical Geometry 3D and Vector Calculus
II Year (3 papers)
Paper IV Modern algebra
Paper V Statistics
Paper VI operations Research
III Year (5 papers)
Paper VII Analysis
Paper VIII Mechanics
Paper
IX Astronomy
Paper X Numerical Analysis
Paper XI Discrete Mathematics
I Year
–
Paper I
–
Calculus
Unit I : Curvature
–
radius of curvature
–
Cartesian and polar
–
centre of curvature
–
Involute and evolute
–
Asymptotes in Cartesian co

ordinates
–
Multipl
e points
–
double
points.
Unit II:
Evaluation of double and triple integrals
–
jocobians, change of variables.
Unit III:
First order differential: equations of higher degree
–
solvable for p,x and y
–
Clairaut’s
form/ linear differential equations of seco
nd order
–
particular integrals for functions of
the form, Xn, eax, eax (f(x). Second order differential equations with variable
coefficients.
Unit IV: Laplace transform

Inverse transform
–
Properties
–
Solving differential
equations. Simultaneous equatio
ns of first order using Laplace transform.
Unit V: Partial differential equations of first order
–
formation
–
different kinds of
solution
–
four standard forms
–
Lagranges method.
Books:
1.
Calculus 1,2 & 3, T.K. Manickavachagom pillai & others.
2.
Calculus 1
&2, S. Arumugam and Isaac.
I year
–
Paper II
–
Classical Algebra
Unit I :
Theory of Equations: Every equation f(x) =0 of nth degree has ‘n’ roots. Symmetric
functions of the roots in terms of the coefficients
–
sum of the rth powers of the roots
–
Newt
on’s
theorem
–
Descartes rule of sign
–
Rolle’s theorem.
Unit II
Reciprocal Equations
–
Transformation of equations
–
solution of cubic and biquadratic equation
–
Cardon’s land Ferrari’s methods
–
Approximate solution of numerical equations

Netwon’s
and
Horner’s methods.
Unit III
Sequences and series: Sequences
–
limits, bounded, monotonic, convergent, oscillatory and
divergent sequence
–
algebra of limits
–
subsequences
–
Cauchy sequences in R and Cauchy’s
general principle of convergence.
Unit IV
Seri
es
–
convergence, divergence
–
geometric, harmonic, exponential, binomial and logratithmic
series
–
Cauchy’s general principle of convergence
–
comparison test
–
tests of convergence of
positive termed series
–
Kummer’s test, ratio test, Raabe’s test, Cauc
hy’s root test, Cauchy’s
condensation test.
Summation of series using exponential, binomial and logarithmic series.
Books for reference:
1.
Sequences and series, S. Arumugam & Others
2.
Algebra
–
Vol. I, T.K. Manickavachagom pillai & Others
3.
Real Analysis
–
Vol.
I, K. Chandrasekara Rao & K.S. Narayanan
4.
Infinite series, Bromwich.
I Year
–
Paper III
–
Analytical Geometry 3D and Vector Calculus
Unit I : Rectangular Cartesian Coordinates in space
–
Distance formula
–
Direction ratio and
cosines
–
Angle between lines
–
simple problems.
Plane
–
different forms of equation
–
angle between two planes
–
perpendicular distance from a
point on a plane
–
projection of a line or a point on a plane.
Unit II: Lines
–
symmetrical form
–
plane and a straight line
–
The perpendicu
lar from a point on
a line
–
Coplanar lines
–
shortest distance between two skew lines and its equation.
Sphere
–
Different forms of equations

plane section
–
the circle and its radius and centre
–
tangent plane
–
condition for tangency
–
touching spheres
–
common tanget plane
–
point of
orthogonality of intersection of two spheres.
Unit III
Vector differentiation
–
Gradient, Divergence and Curl operators
–
solenoidal and irrotational
fields

formulas involving the laplace operator.
Unit IV: Double and tri
ple integrals
–
Jacobian
–
change of variables
–
Vector integration
–
single scalar variables
–
line, surface and volume integrals.
Unit V: Gauss’s Stoke’s and Green’s theorems
–
statements and verification only.
Books for reference:
1.
Analytical Geometry of
3D

