SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE
SATTUR- 626 203 (An Autonomous institution affiliated to the Madurai Kamaraj University, Madurai)
(Re-Accredited with Grade ‘A’ by NAAC)
M.Sc. DEGREE COURSE IN
MATHEMATICS
SYLLABUS AND REGULATIONS
UNDER
CHOICE BASED CREDIT SYSTEM (CBCS)
(Those who are joining in 2016-2017 and after)
SRNMC Regulation-2016 Syllabus
Objectives
The syllabus for Mathematics has been designed in such a way that the
students, whenthey go out, will be capable of facing the competitive
situation prevailing now. The focus is on getting placement for all the
students.
Eligibility
A candidate with a pass in B.Sc Mathematics degree conducted by
the Madurai Kamaraj University or any other university duly
recognized by the syndicate of Madurai Kamaraj University as
equivalent thereto is eligible to join the course.
Evaluation
The performance of the student is evaluated in terms of percentage of marks with a
provision for conversion to grade points. Evaluation for each course shall be done by a
continuous internal assessment by the concerned course teachers as well as by an end semester
examination which will be a written type examination of 3 hours duration. The ratio of marks
to be allotted to continous internal assessment and to end semester examination is 25:75( i.e
internal 25 marks and external 75 marks for theory), Practical 40 : 60.
The components for continuous internal assessment are:
Theory:
Two tests and their average ---15 marks
Seminar/Group Discussion --- 5 marks
Assignment --- 5 marks
Total --- 25 marks
Practical:
Two tests and their average ---20 marks
Record --- 5 marks
Observation Evaluation ---15 marks
Total --- 40 marks
SRNMC Regulation-2016 Syllabus
Passing Minimum
A) Theory:
1. No separate pass minimum for internal
2. 45% is the pass minimum for the External
3. 50% of the aggregate (external+ internal)
B) Practical:
1. No separate pass minimum for internal
2. 45% is the pass minimum for the External
3. 50% of the aggregate (external+ internal)
C) Project:
1. No separate pass minimum for internal
2. 45% is the pass minimum for the External
3. 50% of the aggregate (external+ internal)
4. Minimum of 25 pages in the project work excluding
1. Introduction
2. Reference
3. Bibliography
4. Tables
5. Graphs
Passing Minimum
A candidate passes the P.G. program by scoring a minimum of 50%
(internal + external) in each paper of the course. No minimum mark for internal
assessment. External minimum for external assessment is 45% and external
minimum is 34 out of 75.
Duration of the Course
The duration of the course shall be two academic years comprising four semesters.
SRNMC Regulation-2016 Syllabus
Credits
The term „credit‟ refers to the weightage given to the course, usually in relation to the instructional
hours assigned to it. The total credits required for completing Master of Science in Mathematics is 90. The
particulars of the credits for individual components and the courses are placed on Table-1
Extra Credits Paper:
1. This paper is optional. Students may or may not select this paper. If he/she selects this paper
and if he/she passes the paper, then 3 extra credits will be added in his/her total credit to the
degree, even otherwise, it won‟t affect the completion of degree.
2. Though this paper is common to all PG programmes, the syllabus varies according to the
subject selected by the department.
3. The title of this paper is “Model Paper for NET Examinations”
4. Examination for this paper will be held at the end of the 4th
semester examinations.
5. There is no internal examination and only external examination for this paper.
6. Maximum marks for this paper is 100.
Question Type of
Question
No.of
Question
No.of
Question to
be answered
Marks for
Each
question
Total
Marks
A.Q.No(1-5)
Q.No(6-10)
Multiple
choice
(one from
each unit)
5 5 1
10
Sentence from
(one from
each unit)
5 5 1
B.Q.No(11-
15)
Either or type
(one from
each unit)
5 5 7 35
C.Q.No(16-
20)
Open choice
(One from
each unit)
5 3 10 30
SRNMC Regulation-2016 Syllabus
M.Sc., (Mathematics)
Table-1: Course Pattern
(For those who are joining in the academic year 2016-2017 and after)
Semester I II III IV V Total
Hours
Total
Credits
No. of
Courses
I Core
6(5)
Core
6(5)
Core
6(4)
Core
6(4)
Elective
6(4)
30 22 5
II Core
6(5)
Core
6(5)
Core
6(4)
Core
6(4)
Elective
6(4)
30 22 5
III Core
6(5)
Core
6(5)
Core
6(5)
Core
6(4)
Elective
6(4)
30 23 5
IV Core
6(5)
Core
6(5)
Core
6(5)
Elective
6(4)
Project
6(4)
30 23 5
Total
120 90 20
Extra Credits
paper
3
Grand Total 93
SRNMC Regulation-2016 Syllabus
M.Sc., (Mathematics) Table-1: Course Details and Scheme of Examination
(For those who are joining in the academic year 2016-2017 and after)
First Semester
S.
No
Title of the
Paper
Subject
Code Hours /
week Credits
Exam
hrs
Marks
Total
Marks Int Ext
1. Groups and
Rings
P16MAC11 6 5 3 25 75 100
2. Mathematical
Analysis
P16MAC12 6 5 3 25 75 100
3. Differential
Geometry
P16MAC13 6 4 3 25 75 100
4. Mathematical
Statistics
P16MAC14 6 4 3 25 75 100
5.
Elective
a) Classical
Mechanics
b)Graph
Theory
P16MAE11
P16MAE12
6 4 3 25 75 100
SRNMC Regulation-2016 Syllabus
SECOND SEMESTER
S.
No
Title of the
Paper
Subject
Code
Hours/
week Credits
Exam
hrs
Marks Total
Marks Int Ext
1. Linear Algebra P16MAC21 6 5 3 25 75 100
2. Advanced
Mathematical
Analysis
P16MAC22
6 5 3 25 75 100
3. Differential
Equations
P16MAC23 6 4 3 25 75 100
4. Advanced
Mathematical
Statistics
P16MAC24
6 4 3 25 75 100
Elective
a)Combinatorial
Mathematics
b) Fuzzy
Algebra
P16MAE21
P16MAE22
6 4 3 25 75 100
SRNMC Regulation-2016 Syllabus
THIRD SEMESTER
S.
No
Title of the
Paper
Subject
Code Hours
per
week
Credits Exam
hrs
Marks
Total
Marks Int Ext
1. Galois Theory
and Lattices
P16MAC31 6 5 3 25 75 100
2. Measure and
Integration
P16MAC32 6 5 3 25 75 100
3. Topology P16MAC33 6 5 3 25 75 100
4. Stochastic
Processes
P16MAC34 6 4 3 40 75 100
Major
Elective
a) Numerical
Analysis
b) Integral
Equations
P16MAE31
P16MAE32
6
4
3
25
75
100
SRNMC Regulation-2016 Syllabus
FOURTH SEMESTER
S. No Title of the
Paper
Subject
Code
Hours
per
week
Credits Exam
hrs
Marks Total
Marks Int Ext
1. Complex
Analysis
P16MAC41 6 5 3 25 75 100
2. Functional
Analysis
P16MAC42 6 5 3 25 75 100
3. Operations
Research
P16MAC43 6 5 3
25
75 100
4. Major Elective
a) Advanced
Topology
b) Number
Theory and
Cryptography
P16MAE41
P16MAE42
6
4
3
25
75
100
Project P16MAPT41 6 4 3 25 75 100
Extra Credits paper
Model paper for
NET/SET
Examination
P16MAX41 3 3
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE
(An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)
SATTUR – 626 203. Department of Mathematics
(For those who are joining in 2016-2017 and after)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code :P16MAC11
Semester : I No. of Hours allotted : 6 / Week
Paper : Core - Paper I No. of Credits : 5
Title of the Paper - GROUPS AND RINGS
Objectives:
To know more concepts in algebra which helps them to develop thinking and improve
mathematical ability.
To understand the basic algebraic structures prevailing in the set of numbers. Unit I
Counting Principle – Conjugacy – Cauchy‟s Theorem - Sylow‟s Theorem – Second Part
Part of Sylow‟s Theorem – Third part of Sylow‟s Theorem.
Unit II
Direct Products - Finite Abelian Groups –Invariants.
Unit III
Ideals and Quotient Rings- More Ideals and Quotient Rings -The Field of Quotients of
an Integral Domain.
Unit IV
Euclidean Rings - A particular Euclidean Ring.
Unit V
Polynomial Rings - Polynomials over the Rational Fields - Polynomial Rings over
Commutative rings.
Text Book:
Title of the book : Topics in Algebra
Name of the Author : I.N. Herstein
Publisher
Edition/Year
;John Wiley and Sons
:Second Edition,1999, Third reprint 2008
SRNMC Regulation-2016 Syllabus
Unit I :
Chapter 2: Sections 2.11, 2.12.
Unit II:
Chapter 2: Sections 2.13, 2.14.
Unit III:
Chapter 3: Sections 3.4, 3.5, 3.6.
