Thiagarajar college (autonomous), madurai – 9




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Unit - I (18 Hours)

Elementary Data Structures : Stacks and queues, tree, binary tree, dictionaries – Binary search tree, priority queues – Heaps, heapsort, sets and disjoint set union – Union and Find operations - Graphs – graph representations.

Unit - II (18 Hours)

Divide- And- Conquer: General method - Binary Search - Finding the maximum and minimum – Merge Sort – Quick Sort.

Unit – III (18 Hours)

The Greedy method: General method - Knapsack problem- Tree vertex splitting- Job Sequencing with deadlines- Optimal storage on tapes- optimal merge patterns.



Unit – IV (18 Hours)

Dynamic programming: The General method- Multistage graphs- All pairs shortest paths- Optimal binary search trees.


Unit - V (18 Hours)

Basic traversals and Backtracking techniques for binary tree and graphs - Connected components and spanning trees - Biconnected components and DFS - Backtracking general method – The 8 Queen’s problem - Graph coloring- Hamiltonian cycles.


Text Book : Fundamentals of Computer Algorithms

-Ellis Horowitz, Sartaj Sahani and Sanguthevan Rajasekaran

-Galgotia Publications Pvt Ltd., 2008


Unit

Chapter/Section

I

2(2.1 to 2.6)

II

3(3.1 to 3.5)

III

4(4.1 to 4.4, 4.6, 4.7)

IV

5(5.1 to 5.3, 5.5)

V

6(6.1 to 6.4)

7(7.1, 7.2, 7.4, 7.5)




Reference Book: Computer Algorithms - Sare Baase and Allan Van Gelder

Pearson Education Asia, 2002


THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009

(Re- Accredited with 'A' Grade by NAAC)

Department of Mathematics

(From 2011 – 2013 batch onwards)

Course : M.Sc. Code No. :

Semester : III No. of hours allotted : 2

Paper : Non Major Elective No. of credits : 2

Title of the Paper : Fourier Transforms


Course objective : To introduce the Fourier transforms and its different forms


Unit – I

Fourier integral formula – Weierstrss M test – Functions of exponential order – Riemann – Lebesgue Theorem – Fourier integral theorem – Different forms of Fourier integral formula – Dirichelets integral – Fejer’s integral – Applications of Fourier integral formula.


Unit – II

Fourier sine transform of F(x) - Fourier cosine transform of F(x) – Infinite Fourier transform of F(x) – The finite Fourier sine transform of F(x) – The finite Fourier cosine transform of F(x)



Unit

Chapter/section

I

2

II

3



Text Book:

Fourier series and Fourier transforms and their applications

  • Goyal and Gupta, Pragati Prakasham, Meerut, 3rd edition 1995



Reference Book:

Laplace and Fourier transforms

Goyal and Gupta, Pragati Prakasham, Meerut, 12th edition 1998


THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009

(Re- Accredited with 'A' Grade by NAAC)

Department of Mathematics

(From 2011 – 2014 batch onwards)

Course : M.Sc. Code No. :

Semester : III No. of hours allotted :

Paper : Self study No. of credits : 5

Title of the Paper : Fuzzy Graph Theory


Course objective: To introduce the fuzzy concepts in Graph Theory

Unit - I

Fuzzy Sets and Fuzzy Relations: Introduction – Fuzzy sets and fuzzy set operators – Fuzzy relations – Composition of fuzzy relations – Properties of fuzzy relation.


Unit – II

Fuzzy Graph: Introduction to fuzzy graph – Operations on fuzzy graph – Complement of a fuzzy graph - Cartesian product and composition – Union and Join.

Unit - III

Fuzzy Tree and Fuzzy Forest: Paths and Connectedness – Fuzzy Bridges and Fuzzy cut nodes – Fuzzy forests and fuzzy trees – Geodesics – Triangle and Parallelograms laws.


Unit - IV

Fuzzy Bipartite Graphs: Fuzzy Independent set and Fuzzy Bipartite graph – Fuzzy Bipartite part and Maximal Bipartite part – Maximal Fuzzy Bipartite part algorithm.


Unit – V

Domination in Fuzzy Graphs: Dominating Set – Fuzzy Independent Set – Bounds for (G) - More Adjacency in Fuzzy graph.


Text Book:

A First Look at Fuzzy Graph Theory – A. Nagoorgani and V. T. Chandrasekaran,

Allied Publishers Pvt. Ltd., 2010


Unit

Chapter/Section

I

1.1 – 1.5

II

2.1 – 2.2

III

3.1 – 3.3

IV

4.1 – 4.3

V

5.1 – 5.4



Reference Book:

Fuzzy Graphs and Fuzzy Hypergraphs - John N. Mordeson, Premchand S. Nair,

Physica-Verlag Heidelberg, 2000.