Part II, Manickavachagom Pillai
2.
Analytical Geometry of 3D & Vector Calculus
–
P. Duraipandian & Others
3.
Analytical Geometry of 3D & Vector Calculus
–
S. Arumugam & Others
4.
Vector Analysis, K. Viswanathan.
II year
–
PaperIV
–
Modern Algebra
Unit I :
Sets
–
functions
–
relations
–
partitions
–
composition of functions
–
groups
–
subgroups
–
cyclic
groups.
Unit II:
Normal subgroups
–
cosets
–
lagrage’s theorem
–
Quotient groups
–
Homomorphism
–
Kernel
–
Cayley’s theorem
–
Fundamental theorem of homomorphism
.
Unit III:
Rings
–
types
–
subring
–
ordered integral domain
–
ideals
–
Quotient rings
–
P.I.D.
–
Homomorphism of rings
–
fundamental theorem of homomorphism
–
Euclidean rings.
Unit IV: Definition and example of vector speaces
–
subspaces
–
sum and direct
sum of
subspaces
–
linear span, linear dependence, independence and their basic properties
–
Basis
–
finite dimensional vector spaces
–
dimension of sums of subspaces
–
Quotient space and its
dimension.
Unit V:
Linear transformation and their representati
on as matrices
–
Algebra of linear transformations
–
dual spaces
–
Eigen values & eigen vectors of a linear transformation
–
inner product spaces
–
Schwartz inequality
–
orthogonal sets and basis
–
Gram Schmidt orthogonalization process.
Reference books:
1
.Modern Algebra, S. Arumugam and Issac
2. Modern Algebra, Vasistha
3. Topics in Algebra, I.N. Herstein, Vikas Publishers
II year
–
Paper V
–
Statistics
Unit I :
Correlation
–
Karl Pearson’s coefficient of Correlation, Lines of Regression
–
Regression
coeff
icients
–
Rank correlation.
Unit II:
Probability
–
Definition
–
application of addition and multiplication, theorems
–
conditional,
Probability
–
Mathematical Expectations
–
Moment generating function
–
special distributions,
(Binomial distribution, Poisso
n distribution, Normal distribution
–
properties).
Unit
–
III:
Association of attributes
–
Coefficient of association
–
consistency
–
time series
–
Definition
–
Components of a time series
–
Seasonal and cyclic variations.
Unit
–
IV
Sampling
–
definition
–
large samples. Small samples
–
Population with one sample and
population with two samples
–
students
–
t

test

applications
–
chi
–
square test and goodness of
fit
–
applications.
Unit
–
V
Index numbers
–
Types of Index Numbers
–
Tests
–
Unit test, Commodit
y reversal test, time
reversal test, factor reaversal test
–
Chain index numbers
–
cost of living index

Interpolation
–
finite differences operators


Newton’s forward, backward interpolation formulae,
Lagrange’s formula.
Books:
1.
Statistics:
S. Arumugam & others
2.
Statistics: D.C. Saucheti & Kapoor
3.
Statistics: Mangaladas & Others
4.
Statistics: T. Sankaranarayana & Others.
II Year
–
Paper VI

Operations Research
Unit: 1
Linear programming problem
–
Mathematical formulation
–
Graphical method of so
lution

simplex method
–
The big M method (Charnes method of penalties)
–
Two phase simplex
method
–
Duality
–
Dual simplex method
–
integer programming.
Unit
–
II
Transportation problem
–
mathematical formulation
–
North
–
west corner rule
–
Vogel’s
appr
oximation method (unit penalty method )
–
method of matrix minima
–
optimality test
–
maximization
–
Assignment problem
–
mathematical formulation
–
method of solution
–
maximization of the effective matrix.
Unit III:
Sequencing problem
–
introduction
–
n
jobs and two machines
–
n jobs and three machines
–
two
jobs and n machines
–
graphical method
–
inventory models: types of inventory modals:
Deterministic: 1) Uniform rate of demand, infinite rate of production and no shortage
–
2)
Uniform rate of demand,
finite rate of replenishment and no shortage
–
3) Uniform rate of
demand, instantaneous production with shortages
–
4) Uniform rate of demand, instantaneous
production with shortage and fixed time.
Unit IV:
Probabilistic Models: Newspaper boy problem
–
discrete and continuous type cases