Unit IV:
Chapter 3: Sections 3.7, 3.8.
Unit V:
Chapter 3: Sections 3.9, 3.10 and 3.11.
Reference Books:
Reference Book - 1:
Title of the book : University Algebra
Name of the Author : N.S.Goplakrishnan
Publisher
Edition/Year
Reference Book - 2
Title of the book
: New Age Inernational Pvt Ltd, Newdelhi
: Second Edition
: Basic Abstract Algebra
Name of the Author : P.B. Bhattacharya
Publisher
Edition/Year
: S.K. Jain, S.R. Nagpaul Cambridge University Press
: 1995 Reprinted 2009
Prepared by : Dr. V.Thiripurasundari
Signature :
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE (An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)
SATTUR – 626 203.
Department of Mathematics
(For those who are joining in 2016-2017 and after)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code :P16MAC12
Semester : I No.of Hours allotted : 6 / Week
Paper : Core - Paper II No.of Credits : 5
Title of the Paper - MATHEMATICAL ANALYSIS
Objectives:
To give a comprehensive idea about the underlying principles of real analysis.
To enable the students to have a good foundation in all the concepts in sequences
and series.
Unit I
Finite, countable and uncountable sets - Metric spaces.
Unit II
Compact sets, Perfect Sets and Connected Sets. Convergent sequences, subsequences
and Cauchy sequences - Upper and lower limits - Some special sequences.
Unit III
Series - Series of Non-negative Terms - The Number e. The Root and Ratio Tests -
Power Series - Summation by parts - absolute convergence - addition and multiplication of
series.
Unit IV
Limits of function - Continuous Functions - Continuity and Compactness - continuity
and Connectedness – Discontinuities - monotonic functions - infinite limits and limits at
infinity.
Unit V
The derivative of Real function - Mean Value Theorems - The continuity of
derivatives - L‟Hospital‟s Rule -Derivatives of Higher Order - Taylor‟s Theorem,
Differentiation of vector-valued Functions.
SRNMC Regulation-2016 Syllabus
Text Book:
Title of the book
: Principles of Mathematical Analysis
Name of the Author : Walter Rudin
Publisher
Edition/Year
Unit I :
: McGraw Hill, International student edition
: Third Edition,1976
Chapter 2: Sections 2.1 to 2.30
Unit II:
Chapter 2: Sections 2.31 to 2.47.
Chapter 3: Sections 3.1 to 3.20.
Unit III:
Chapter 3: Sections 3.21 to 3.55.
Unit IV:
Chapter 4: Sections 4.1 to 4.34.
Unit V :
Chapter 5: Sections 5.1 to 5.19.
Reference Book:
Reference Book - 1
Title of the book : Mathematical Analysis
Name of the Author : Tom M.Apostal
Publisher
Edition/Year
Reference Book - 2
Title of the book
: Addision-Wesley Pub Company
: Second Edition, 1978
: Real Analysis
Name of the Author : N.L.Carothers
Publisher
Edition/Year
: Cambridge University Press
: First South Asian Edition 2006
Prepared by : Dr. S.Rajaram
Signature :
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE
(An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)
SATTUR – 626 203.
Department of Mathematics (For those who are joining in 2016-2017 and after)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code :P16MAC13
Semester : I No.of Hours allotted : 6 / Week
Paper : Core - Paper III No.of Credits : 4
Title of the Paper - DIFFERENTIAL GEOMETRY
Objectives:
To get clear idea on three dimensional surfaces.
To get new ideas and techniques which play a prominent role in current research in global differential geometry.
Unit I
Introductory remarks about space curves, definition, arc length, tangent, normal and
binormal - Curvature and torsion of a curve given as the intersection of two surfaces -
Contact between curves and surfaces - Tangent surface - Involutes and Evolutes.
Unit II
Intrinsic equations - Fundamental existence theorem for space curves – Helics -
Definition of a surface, curves on surface - Surfaces of revolution - Helicoids.
Unit III
Metric - Direction Coefficients - Family of curves - Isometric correspondence-
Intrinsic Properties – Geodesics - Canonical geodesic equations - Normal property of
geodesics.
Unit IV
Geodesic Curvature - Gauss Bonnet Theorem - Gaussian curvature – Surface of
constant curvature – Minding Theorem.
Unit V
The Second fundamental form - Principal curvatures - Lines of curvature –
Developables - Developables associated with space curves - Developables associated with
curves on surfaces - Minimal surfaces - Ruled surfaces.
SRNMC Regulation-2016 Syllabus
Text Book:
1.Title of the book : An introduction to differential geometry
Name of the Authos : T.G.Willmore
Publisher : Oxford University Press
Edition/Year : 1959, Twenty third impression 2008
Unit I :
Chapter 1: Sections 1 to 7
Unit II :
Chapter 1: Section 8 & 9.
Chapter 2 : Sections 1 to 4
Unit III:
Chapter 2: Sections 5 to 12.
Unit IV :
Chapter 2: Section 15 to 18.
Unit V:
Chapter 3: Sections 1 to 8.
Reference Book:
Reference Book - 1
Title of the book : Differential Geometry of Three Dimensions
Name of the Author : Charles Emest Weatherburn
Publisher : The University Press
Edition/Year : 1998
Reference Book - 2
Title of the book : Differential Geometry : A first Course
Name of the Author : D.Somasundaram
Publisher :Narosa Publishing House
Edition/Year : 2006
Prepared by : Dr. S. Murugesan
Signature :
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE
(An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)
SATTUR – 626 203.
Department of Mathematics (For those who are joining in 2016-2017 and after)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code :P16MAC14
Semester : I No.of Hours allotted : 6 / Week
Paper : Core - Paper IV No.of Credits : 4
Title of the Paper – MATHEMATICAL STATISTICS
Objectives:
To develop the ability in the students to understand more concepts in Statistics.
To know more about various distributions.
Unit I
The probability set functions, Conditional probability and independence, random
variables of the discrete type, random variables of the continuous type, properties of the
distribution function, expectation of a random variable, some special expectations, Chebyshev‟s
inequality.
Unit II
Distributions of two random variables, conditional distributions and expectations, the
correlation coefficient, independent random variables, extension to several random variables.
Unit III
The binomial and related distributions, Poisson distribution, The gamma and Chi-
square distributions, the normal distribution, the Bivariate normal distribution.
Unit IV
Sampling theory, transformations of variables of the discrete type, transformations of
variables of the continuous type, the Beta, t, F distributions, extensions of the change-of-
variable technique, distributions of order statistics, The moment generating function
technique, the distributions of X and nS2 /σ
2, expectations of functions of random variables.
Unit V
Convergence in distribution, convergence in probability, limiting moment generating
functions, the central limit theorem, some theorems on limiting distributions.
SRNMC Regulation-2016 Syllabus
Text Book:
Title of the book : Introduction to Mathematical Statistics
Names of the Authors : R.V.Hogg and A.T.Craig
Publisher : Pearson Education, Asia
Edition/year : V Edition, 2002
Unit I:
Chapter 1: Sections : 1.3 to 1.10.
Unit II
Chapter 2: Sections: 2.1 to 2.5.
Unit III
Chapter 3: Sections: 3.1 to 3.5.
Unit IV
Chapter 4: Sections: 4.1 to 4.9.
Unit V
Chapter 5: Sections : 5.1 to 5.5.
Reference Book:
Reference Book - 1
Title of the book : An Introductory Statistics
Name of the Author : Ross, Sheldon.M
Publisher : USA Academic Press
Edition/Year : 2006
Reference Book – 2
Title of the book : Introduction to Probability Theory and its Applications
Name of the Author : William Feller
Publisher : Wiley India
Edition/Year: : 3rd
Edition Volume I /2011 Prepared by : Dr. N. Soundararaj
Signature :
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE
(An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)
SATTUR – 626 203.
Department of Mathematics
(For those who are joining in 2016-2017 and after)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code :P16MAE11
Semester : I No.of Hours allotted : 6 / Week
Paper : Paper V Elective I (a) No.of Credits : 4
Title of the Paper - CLASSICAL MECHANICS
Objectives:
To promote logical thinking to understand the basic principles
of mechanics to be applied to practical problems.
To provide strong foundation about elementary principles and variational
Principles of mechanics
Unit I
Mechanics of a particle, Mechanics of a system of particles, Constraints.
Unit II
D‟Alembert‟s principle and Lagrange‟s equations, velocity dependent potentials and
the dissipation function, Hamilton‟s principle, some techniques of the calculus of variations.
Unit III
Derivation of Lagrange‟s equations from Hamilton‟s principle, Extension of
Hamilton‟s principle to nonholonomic systems, Advantage of a variational principle
formulation, Conservation theorems and Symmetry properties.
Unit IV
Reduction to the equivalent one – body problem, the equations of motion and first
integrals. The equivalent one – dimensional problem and classification of orbits, the Virial
theorem.
Unit V
The differential equation for the orbit and integrable power-law potentials, conditions
for closed orbits (Bertrand‟s theorem), The Kepler problem: Inverse square law of force, The
motion in time in the Kepler problem, The Laplace – Runge- Lenz vector.
SRNMC Regulation-2016 Syllabus
Text Book:
Title of the book
: Classical Mechanics
Name of the Author : H.Goldstein
Publisher
Edition/Year
Unit I :
: Addison Wesley, New York
: Second edition, 1980
Chapter 1: Sections 1.1 – 1.3
Unit II :
Chapter 1: Sections 1.4 - 1.5.
Chapter 2: Sections 2.1 – 2.2
Unit III:
Chapter 2: Sections 2.3 – 2.6
Unit IV :
`Chapter 3: Sections 3.1 – 3.4
Unit V:
Chapter 3: Sections 3.5 – 3.9.
Reference Books
Reference Book - 1
Title of the book : Classical Mechanics
Name of the Author : D.T.Greenwood,
Publisher
Edition/Year
Reference Book - 2
: Prentice Hall of India Pvt. ltd,NewDelhi
: 1979
Title of the book : Classical Mechanics
Name of the Author : D.E.Rutherford
Publisher : Oliver and Boyd
Edition/Year : 1987
Prepared by : Dr.N.Soundararaj
Signature :
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE
(An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)
SATTUR – 626 203. Department of Mathematics
(For those who are joining in 2016-2017 and after)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code :P16MAE12
Semester : I No.of Hours allotted : 6 / Week
Paper : Paper V - Elective I(b) No.of Credits : 4
Title of the Paper - GRAPH THEORY
Objectives:
To motivate the students about the fundamental principles of graph theory.
To give clear idea about the terms and definitions and problems of graph theory.
Unit I
Graphs and simple graphs, graph isomorphism, the incidence and adjacency matrices,
Subgraphs, Vertex degrees, Paths and Connection, Cycles, the shortest path problem,
Sperner‟s lemma.
Unit II
Trees, cut edges and Bonds, cut vertices, cayley‟s formula, The connector problem,
connectivity, blocks, construction of reliable communication networks.
Unit III
Euler tours, Hamilton cycles, the Chinese postman problem, the travelling salesman
problem.
Unit IV
Matchings, Matchings and coverings in bipartite graphs, Perfect matchings. The
personnel assignment problem, the optimal assignment problem.
Unit V
Edge chromatic number, Vizing‟s theorem, the timetabling problem.
SRNMC Regulation-2016 Syllabus
Text Book:
Title of the book
: Graph theory with Applications
Names of the authors : J.A. Bondy and U.S.R.Murty
Publisher
Edition/Year
Unit I :
: North Holand
: 5thprinting /1983
Chapter 1: Sections 1.1 – 1.9
Unit II :
Chapter 2: Sections 2.1 – 2.5.
Chapter 3: Sections 3.1 – 3.3
Unit III:
Chapter 4: Sections 4.1 – 4.4
Unit IV :
Chapter 5: Sections 5.1 – 5.5
Unit V:
Chapter 6: Sections 6.1 – 6.3.
Reference Book:
Reference Book - 1
Title of the book : Graph Theory with applications to Engineering and Computer Science
Name of the Author : Narasing Deo,
Publisher
Edition/Year
Reference Book – 2
Title of the book
: Pretice Hall of India(P) Ltd,NewDelhi
: 2007
: Introduction to Graph Theroy
Name of the Author : Douglas B.West
Publisher
Edition/Year
: Pearson Education Ltd
: 2nd
/ 2002
Prepared by : Dr. R. Sridevi
Signature :
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE
(An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)
SATTUR – 626 203.
Department of Mathematics (For those who are joining in 2016 -2017 and after)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code :P16MAC21
Semester : II No. of Hours allotted : 6 / Week
Paper : Core - Paper VI No. of Credits : 5
Title of the Paper- LINEAR ALGEBRA
Objectives:
To know more concepts in algebra which helps them to develop thinking and
improve mathematical ability.
To study concrete examples and to do problems.
Unit I
Dual spaces – Annihilator - Inner Product spaces – Schwarz inequality – Orthogonal –
Orthonormal set – Gram-Schmidt Orthogonalization Process - Modules – Submodules.
Unit II
The algebra of linear transformations – Regular – Singular – Range - Characteristic roots
- Matrix of linear transformations.
Unit III
Canonical forms - Triangular form -Nilpotent transformations – Index of Nilpotence – A decomposition of V: Jordan form.
Unit IV
Rational Canonical form - Trace and Transpose.
Unit V
Determinants – Cramer‟s Rule – Secular equation - Hermitian - Unitary and Normal
Transformations.
SRNMC Regulation-2016 Syllabus
Text Book:
Title of the book
: Topics in Algebra
Name of the author : I.N.Herstein
Publisher
Edition/Year
Unit I :
: John Wiley and Sons
: Second Edition 1999 Reprint 2008
Chapter 4: Sections 4.3, 4.4, 4.5.
Unit II :
Chapter 6: Sections 6.1, 6.2, 6.3.
Unit III:
Chapter 6: Sections 6.4, 6.5, 6.6.
Unit IV :
Chapter 6: Sections 6.7, 6.8.
Unit V:
Chapter 6: Sections 6.9 and 6.10.
Reference Books:
Reference Book - 1
Title of the book : A first Course in Algebra
Name of the Author: J.B. Fraleigh
Publisher
Edition/Year
Reference Book - 2
: Addition –Wiely Longman Znc.Reading, Massachuetts
: 1991
Title of the book : Basic Abstract Algebra
Name of the Author: P.M. Bhattacharya
Publisher
Edition/Year
: S.K. Jain, S.R. Nagpaul Cambridge University Press
: Second Edition, 1995, Reprinted 2009
Prepared by : Dr. V.Thiripurasundari
Signature :
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE (An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)
SATTUR – 626 203.
Department of Mathematics
(For those who are joining in 2016 -2017 and after)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code :P16MAC22
Semester : II No.of Hours allotted : 6 / Week
Paper : Core - Paper VII No.of Credits : 5
Title of the Paper - ADVANCED MATHEMATICAL ANALYSIS Objectives:
To develop the firm footing in Analysis.
To introduce Riemann integration.
Unit I
Definitions and existence of the integral - Properties of the Integral - Integration and
Differentiation - Integration of vector valued functions - Rectifiable curves.
Unit II
Uniform convergence - uniform convergence and continuity - uniform convergence and
differentiation - equicontinuous families of functions -The Weierstrass theorem.
Unit III
Power series - The exponential and logarithmic functions - The trigonometric
Functions - The algebraic completeness of the Complex field - Fourier series - The Gamma
function.
Unit IV
Linear Transformations – Differentiation – The contraction principle – The inverse
function theorem.
Unit V
The implicit function theorem – Determinants- Jacobians
SRNMC Regulation-2016 Syllabus
Text Book:
Title of the book
: Principles of Mathematical Analysis
Name of the author : Walter Rudin
Publisher
Edition/Year
Unit I :
: McGraw Hill
: Third Edition, International Student Edition 1976
Chapter 6: Sections 6.1 – 6.27.
Unit II :
Chapter 7: Sections 7.1 – 7.26.
Unit III:
Chapter 8: Sections 8.1 – 8.21.
Unit IV :
Chapter 9: Sections 9.1 – 9.25.
Unit V:
Chapter 9: Sections 9.26 – 9.29, 9.33 to 9.38.
Reference Book:
Reference Book - 1
Title of the book : Mathematical Analysis
Name of the Author : Jom M.Apostal
Publisher
Edition/Year
Reference Book - 2
Title of the book
: Addision-Wesley Pub. Company
: Second Edition, 1978.
: Real Analysis
Name of the Author : N.L.Carothers
Publisher
Edition/Year
: Cambridge University Press
: First South Asian Edition 2006
Prepared by : Dr.S.Rajaram
Signature :
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE
(An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)
SATTUR – 626 203.
Department of Mathematics
(For those who are joining in 2016 -2017 and after)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code :P16MAC23
Semester : II No.of Hours allotted : 6 / Week
Paper : Core - Paper VIII No.of Credits : 4
Title of the Paper- DIFFERENTIAL EQUATIONS
Objectives:
To introduce the methods of solving ordinary differential equations.
To introduce the methods of solving partial differential equations.
Unit I
Introduction - Initial value problems for the homogeneous equation - Solutions of the
homogeneous equation -The Wronskian and linear independence - Reduction of the order of
a homogeneous equations with analytic coefficients - The Legendre equation.
Unit II
Introduction - The Euler equation - Second order equations with regular singular
points- example -Second order equations with regular singular points-The general case - The
Bessel equation, The Bessel equation (continued).
Unit III
Introduction- Equations with variable separated - Exact equations - The method of
successive approximations - The Lipschitz condition - Convergence of the successive
approximations- Approximations to and Uniqueness of, solutions.