Inventory
models with one price break.
Queueing Theory: General concept and definitions
–
classification of queues
–
Poisson process,
properties of poisson process
–
models: 1) (M/M/1) : (∞/FCFS), 2)(M/M/1): (N/FCFS),
3)(µ/M/S): (∞/FCFS).
Unit V: Network Analysis: Drawing network diagram
–
Critical path method
–
labelling method
–
concept of slack and floats on network
–
PERT
–
Algorithm for PERT
–
Differences in PERT
and CPM.
Resource Analysis in Network Scheduling :
Project cost
–
Crashing cost
–
Time

cost
optimization algorithm
–
Resource allocation and scheduling.
Books for Reference:
1.
Operations Research : Kantiswarup, P.K. Gupta and Man Mohan.
2.
Operations Research : P.K. Gupta, D.S. Hira.
3.
Operations Research : V.K.
Kapoor
4.
Operations Research : S.D. Sharma
5.
Operations Research : Mangaladoss.
III Year
–
Paper VII
–
Analysis
Unit I:
Metric spaces
–
open sets
–
Interior of a set
–
closed sets
–
closure
–
completeness
–
Cantor’s
intersections theorem
–
Baire
–
Category
Theorem.
Unit II:
Continuity of functions
–
Continuity of compositions of functions
–
Equivalent conditions for
continuity
–
Algebra of continuous functions
–
hemeomorphism
–
uniform continuity
–
discontinuities connectednon
–
connected subsets of R
–
Con
nectedness and continuity
–
continuous image of a connected set is connected
–
intermediate value theorem.
Unit III:
Compactness
–
open cover
–
compact metric spaces
–
Herni Borel theorem. Compactness and
continuity
–
continuous image of compact metric spa
ce is compact
–
Continuous function on a
compact metric space in uniformly continuous
–
Equivalent forms of compactness
–
Every
compact metric space is totally bounded
–
Bolano
–
Weierstrass property
–
sequentially compact
metric space.
Unit IV:
Algebra o
f complex numbers
–
circles and straight lines
–
regions in the complex plane
–
Analytic functions Cauchy
–
Rienann equations
–
Harmonic functions
–
Bilinear transformation
translation, rotation, inversion
–
Cross
–
ratio

Fixed points
–
Special bilinear t
ransformations.
Unit V: Complex Integration
–
Cauchy’s integral theorem
–
Its extension
–
Cauchy’s integral
formula
–
Morera’s theorem
–
Liouville’s theorem
–
fundamental theorem of algebra
–
Taylor’s
series
–
Laurent’s series
–
Singularities. Residues
–
R
esidue Theorem
–
Evaluation of definite
integrals of the following types.
∫
0
2π
F (Cos x, sin x) dx
2 ∫

∞
∞
dx
Books for reference:
1.
Modern Analysis
–
Arumugam and Issac.
2.
Real Analysis
–
Vol. III
–
K. Chandrasekhara Rao and K.S. Narayanan, S. V
iswanathan
Publisher.
3.
Complex Analysis
–
Narayanan & Manicavachagam Pillai
4.
Complex Analysis
–
S. Arumugam & Issac.
5.
Complex Analysis
–
P. Durai Pandian
6.
Complex Analysis
–
Karunakaran, Narosa Publishers.
III Year
–
Paper VIII
–
Mechanics
Unit I:
Forces acting at a point
–
parallelogram of forces
–
triangle of forces
–
Lami’s theorem, Parallel
forces and moments
–
Couples
–
Equilibrium of three forces acting on a rigid body
–
Coplanar
forces
–
Reduction of any number of Coplanar forces theorems. Ge
neral conditions of quilibrium
of a system of Coplanar forces.
Unit II:
Friction
–
Laws of friction
–
Equilibrium of a particle (i) on a rough inclined plane. (ii) under a
force parallel to the plane (iii) under any force
–
Equilibrium of strings
–
Equatio
n of the
common catenary
–
Tension at any point
–
Geometrical properties of common catenary
–
uniform chain under the action of gravity
–
Suspension bridge.
Unit III:
Dynamics
–
Projectiles
–
Equation of path, Range etc
–
Range on an inclined plane
–
Motio
n on
an inclined plane. Impulsive forces
–
Collision of elastic bodies
–
Laws of impact
–
direct and
oblique impact
–
Impact on a fixed plane.
Unit IV:
Simple harmonic motion in a straight line
–
Geometrical representation
–
Composition of SHM’s
of the sam
e period in the same line and along two perpendicular directions
–
Particles suspended
by spring
–
S.H.M. on a curve
–
Simple pendulum
–
Simple Equivalent pendulum
–
The seconds
pendulum.
Unit V:
Motion under the action of Central forces
–
velocity and a
cceleration in polar coordinates
–
Differential equation of central orbit
–
Pedal equation of central orbit
–
Apses
–
Apsidal
distances
–
Inverse square law.
Books for Reference:
1.
Statics and Dynamics: S. Narayanan
2.
Statics and Dynamics : M.K. Cenkataraman
3.
S
tatics: Manickavachagom pillai
4.
Dynamics: Duraipandian.
III Year
–
Paper IX
–
Astronomy
Unit I:
Spherical Trigonometry (only formulae) celestial sphere
–
four systems of coordinates
–
Diurnal
motion
–
Zones of the earth
–
Perpetual day and night
–
Terrestrial longitude and latitude
–
International date line.
Unit II:
Dip of horizon
–
effects
–
Twili
ght
–
shortest twilight.
Unit III:
Refraction
–
Tangent formula
–
Cassini’s formula
–
Effects
–
Horizontal refraction
–
Geocentric
parallax.
Unit IV:
Kepler’s laws
–
verification
–
Newton’s deductions
–
Anomalies
–
Planets
–
Inferior and
superior planet
–
Bode’s law
–
Elongation
–
Sidereal period
–
Synodic period
–
Phase of the
planet
–
Stationary positions of a planet.
Unit V :
Moon
–
Phase
–
sidereal and synodic period
–
elongation
–
Metonic cycle
–
golden number
–
Eclipses
–
Lunar and solar eclipses
–
co
nditions
–
Synodic period of the nodes
–
Ecliptic limits
–
Maximum and minimum number of eclipses near a node and in a year
–
Saros
–
Lunar and solar
eclipses compared.
Books:
1.
Astronomy : S. Kumaravelu & Susheela Kumaravelu.
2.
Astronomy: G.V. Ramachandran
3.
As
tronomy: K. Subramanian and L.V. Subramanian
III Year
–
Paper X
–
Numerical Analysis
Unit I :
Finite differences
–
difference table
–
operators E,∆ and