Unit IV
Partial differential equations – origins of First-order Partial Differential Equations –
Linear equations of the first order – Integral Surfaces Passing Through a given curve –
Surfaces orthogonal to a given system of surfaces.
Unit V
Nonlinear Partial Differential Equations of the First Order – Compatible systems of
First-order Equations – Charpit‟s method – Special Types of first-order Equations.
SRNMC Regulation-2016 Syllabus
Text Books:
Text Book - 1
Title of the book : An introduction to ordinary differential equations
Name of the author : E.A. Coddington
Publisher : Prentice Hall of India
Edition/Year : 2010
Text Book - 2
Title of the book : Elements of Partial Differential Equations
Name of the author : I.N. Sneddon
Publisher : Tata McGraw Hill Book Company
Edition/Year : 1988
Unit I : (From Textbook-1)
Chapter 3: Sections 1 to 8.
Unit II : (From Textbook -1)
Chapter 4: Sections 1 to 4,7,8.
Unit III: (From Textbook-1)
Chapter 5: Sections 1 to 6, 8.
Unit IV: (From Textbook -2)
Chapter 2: Sections 2.1, 2.2, 2.4 to 2.6
Unit V: (From Textbook -2)
Chapter 2: Sections 2.7, 2.9 to 2.11.
Reference Books:
Reference Book - 1
Title of the book : Differential Equations
Name of the Author : G.F.Simmons
Publisher : Tata McGraw-Hill Education
Edition/Year : 01-May-2006
Reference Book - 2
Title of the book : An Introduction to partial differential equation
Name of the Author : Yehuda Pinchover and Jacob Rubinstein
Publisher : Cambridge University press
Edition/Year : 2005
Prepared by :Dr.K.Nagarajan
Signature :
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE
(An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)
SATTUR – 626 203.
Department of Mathematics (For those who are joining in 2016 -2017 and after)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code :P16MAC24
Semester : II No.of Hours allotted : 6 / Week
Paper : Core - Paper IX No.of Credits : 4
Title of the Paper – ADVANCED MATHEMATICAL STATISTICS Objectives:
To develop the skills in students to apply statistical methods to real problems.
To understand more concepts in statistics and to test hypothesis of different types.
Unit I
Point estimation, confidence intervals for means, confidence intervals for differences
of means, tests of statistical hypotheses.
Unit II
Measures of quality of estimators, a sufficient statistics for a parameter, properties of
a sufficient statistic, Completeness and uniqueness, the exponential class of probability
density functions, functions of a parameter. .
Unit III
Bayesian estimation, Fisher information and the Rao-Cramer inequality, Limiting
distributions of maximum likelihood estimators.
Unit IV
Certain best tests, uniformly most powerful tests, likelihood ratio tests.
Unit V
Distributions of certain quadratic forms, A test of equality of several means, non-
Central 2 and non-central F, Multiple comparisons, The analysis of variance.
SRNMC Regulation-2016 Syllabus
Text Book:
Title of the book
: Introduction to Mathematical Statistics
Name of the author : R.V.Hogg and A.T.Craig
Publisher
Edition/Year
UNIT I :
: Pearson Education, Asia
: V Edition , 2002
Chapter 6: Sections : 6.1 to 6.4.
UNIT II:
Chapter 7: Sections: 7.1 to 7.6.
UNIT III:
Chapter 8: Sections: 8.1 to 8.3.
UNIT IV:
Chapter 9: Sections: 9.1 to 9.3.
UNIT V:
Chapter 10: Sections : 10.1 to 10.5.
Reference Book:
Reference Book - 1
Title of the book : An Introductory Statistics
Name of the Author : Ross,Sheldom.M
Publisher
Edition/Year
Reference Book - 2
Title of the book
: USA, Academic Press
: 2006
: Introduction to Probability Theory and its Applications
Name of the Author : William Feller
Publisher
Edition/Year
: Wiley India
: 3rd
Edition Volume I /2011
Prepared by : Dr. N. Soundararaj
Signature :
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE (An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)
SATTUR – 626 203.
Department of Mathematics
(For those who are joining in 2016 -2017 and after)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code :P16MAE21
Semester : II No.of Hours allotted : 6 / Week
Paper : Paper X - Elective II(a) No.of Credits : 4
Title of the Paper - COMBINATORIAL MATHEMATICS
Objectives:
To introduce the calculating capacity by dealing with enumerating problems.
To know about various application of mathematics in practical situations.
Unit I
Introduction – the rules of sum and product – permutations – combinations –
distribution of distinct objects – Distribution of non distinct objects.
Unit II
Introduction – generating functions for combinations – enumerators for permutations
– distributions of distinct objects into non distinct cells – partitions of integers – elementary
relations.
Unit III
Introduction – Linear recurrence relations with constant coefficients – Solution by the
technique of generating functions – Recurrence relations with two indices.
Unit IV
Introduction – The principle of inclusion and exclusion – The general formula –
Derangements – Permutations with Restrictions on relative positions.
Unit V
Introduction – Equivalence classes under permutation Groups – Equivalence classes
of functions – Weights and inventories of functions – Polya‟s fundamental theorem –
Generalization of Polya‟s Theorem.
SRNMC Regulation-2016 Syllabus
Text Book:
Title of the book
: Introduction to Combinatorial Mathematics
Name of the author : C.L. Liu
Publisher
Edition/Year
Unit I :
: McGraw Hill
: 1968
Chapter 1: Sections 1.1 – 1.6.
Unit II :
Chapter 2: Sections 2.1 – 2.5 and 2.7.
Unit III:
Chapter 3: Sections 3.1,3.2, 3.3 and 3.5.
Unit IV :
Chapter 4: Sections 4.1 – 4.5 .
Unit V:
Chapter 5: Sections 5.1, 5.3 – 5.7.
Reference Book:
Reference Book - 1
Title of the book : A first course in Combinatorial Mathematics
Name of the Author : Ian Anderson
Publisher
Edition/Year
Reference Book - 2
Title of the book
: Oxford University Press
: 2005
: A Course in Combinatorics
Name of the Author : J.H.Van Lint,R.M.Wilson
Publisher
Edition/Year
: Cambridge University Press
: First Southasian Edition 2002
Prepared by : Dr. K.Nagarajan
Signature :
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE
(An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)
SATTUR – 626 203.
Department of Mathematics (For those who are joining in 2016 -2017 and after)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code :P16MAE22
Semester : II No.of Hours allotted : 6 / Week
Paper : Paper X Elective II(b) No.of Credits : 4
Title of the Paper- FUZZY ALGEBRA
Objectives:
To impart the students with fundamentals of Fuzzy set theory and its applications.
To inculcate the habit of viewing objects as graded ones.
Unit I
Fuzzy sets – Basic types – Fuzzy sets – Basic concepts – Additional properties of α –
cuts – Representation of fuzzy sets – Extension principle for fuzzy sets – Types of operations
– Fuzzy complements.
Unit II
Fuzzy numbers – Linguistic variables – arithmetic operations on intervals – arithmetic
operation on fuzzy numbers, fuzzy equations.
Unit III
Fuzzy relation – Crisp versus fuzzy relations – projections and cyclinderic Extensions
– Binary fuzzy relations on a single set – Fuzzy equivalence relations- Fuzzy compatibility
relations – Fuzzy ordering relations, fuzzy morphisms.
Unit IV
Definition of Fuzzy Subgroups – Examples and Properties – Union of two fuzzy
subgroups – Fuzzy subgroups generated by a Fuzzy subsets – Fuzzy Normal Subgroups.
Unit V
Fuzzy normal subgroups under homomorphisms – Characteristics subgroups –Fuzzy
conjugate subgroups – Fuzzy Sylow subgroups
SRNMC Regulation-2016 Syllabus
Text Books:
Text Book-1
Title of the book
: Fuzzy sets and Fuzzy logic – Theory and applications
Name of the Author : George J.Klir and B.Yuan
Publisher : Second edition, 2008
Edition/Year : Prentice Hall of India
Text Book-2
Title of the Book : Fuzzy Algebra Vol I
Name of the Author : Rajeshkumar
Publisher
Edition/ Year
: University of Delhi, Publication Division
: 1993
Unit I : (From Text Book – 1)
Chapter 1: (1.2 to 1.4)
Chapter 2: (2.1 to 2.3)
Unit II : (From Text Book – 1)
Chapter 3: (3.1, 3.2)
Chapter 4: (4.1 to 4.4, 4.6)
Unit III : (From Text Book – 1)
Chapter 5: (5.1 to 5.8)
Unit IV : (From Text Book – 2)
Chapter 1: (1.2.16 – 1.2.21)
Chapter 2: 2.1. 2.2,2.3(upto 2.3.3)
Unit V : (From Text Book – 2)
Chapter 2: (2.3.4 -2.3.14, 2.4)
Reference Books:
Reference Book - 1
Title of the book : Fuzzy set Theory and its applications
Name of the Author : H.J.Zimmer Mann
Publisher
Edition/Year
: Springer International Ltd
: Fourth Edition, 2006
SRNMC Regulation-2016 Syllabus
Reference Book - 2
Title of the book : Fuzzy Commutative Algebra
Name of the Author : John .N Mordeson and T.S.Malik
Publisher : World Scientific Publishing Com.Pvt. Ltd
Edition/Year : 1998
Prepared by : Dr.S.Murugesan
Signature :
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE
(An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)
SATTUR – 626 203.
Department of Mathematics
(For those who are joining in 2016 -2017 and after)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code :P16MAC31
Semester : III No. of Hours allotted : 6 / Week
Paper : Core - Paper XI No. of Credits : 5
Title of the Paper-GALOIS THEORY AND LATTICES
Objectives:
To make them understand the aspects of field theory.
To know more concepts in Extension fields.
Unit I
Extension fields, the transcendence of e.
Unit II
Roots of polynomials, Construction with straightedge and compass, More about roots.
Unit III The elements of Galois Theory. Solvability by radicals.
Unit IV
Galois groups over the rationals, Finite fields.
Unit V Lattices
Lattices and Posets, Lattices as Posets, Lattices and Semilattices, Sublattices, Direct
Products, Distributive lattices, Modular and Geometric lattices.
SRNMC Regulation-2016 Syllabus
Text Book 1
Titleof the book
: Topics in Algebra
Name of the authors : I. N. Herstein
Publisher : John Wiley and Sons
Edition/Year : Second Edition 1999
Text Book 2
Title of the book : Modern AppliedAlgebra
Name of the authors : Garret Birkhoff &H Thomas C. Bartee
Publisher : C. B. S.
Edition/Year :
Unit I : (From Text Book 1)
Chapter 5: Sections 5.1 to 5.2
Unit II :
Chapter 5: Sections 5.3, 5.4, 5.5.
Unit III :
Chapter 5: Sections 5.6, 5.7.
Unit IV :
Chapter 5: Sections 5.8 and Chapter 7, Section 7.1.
Unit V : (From Text Book 2) Chapter 9 ( Sections 9.1 to 9.6 )
Reference Books:
Reference Book - 1
Title of the book : A first Course in Algebra
Name of the Author : J.B. Fraleigh
Publisher : Addition –Wiely Longman Znc.Reading, Massachuetts
Edition/Year : 1999
Reference Book - 2
Title of the book : Basic Abstract Algebra
Name of the Author : P.B. Bhattacharya S K Jain, S.R Napul
Publisher :
Edition/Year :
: Cambridge University Press
Second Edition, 1995,(Reprinted 2009)
Prepared by : Dr. K. Nagarajan
Signature :
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE (An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)
SATTUR – 626 203.
Department of Mathematics
(For those who are joining in 2016 -2017 and after)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code : P16MAC32
Semester : III No.of Hours allotted : 6 / Week
Paper : Core - Paper XII No.of Credits : 5
Title of the Paper MEASURE AND INTEGRATION
Objectives:
To give the comprehensive idea about the underlying principles of Lebesgue measure.
To describe the properties of Lebesgue measure.
Unit I
Lebesgue Outer Measure - Measurable Sets-Regularity .
Unit II
Measurable Functions - Borel and Lebesgue Measurability.
Unit III
Integration of Non-negative Functions – The general integral – Integration of series.
Unit IV
Riemann and Lebesgue integrals – The Four Derivatives – Continuous Non -
Differentiable Functions.
Unit V
Functions of Bounded Variations – Lebesgue Differentiation Theorem –
Differentiation and integration – The Lebesgue Set.
SRNMC Regulation-2016 Syllabus
Text Book:
Title of the book
: Measure Theory and Integration
Name of the author : G. de Barra
Publisher
Edition/Year
Unit I :
: New Age International (P) Limited, Publishers
( formerly Willey Eastern Ltd)
: Reprint 2008.
Chapter 2: Sections 2.1 , 2.2 and 2.3.
Unit II :
Chapter 2: Sections 2.4 and 2.5.
Unit III :
Chapter 3: Sections 3.1, 3.2 and 3.3.
Unit IV :
Chapter 3: Sections 3.4,
Chapter 4: Sections 4.1 and 4.2.
Unit V :
Chapter 4: Sections 4.3 to 4.6.
Reference Book:
Reference Book - 1
Title of the book : Real Analysis
Name of the Author : H.L.Royden
Publisher
Edition/Year
Reference Book - 2
Title of the book
: MacMillan, New York
: Third Edition, 1988
: Measure Theroy
Name of the Author : Paul RHalmos
Publisher
Edition/Year
: Naros Publishing House
: Springer International Student Edition /1981
Prepared by : Dr. K.Nagarajan
Signature :
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE (An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)
SATTUR – 626 203.
Department of Mathematics
(For those who are joining in 2016 -2017 and after)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code :P16MAC33
Semester : III No.of Hours allotted : 6 / Week
Paper : Core - Paper XIII No.of Credits : 5
Title of the Paper -TOPOLOGY Objectives:
To lay the foundations for future study in analysis, in geometry and in algebraic
topology.
To develop the firm footing on the core subject of topology.
Unit I
Topological Spaces – Basics for a topology – The order topology – The product
topology on X x Y – The subspace topology – Closed sets and limits points – Continuous
functions – The product topology.
Unit II
The metric topology – Connected spaces – Connected subspaces of the real line.
Unit III
Compact spaces – Compact subspaces of the real line – Limit Point compactness –
Local Compactness.
Unit IV
Countability axioms – The separation axioms – Normal spaces.
Unit V
The Uryshon lemma – Completely regular - The Urysohn metrization Theorem – -
Imbedding Theroem – The Tietze Extension Theorem. .
SRNMC Regulation-2016 Syllabus
Text Book:
Title of the book
: Topology
Name of the author : James R.Munkres
Publisher
Edition/Year
Unit I :
: Prentice – Hall of India, Private Ltd, New Delhi
: Second Edition, 2011
Chapter 2: Sections 12 – 19
Unit II :
Chapter 2: Sections 20, 21.
Chapter 3: Sections 23, 24.
Unit III:
Chapter 3: Sections 26 to 29.
Unit IV :
Chapter 4: Section 30, 31, 32.
Unit V:
Chapter 4: Sections 33,34, 35.
Reference Book:
Reference Book - 1
Title of the book : Introduction to Topology and Modern Analysis
Name of the Author : G.F. Simmons
Publisher
Edition/Year
Reference Book - 2
Title of the book
: Tata MacGrow Hill
: 2008
: Toplogy
Name of the Author : N James Dugundj
Publisher
Edition/Year
: Universal Book Stall, New Delhi
:1990
Prepared by : Dr. B. Meeradevi
Signature :
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE
(An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)
SATTUR – 626 203.
Department of Mathematics (For those who are joining in 2016 -2017 and after)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code :P16MAC34
Semester : III No.of Hours allotted : 6 / Week
Paper : Core - Paper XIV No.of Credits : 4
Title of the Paper– STOCHASTIC PROCESSES
Objectives:
T o understand the concepts of Stochastic processes
Develop skills to know the nature of states of Markov Models.
Unit I
GENERATING FUNCTIONS AND MARKOV CHAINS
Generating Functions – Probability Generating Functions : Mean and Variance of
Bernoulli, Poisson, Geometric and Logarithmic distributions - Solutions to difference equations
using generating functions and method of characteristic functions - Definitions and Examples of
Stochastic processes - Markov Chains : Definitions and Examples – Transition Matrix –
Probability Distribution - Order of a Markov Chain – Markov chains as graphs - Higher Transition
Probabilities.
Unit II
STATES AND STABILITY OF MARKOV CHAIN
Classification of States and Markov Chain : Transient and persistent states - Determination of higher
transition probabilities - Stability of a Markov System , Ergodic theorem – Graph theoretic approach.
Unit III
POISSON PROCESS
Poisson Process and its Extensions: Poisson Process – Properties of Poisson process – Poisson process
and related distributions –Generalization of Poisson Process – Poisson cluster process - Pure birth
process: Yule furry process –birth immigration process- Time dependent Poisson Process
SRNMC Regulation-2016 Syllabus
Unit-IV BIRTH DEATH PROCESS AND RENEWAL PROCESS
Birth-Death Process - Renewal Processes in Continuous Time –Renewal equation -
Stopping time - Wald‟s Equation – Elementary renewal theorems –Central limit theorem
on Renewals
Unit-V WIENER PROCESS
Markov Processes with Continuous State Space: Introduction –Brownian Motion – Wiener Process-
Differential equations for a Wiener Process - Kolmogorov equations – First Passage time distribution
for Wiener Process- Ornstein Uhlenbeck Process.
Text Book:
Title of the book : Stochastic Processes
Name of the author : J.MEDHI
Publisher
Edition/Year
Unit 1:
: New Age International Publishers
: Third Edition, 2009
Unit 2:
Unit 3:
Unit 4:
Unit 5:
Chapter 1: Sections 1.1.1, 1.1.2 , 1.5, Appendix: pp456-461
Chapter 2: Sections 2.1 to 2.3.