Relations between these operatous
–
Factorial notation
–
Expressing a given polynomial in
factorial notation
–
Difference equation
–
Linear difference equations
–
Homogeneans linear difference equation with constant
coefficients.
Unit II
Interpolation using finite differences
–
Newton
–
Gregory formula for forward interpolation
–
Divided diffe
rences
–
Properties
–
Newton’s formula for unequal intervals

Lagrange’s formula
–
Relation between ordinary differences and divided differences
–
inverse interpolation.
Unit III
Numerical differentiation and integration
–
General Quadratue formula for e
quidistant ordinates
–
Trapezoidal Rule
–
Simpson’s one third rule
–
Simpson’s three eight rule
–
Waddle’s rule
–
Cote’s method.
Unit IV:
Numerical solution of ordinary differential equations of first and second orders
–
Piccards
method. Eulers method and
modified Euleis method
–
Taylor’s series method
–
Milne’s method
–
Runge
–
Kutta method of order 2 and 4
–
Solution of algebraic and transcendent equations.
Finding the initial approximate value of the root
–
Iteration method
–
Newton Raphson’s
method.
Un
it V:
Simultaneous linear algebraic equations
–
Different methods of obtaining the solution
–
The
elimination method by Gauss
–
Jordan method
–
Grouts’ method
–
Method of factorization .
Books:
Calculus of finite differences and Numerical Analysis, P.P. Gu
pta & G.S. Malik, Krishna
Prakasham Mardin, Mecrutt.
III Year
–
Paper XI
–
Discrete Mathematics
Unit I:
Definition and examples of graphs
–
degrees
–
subgraphs
–
ismorphims
–
Ramsey numbers
–
independent sets and coverings
–
intersection graphs and
line graphs
–
matrices
–
operations in
graphs
–
degree sequences, graphic sequences.
Unit II:
Walks
–
trails and paths
–
connectedness and components
–
blocks
–
connectivity
–
Eulerian
graphs
–
Hamiltonian graphs
–
trees
–
characterization of trees
–
centr
e of a tree.
Unit III:
Planas graph and their properties
–
characterization of planas graphs
–
thickness
–
crossing and
outerplanarity
–
Chromatic number
–
chromatic index
–
five colour theorm
–
four colour
problem
–
chromatic polynomials
–
Directed
graphs and basic properties
–
paths and connections
in digraphs
–
digraphs and matrices
–
tournaments.
Unit IV:
Permutations
–
ordered selections
–
unordered selections
–
further remarks on binomial theorem
–
Pairings within a set
–
pairings between sets,

an optimal assignment problem.
Unit V:
Recurrence relations
–
Fibonacci type relations
–
Using generating functions
–
miscellaneous
methods
–
The inclusion exclusion principle and rook polynomials.
Text Books:
1.
Invitation to graph theory, S. Arumugam and
S. Ramachandran, Scitech Publications.
2.
A first course in combinational mathematics, Ian Anderson (Oxford applied Math. Series)
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