Chapter 2: Sections 2.4 to 2.7.
Chapter 3: Sections 3.1 to 3.3.
Chapter 3: Sections 3.4
Chapter 6: Sections 6.2 to 6.5.1, 6.5.5
Chapter 4: Sections 4.1 to 4.6.
Reference Book:
Reference Book - 1
Title of the book
: Introduction to Stochastic Processes
Name of the Author : Paul G. Hoel, Sidney C. Port, Charles J. Stone,
Publisher :
Edition/Year :
SRNMC Regulation-2016 Syllabus
Reference Book - 2
Title of the book : Haughton Mifflin Comp.,
Name of the Author : A First Course in Stochastic Processes
Publisher : Samuel Karlin and Howard M.Taylor Academic Press
Edition / Year : 1972
Prepared by : Dr. S. Murugesan
Signature :
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE (An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)
SATTUR – 626 203.
Department of Mathematics
(For the candidates admitted from the year 2016-2017 onwards)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code : P16MAE31 Semester : III No. of Hours allotted : 6 / Week
Part : Paper XV – Elective III(a) Credits :4
Title of the Paper-NUMERICAL ANALYSIS
Objectives:
To provide the student an understanding of the basic principles of numerical
methods and to apply them in solving algebraic equations and ordinary differential
equations numerically.
To introduce various difference operators to enable the students to apply them in
Interpolation and numerical differentiation and integration.
Unit I :
Introduction - Bisection method – Method of False Position - Iteration Method – Newton-
Raphson Method – Ramanujan‟s Method
Unit II :
Secant Method–Muller‟s Method–Graffe‟s Root-Squaring Method–Lin-Bairstow‟s Method–
Quotient-Difference Method–Solution to Systems of Nonlinear Equations.
Unit III:
Introduction - Numerical Differentiation - Maximum and Minimum Values of a
Tabulated Function-Numerical Integration-Euler –Maclaurin Formula – Numerical Integration
with Different Step Sizes.
Unit IV :
Numerical Solution of Ordinary Differential Equations – Introduction – Solution by Taylor‟s
Series – Picard‟s Method of Successive Approximations – Euler‟s Method–Runge–Kutta
Maethods –Predictor-Corrector Methods.
Unit V:
Numerical Solution of Partial Differential Equations – Introduction –Laplace‟s Equation –
Finite-difference Approximations to Derivatives–Solution of Laplace‟s Equation.
SRNMC Regulation-2016 Syllabus
Text Book:
Title of the book : Introductory Methods of Numerical Analysis
Name(s) of the Author(s): S.S. Sastry
Publisher : PHI Learning Private Limited
Edition/Year : Fifth Edition, 2012.
Unit I
Chapter 2: Sections 2.1 – 2.6
Unit II
Chapter 2: Sections 2.7 – 2.12
Unit III
Chapter 6: Sections 6.1 – 6.6
Unit IV
Chapter 8: Sections 8.1 – 8.6
Unit V
Chapter 9: Sections 9.1 – 9.4
Reference Books:
Reference Book: 1.
Title of the book : Applied Numerical Analysis,
Name(s) of the Author(s): C.F.Gerald and P.O.Wheatley,
Publisher : Addison Wesley,
Edition/Year : Fifth Edition, 2008
Reference Book – 2 ,
Title of the book : Elementary Numerical Analysis.
Name(s) of the Author(s): Samuel D Conte and Carl de Boor,
Publisher : Tata MacGraw Hill Pvt.Ltd,
Edition/Year : Third Edition, 1980.
Prepared by : Mr. D. K. Nathan
Signature :
SRNMC Regulation-2016 Syllabus
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIALCOLLEGE (An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)
SATTUR – 626 203. Department of Mathematics
(For those who are joining in 2016 -2017 and after)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code : P16MAE32
Semester : III No.of Hours allotted : 6 / Week
Paper : Paper XV - Elective III(b) No.of Credits : 4
Title of the Paper-INTEGRAL EQUATIONS
Objectives:
To provide the basic knowledge of Integral Equations.
To introduce various difference applications of Integral Equations.
Unit I
Integral Equation – Differentiation of a function Under an Integral Sign- Relation between
Differential and Integral Equations- Illustrative Examples.
Unit II
Solution of Nonhomogeneous Volterra‟s Intergral Equation of Second kind by the Method of
Successive Substitution- Solution of Non-homogeneous Volterra‟s Intergral Equation of Second
Kind by the Method of Successive Approximation-Determination of Some Resolvent Kernels-
Volterra Intergral Equation of the First Kind-Solution of the Fredholm Intergral Equation by the
Method of Successive Substitutions- Iterated Kernels-Solution of the Fredholm Intergral Equation
by the Method of Successive Approximation- Reciprocal Functions- Volterra Soluctions of
Fredholm‟s Equations.
Unit III
Fredholm First Theorem-prove that the solution-Every Zero of Fredholm Function is a pole of
the Resolvent Kernel-If a real Kernel has a Complex Eigen Value then it also Contains the
Conjugate Eigen Value to -Hadamard‟s Theorem-Convergence proof-Fredholm second-Theorem-
Fredholm‟s Assiciated Equation. Characteristic Solutions-Fredholm‟s Third Theorem.
Unit IV
All Iterated Kernels of a Symmetric Kernel are also Symmetric-Orthogonality-Orthogonality of
Fundamental Functions –Eigen Value of Symmetric Kernel are Real.Real Charateristic Constants-
Expansion of a Symmetric Kernel in Eigen Functions-Symmetric Kernels with a Finite Number of
SRNMC Regulation-2016 Syllabus
Eigen Values-Symmetric Kernels –with a Finite Eigen Value - Sequence of the pth Power of the
Eigen Value of the Iterated Kernal-Fourier series of power of the Eigen Value of the Iterated
Kernal-Hillbert – Schmidt Theorem- The inequalities of Schwarz and Minkowski-Hilbert‟s
Theorem-Complete Normalized Orthogonal System of Fundamental Functions-Bessel Intequality-
Riesz –Fischer Theorem-Representation by a liner Combination of the Charateristic Functions-
Schidt‟s Solution of the Non-Homogeneous Integral Equation – Solution of the Non-Homogeneous
Integral Equation-Solution of the Fredholm Integral Equation of first Kind-
Unit V
Introduction – Initial Value Problem- Boundary Value Problem – Deformation of a Rod –
Determination of Periodic Solutions-Green‟s Function.Construction of Green‟s Function-Particular
Case-Influence Function Construction of Green‟s Function when the Boundary Value Problem
Contains a Parameter.
Text Book:
Title of the book
: Integral Equations
Name of the author : Shanti Swarup and Shiv Raj Sing
Publisher : Krishna Prakashan Media (P) Ltd. India
Edition / Year : 25th
Edition, 2015.
Unit I : .
Chapter 1: All Sections
Unit II :
Chapter 2: All Sections
Unit III :
Chapter 3: Sections 3.1 to 3.10
Unit IV :
Chapter 4: All Sections
Unit V :
Chapter 5 : All Sections
Reference Books:
Reference Book - 1
Title of the book : Integral Equations
Name of the author : David Porter & David S.G. Stirling
Publisher
Edition/Year
: Cambridge University Press ,NewYork.
: First Edition 1990.
SRNMC Regulation-2016 Syllabus
Reference Book – 2
Title of the book : Integral Equations and Boundary Value Problems
Name of the author : Dr. M.D.Raisinghania
Publisher : S. CHAND & COMPANY PVT.LTD
Edition/Year : Second Edition, 2008
Prepared by : Dr.N.Soundararaj
Signature :
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE
(An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)
SATTUR – 626 203.
Department of Mathematics (For those who are joining in 2016 -2017 and after)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code :P16MAC41
Semester : IV No.of Hours allotted : 6 / Week
Paper : Core - Paper XVI No.of Credits : 5
Title of the Paper :COMPLEX ANALYSIS
Objectives:
To give a comprehensive idea about the underlying principles of Complex analysis.
To introduce the theory of analytic function, complex integration and bilinear
transformations.
Unit I: Complex Functions
Concept of Analytic Functions – Limits and Continuity – Analytic Functions –
Polynomials – Rational Functions – Elementary Theory of Power Series - Sequences -
Series – Uniform Convergence – Power series – Abel‟s Limit Theorem.
Unit II: Analytic Functions as Mappings
Conformality – Arcs and Closed Curves – Analytic Functions in Regions – Conformal
Mapping-Lengths and Arcs-Linear Tranformations – The Linear Group – The Cross Ratio -
Symmetry.
Unit III : Complex Integration
Line Integrals –Rectifiable Area – Line Integrals as Functions of Arcs – Cauchy‟s
Theorem for a Rectangle – Cauchy‟s Theorem in a Disk - The Index of a Point with Respect
to a Closed Curve – The Integral Formula - Higher Derivatives.
Unit IV : Local Properties of Analytical Functions
Removable Singularities – Taylor‟s Theorem – Zeros and Poles – The Local Mapping
– The Maximum Principle - Chains and Cycles - Simple Connectivity – Homology - The
General Cauchy‟s Theorem - The Residue Theorem – The Argument Principle – Evaluation
of Definite Integrals.
SRNMC Regulation-2016 Syllabus
Unit V : Harmonic Functions, Series and Product Developments
Definition and Basic Properties – The Mean - Value Property – Poission‟s Formula –
Schwarz‟s Theorem – The Reflection Principle - Power Series – Expansions - Weierstrass‟s
Theorem – The Taylor Series – The Laurent Series.
Text Book:
Title of the book : Complex Analysis
Name of the author : V. Ahlfors
Publisher
Edition/Year
Unit I :
: MeGraw Hill ISE
: III Edition 1981
Chapter 2: Sections 1, 2.
Unit II :
Chapter 3 : Sections 2, 3 ( 3.1 to 3.3 only) .
Unit III :
Chapter 4: Sections 1, 2.
Unit IV :
Chapter 4: Sections 3, 4(4.1 to 4.5 only) and 5
Unit V :
Chapter 4 : Section 6
Chapter 5 : Section 1.
Reference Book:
Reference Book - 1
Title of the book : Complex Analysis
Name of the Author : V.Karunagaran ,
Publisher
Edition/Year
Reference Book - 2
Title of the book
: Narosa Publications,
: Second Edition,
: Introduction to Complex Analysis
Name of the Author : H.A Pirestley
Publisher
Edition/Year
: Oxford University Press,
: Second Edition /2006
Prepared by : Dr.S.Murugesan
Signature :
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE
(An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)
SATTUR – 626 203.
Department of Mathematics (For those who are joining in 2016 -2017 and after)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code :P16MAC42
Semester : IV No.of Hours allotted : 6 / Week
Paper : Core - Paper XVII No.of Credits : 5
Title of the Paper -FUNCTIONAL ANALYSIS
Objectives:
To enrich the students with the advanced topics of functional analysis.
To get the comprehensive idea about the core principles of Gelfand mappings.
Unit I
Normed Spaces - Continuity of Linear maps .
Unit II
Hahn-Banach Theorems – Banach spaces.
Unit III
Uniform Boundedness Principle – Closed Graph Theorem and Open Mapping
Theorem , Bounded inverse Theorem.
Unit IV
Inner Product spaces – Orthonomal sets – Projection and Riesz Represetation
Theroems.
Unit V
Bounded Operators and Adjoints – Normal, Unitary and Self-adjoint operators.
Text Books Title of the book : Functional Analysi
Name of the author: B.V.Limaye
Publisher
Edition/Year
: New Age international Ltd
: Second Edition 1996
SRNMC Regulation-2016 Syllabus
Unit I
Unit II
Unit III
Unit IV
Unit V
:
:
:
:
:
Chapter II: Sections5: 5.1 to 5.7.
Section 6: 6.1 to 6.8
Chapter II : Sections 7 : 7.1 to 7.12
Section 8: 8.1 to 8.4
Chapter III: Sections 9 : 9.1 to 9.3(Pages 138 to 144 only)
Section 10: 10.1 to 10.7
Chapter VI: Sections 21: 21.1 to 21.3(b)
Section22: 22.1 to 22.9
Section 24: 24.1 to 24.06 (Pages 420 to 431 only).
Chapter VII: Section: 25: 25.1 to 25.5
Section 26: 26.1 to 26.5 (Pages 460 to 473)
Reference Book:
Reference Book - 1
Title of the book
: Functional analysis
Name of the Author : Walter Rudin
Publisher
Edition/Year
Reference Book - 2
Title of the book
: Mac Graw Hill international Student Limited
: 1976
: Foundation of Functional Analysis
Name of the Author : S.Poonusamy
Publisher
Edition/Year
: Narosa Publications
: 2006
Prepared by : Dr. S. Murugesan
Signature :
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE
(An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)
SATTUR – 626 203.
Department of Mathematics (For those who are joining in 2016 -2017 and after)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code :P16MAC43
Semester : IV No.of Hours allotted : 6 / Week
Paper : Core - Paper XVIII No.of Credits : 5
Title of the Paper -OPERATIONS RESEARCH
Objectives:
To develop an understanding of various OR tools and their applications to real life
problems.
To become familiar with various OR models.
Unit I : Network Models
Scope of Network Applications - Network Definitions - Minimal Spanning Tree
Algorithm - Shortest Route Problem -Maximal Flow Model - CPM and PERT
Unit II : Queuing Systems
Elements of Queuing Model - Role of Exponential Distribution - Pure Birth and Death
Models, Relationship Between Exponential and Poisson Distributions - Generalized Poisson
Queuing Model
Unit III : Specialized Poisson Queues
Specialized Poisson Queues - M/G/1: (GD/∞/∞) Pollaczek – Khintchine (P-K) Formula -
Other Queuing models - Queuing Decision Models
Unit IV : Classical Optimization Theory
Introduction -Unconstrained Problems - Constrained Problems
Unit V Non Linear Programming Algorithms
Unconstrained Nonlinear Algorithms - Constrained Algorithms
Text Book:
Title of the book
: Operations Research : An Introduction
Name of the author : H. A. Taha
Publisher
Edition/Year
: Prentilce-Hall of India Pvt.Ltd
: VI Edition, 1997
SRNMC Regulation-2016 Syllabus
NOTE: Section C of the Question paper for the end semester examination will contain
only numerical problems.
Unit I :
Chapter 6, Sections 6.1 to 6.5, 6.7.
Unit II :
Chapter 17, Sections 17.1 to 17.5.
Unit III :
Chapter 17, Sections 17.6 to 17.9.
Unit IV :
Chapter 20, Sections 20.1 to 20.3.
Unit V :
Chapter 21, Sections 21.1 and 21.2.
Reference Books
Reference Books -1
Title of the book
Name of the Author
Publisher
Edition/Year
Reference Books -2
Title of the book
Name of the Author
Publisher
Edition/Year
: Linear Programming and Networks Flows
: Mokhtar S. Bazara et. al,
: John Wiley and sons, Singapore,
: 1990
: Principles of Operation Research with applications to
Managerial Decisions
: Harvey M. Wagner
: Pretice Hall of Private Ltd, New Delhi
: Second Edition, 1988
Prepared by : Dr. V.Thiripurasundarai
Signature :
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE (An Autonomous Institution Re-accredited with ‘A’ Grade by NAAC)
SATTUR – 626 203.
Department of Mathematics
(For those who are joining in 2016 -2017 and after)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code : P16MAE41
Semester : IV No.of Hours allotted : 6 / Week
Paper : Paper XIX - Elective IV (a) No.of Credits : 4
Title of the Paper- ADVANCED TOPOLOGY
Objectives:
To enable the students to know more about Topology.
To develop a firm footing on the elective Topology.
Unit I
The Tychonoff Theorem - The Stone-Cech Compactfication – local finiteness.
Unit II
The Nagata-Smirnov Metrization Theorems – Paracompactness – Stone‟s Theorem –
The Smirnov Metrization Theorem.
Unit III
Complete Metric Spaces – A Space Filling Curve.
Unit-IV :
Compactness in Metric Spaces – Pointwise and Compact convergence – Ascolo‟s
Theorem.
Unit-V:
Baire Spaces – A nowhere differentiable function.
Text Book:
Title of the book : TOPOLOGY A first course
Name of the author : James R. Munkres
Publisher : Prentice Hall of India Private Ltd, New Delhi
Edition/Year : Second Edition ,2011
SRNMC Regulation-2016 Syllabus
Unit I
:
Chapter 5: Section 37, 38;
Chapter 6: Section 39
Unit II : Chapter 6: Sections 40 - 42.
Unit III
Unit IV
Unit V
:
:
:
Chapter 7: Sections 43, 44.
Chapter 7: Sections 45 to 47
Chapter 8: Sections 48, 49.
Reference Book:
Reference Books -1
Title of the book
: General Topology
Name of the Author : Stephen Willard
Publisher
Edition/Year
Reference Books -2
Title of the book
: Addison-Wesley Pub.Co.
: 1970
: Toplogy
Name of the Author : James Dugundj
Publisher
Edition/Year
: Universal Book Stall, New Delhi.
: 1990
Prepared by : Dr.N.Soundararaj
Signature :
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE
(An Autonomous Institution Re-accredited with ‘A’ Grade by NAAC)
SATTUR – 626 203.
Department of Mathematics (For those who are joining in 2016 -2017 and after)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code :P16MAE42
Semester : IV No.of Hours allotted : 6 / Week
Paper : Paper XIX – Elective IV(b) No.of Credits : 4
Title of the Paper- NUMBER THEORY AND CRYPTOGRAPHY
Objectives:
To enable the students to know more about numbers.
To provide an introduction to analytic number theory.
To introduce the recent topics of Cryptography with applications.
Unit I
Introduction, Divisibility, Greatest common divisor, Prime numbers, The fundamental
theorem of arithmetic, The series of reciprocals of the primes, The Euclidean algorithm, The
GCD of more than two numbers, The Mobius function µ(n), The Euler totient function φ(n),
A relation connecting φ and µ , A product formula for φ(n), The Dirichlet product of
arithmetical functions, Dirichlet inverses and the Mobius inversion formula , The Mangoldt
function (n).
Unit II
Multiplicative functions , Multiplicative functions and Dirichlet multiplication, The
inverse of a completely multiplicative fucntion. Liouville‟s function (n), The divisor
functions (n), Generalized convolutions Formal power series ,The Bell series of an
arithmetical function, Bell series and Dirichlet multiplication , Derivatives of arithmetical
functions, The Selberg identity.
Unit III
Definition and basic properties of congruences, Residue classes and complete
residue systems, Linear congruences, Reduced residue systems and the Euler-Fermat
theorem, Polynomial congruences modulo p, Langrange‟s theorem . Applications of
Lagrange‟s theorem. Simultaneous linear congruences , The Chinese remainder theorem.
SRNMC Regulation-2016 Syllabus
Unit-IV : Cryptography
Some simple crptosystems – Enciphering matrices.
Unit-V: Public Key
The idea of public key cryptography – RSA – Discrete log(The index – calculus
algorithm is not included) – Knapsack.
Text Books:
Text Books -1
Title of the book : Introduction to Analytic Number Theory
Name of the author: T.M. Apostol
Publisher
Edition/Year
Text Books -2
: Narosa Publishing Ltd, India
: III edition, 1991
Title of the book : A Course in number theory and cryptography
Name of the author: Neal Koblitz
Publisher
Edition/Year
: Springer International Edition,
: Second Edition, Fourth Indian Reprint 2010.
Unit I
Unit II
Unit III
Unit IV
Unit V
: (From Text book – 1)
Chapter 1: Sections 1.1 to 1.8
Chapter 2: Sections 2.1 to 2.8
: (From Text book – 1)
Chapter 2: Sections 2.9 to 2.19
: (From Text book – 1)
Chapter 5 : Sections 5.1 to 5.7.
: (From Text book – 2)
Chapter III: Sections 1 and 2.
: (From Text book – 2)
Chapter IV: Sections 1 to 4.
SRNMC Regulation-2016 Syllabus
Reference Books:
Reference Books -1
Title of the book
: An Intoruction to Theory of Numbers
Name of the Author : Niven and Zuckermann
Publisher
Edition/Year
Reference Books -2
Title of the book
: Wiley Eastern Ltd.
: 13rd Edition / 1972
: Introduction to cryptographyy
Name of the Author : Neal Konlitz
Publisher
Edition/Year
: Chapman and Hall /CRC
: 2nd
Edition /2007
Prepared by : Dr. K.Nagarajan
Signature
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE
(An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)
SATTUR – 626 203.
Department of Mathematics
(Those who joined in 2016-2017 and after)
SYLLABUS
Programme : M.Sc.,Mathematics Subject Code :P16MAPT41
Semester : IV No.of Hours allotted :6/Week
Paper : Core-Paper XX No.of Credits :4
Title of the Paper-PROJECT
Objectives:
To develop the ability of the students to prepare a project.
To get clear idea about the new concepts in Mathematics apart from the syllabus.
Regulations for the Project Report
The topic of the project may be based on research articles from mathematical journals or
any topic not covered in the M. Sc syllabus.
Evaluation method for project
Max Marks
Internal External Credits
Project Report 40 40
Viva Voce 20
Total 100 4
1. Internal examiners are the respective supervisors.
2. Project Reports are evaluated by both internal and external Examiners
3. Viva Voce examination is conducted evaluated by the external examiner.
The format of the project report should have the following components.
First page should contain:
Title of the project report.
Name of the candidate
Register number.
Name of the supervisor.
Address of the institution
Month & year of submission.
SRNMC Regulation-2016 Syllabus
Contents .
Declaration by candidate
Certificate by supervisor.
Acknowledgement
Preface
Chapter 1 - Preliminaries.
Other chapters.
References.
The report of the project must be in the prescribed form. It should be typed
neatly in MSword with the equation editor or using Latex. The font size of the letter
should be 12 or 13 points with double space.
The number of pages in the project may vary from 40 to 50 .
Each page should contain atleast 18 lines.
Four copies of the project report with binding should be submitted.
Prepared by:
Signature :
SRNMC Regulation-2016 Syllabus
SRI S.RAMASAMY NAIDU MEMORIAL COLLEGE
(An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)
SATTUR – 626 203.
Department of Mathematics
(Those who joined in 2016-2017 and after)
SYLLABUS
Programme : M. Sc., Mathematics Subject Code :P16MAX41
Semester : IV No. of Credits : 3
Extra Credit paper
Title of the Paper: Model Paper for NET/SET Examination
Objectives:
To create an awareness of the NET/SET Examination
To make the students prepared for NET / SET Examinations
UNIT-I
Algebra: Permutations- Combinations- Pigeon – hole principle – inclusion –exclusion
principle - derangements- Group – subgroups , normal subgroups- quotient group –
homeomorphisms- cyclic groups – permutation groups- cayley‟s theorem – Sylow‟s theorems
–Rings- Ideals – U.F.D – P.I.D- Euclidean Domain.
UNIT-II
Linear Algebra: Vector spaces- subspaces – Linear dependence – basis – dimension –
algebra of linear transformations – Algebra of matrices – rank and determinant of matrices –
linear equations – Eigen values & Eigen vectors – Cayley Hamilton theorem – Matrix
representation of Linear transformation, Change of basis – Canonical forms – diagonal forms
– triangular forms – Jordan forms – Inner product spaces – orthonormal basis – Quadratic
Forms .
UNIT-III
Analysis: Finite , countable and uncountable sets – Archimedean property – supremun-
infimum - Sequences and Series – liminf - limsup – Continuity – Uniform Continuity –
Differentiability – Mean value theorem – Sequence and series of functions – Uniform
convergence – Riemann Integral – improper Integral‟s – Functions of general valuables –
directional derivative- partial derivative – derivative, as a Linear transformations – Metric
spaces – compactness – connectedness – space of all continuous functions.
SRNMC Regulation-2016 Syllabus
UNIT-IV
Complex Analysis : Analytic functions – C-R equations - Cantour Integral – Cauchy‟s
theorem – Cauchy‟s integral formula – Lioville‟s theorem – Maximum modulus principle –
Schwarz lemma – Open mappings – Mobius transformations – Taylor series- Calculus of
residues.
Topology: basis – dense sets – subspace and product topology – Separation axioms –
connectedness and compactness.
UNIT-V
Differential equations ODE : existence and uniqueness of solutions of initial value pbms
for first order ordinary differential equations – Singular solutions of first order ODE –
General theory of homogeneous and non homogeneous linear ODE – Variations of
parameters – Sturm – Lioville boundary value problem.
PDE :
Lagrange and Charpit methods for solving first order PDC – classification of second order
PDE- General solutions of higher order PDE, with constant coefficients.
Sample space, discrete probability, independent events, Bayes theorem. Random variables
and distribution functions (univariate and multivariate); expectation and moments.
Independent random variables, marginal and conditional distributions. Characteristic
functions. Probability inequalities (Tchebyshef, Markov, Jensen). Modes of convergence,
weak and strong laws of large numbers. Central Limit theorems (i.i.d.case).
Markov chains with finite and countable state space, classification of states, limiting
behaviour of n-step transition probabilities, stationary distribution.
Reference Books:
UNIT I: Topics in Algebra by I.N. Herstein WILEY Publication, second edition .
Conlemporary, Abstaract Algebra, Joseph A Gallian, Narosa Publicizing House,
Fourth Edition.
SRNMC Regulation-2016 Syllabus
UNIT II: Linear Algebra byTenneth Hoffman RAY KUNZE, PHI Learning Private
Limited second edition. Linear Algebra, Stephen H.Friedbery, Arnold J.Insel,
Lawrence E.Spence,PHI Learning Private Limited Fourth edition
UNIT III: Principles of Mathematical Analysis by Walter Rudin, MOGRAW-HILL
Publication, third edition.
Real Analysis, N.L. Carothers, Cambridge University Press.
UNIT IV: Foundation of Complex Analysis by S. Ponnusamy, Narosa Publications, second
edition. Topology by James R. Munkers PHI learning private Limited, second
edition. Function of one complex variable, John. B. Conway, Narosa publishing
House, Second edition.
UNIT V: Differential equations by D. Raisinghania
An Introduction to Ordinary Differential Equations
A. Codington, PHI learning private Limited.
Prepared by:
Signature :
CHAIRMAN DEAN
SRNMC Regulation-2016 Syllabus