M.Phil. (Mathematics)

(2011 – 2012 Batch onwards)


THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 9

(Re – Accredited with ‘A’ Grade by NAAC)

DEPARTMENT OF MATHEMATICS


M.Phil. MATHEMATICS

COURSE STRUCTURE (w.e.f. FROM 2011 – 2012 batch onwards)


Semester – I



Code

No

Subject

Contact

Hrs /

Week

Credits

Total No

of Hrs

Allotted

Max

Marks

CA

Max

Marks

SE

Total




Research Methodology

9




135

100

100

200




Functional Analysis

9




135

100

100

200




Elective Paper *

9




135

100

100

200



Semester – Ii



Code

No

Subject

Contact

Hrs /

Week

Credits

Total No

of Hrs

Allotted

Max

Marks

CA

Max

Marks

SE

Total




Dissertation










100

100

200



* ELECTIVE PAPER: (In - depth study papers): (One paper is to be chosen)

1. Advanced Graph Theory

2. ODE and Stability theory

3. Computational Complexity


Question paper pattern:


5 Internal choice questions 5 x 20 = 100 Marks


THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009

(Re- Accredited with 'A' Grade by NAAC)

Department of Mathematics

(From 2011 – 2012 batch onwards)

Course : M.Phil. Code No. :

Semester : I No. of hours allotted : 9

Paper : Core 1 No. of credits :

Title of the Paper : Research Methodology


Course objective: To pay due attention to designing and adhering to the appropriate methodologies throughout for improving the quality of research and to give a brief treatment of tensor products and simple properties of the formation of fractions.


Unit - I

Research Methodology : Meaning of Research – Objectives of Research – Motivation in Research – Types of Research – Research Approaches – Significance of Research – Research Methods versus Methodology – Research and Scientific Method – Importance of Knowing How Research is Done – Research Process – Criteria of Good Research – Problems- Encountered by Researchers in India – What is a Research Problem? – Selecting the Problem – Necessity of Defining the problem – Techniques Involved in Defining a Problem – Meaning of Research Design – Need for Research Design – Features of a Good Design – Import Concepts Relating to Research Design – Different Research Designs – Basic Principles of Experimental Designs.


Unit - II

LATEX : The Basics – The Document – Bibliography – Bibliographic Databases – Table of contents , Index and Glossary – Displayed Text – Rows and Columns – Typesetting Mathematics.


Unit III

Modules : Modules and module homomorphisms - Submodules and quotient modules - Operations and submodules – Direct sum and product – Finitely generated modules – Exact sequences – Tensor product of modules –Restriction and extension of scalars – Exactness properties of the tensor product – Algebras – Tensor product of algebras .


Unit IV

Rings and Modules of fractions : Local properties – Extended and contracted ideals in rings of fractions - Primary Decomposition.


Unit V

Integral Dependence and Valuation : Integral dependence – The going-up theorem – Integrally closed integral domains – The going- down theorem – Valuation rings – Chain conditions - Noetherian rings – Primary Decomposition in Noetherian rings.

Text Books:

1. Research Methodology, Methods and Techniques (Second Revised Edition) - C.R. Kothari, New Age International Publishers, Reprint 2010

2. LATEX Tutorials, A Primer - Indian TEX Users Group, Trivandrum, India, 2003

3. Introduction to Commutative Algebra - M.F. Atiyah, I.G. GeMacdonald ,

Addison – Wesley Publishing Company 1969



Unit

Book

Chapter/Section

I

1

Chapters 1, 2 and 3

II

2

Chapters I - VIII

III

3

Chapter 2

IV

3

Chapters 3 and 4

V

3

Chapters 5, 6 and 7



Reference Books:

1. Research Methodology - R. Panneerselvam, Prentice Hall of India, New Delhi -110 001, 2007

2. Algebra - Thomas W. Hungerford, Springer International edition, 2008

THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009

(Re- Accredited with 'A' Grade by NAAC)

Department of Mathematics

(From 2011 – 2012 batch onwards)

Course : M.Phil. Code No. :

Semester : I No. of hours allotted : 9

Paper : Core 2 No. of credits :

Title of the Paper : Functional Analysis


Course objective : To study certain topological-algebraic structures and the methods by which knowledge of these structures can be applied to analytic problem.

To study the basic properties of Fourier transform.


Unit - I

Banach spaces: Definition and Examples – Continuous linear transformations – The Hahn – Banach Theorem – The natural imbedding of N in N** - The open mapping theorem – The conjucate of an operator.


Unit - II

Finite – dimensional spectral theory : Matrices – Determinants and the spectrum of an operator – The spectral theorem


Unit - III

Banach Algebras: Definition and examples – Regular and singular elements – Topological divisors of zero – The spectrum – The formula for the spectral radius – The radial and semi-simplicity – The Gelfand mapping – Application of the formula r(x) = lim ||xn|| 1/n


Unit - IV

Integration on product spaces : Measurability on Cartesian products – Product measure – The Fubini theorem – Completion of product measures – Convolutions – Distribution functions


Unit – V

Fourier transforms: Formal properties – The inversion theorem – The Plancherel theorem – The Banach Algebra L1


Text Book:

1) Introduction to Topology and Modern Analysis

-G.F. Simmons, McGraw – Hill International editions, 1963

2) Real and Complex analysis

- Walter Rudin, Tata McGraw – Hill International edition, Ninth Reprint, 2010.


Unit

Book

Chapter/Section

I

1

9(Full)

II

1

11(sections 60 – 62)

III

1

12(Full), 13(sections 70 – 71)

IV

2

8(Full)

V

2

9(Full)



Reference book: 1) Functional Analysis - Walter Rudin, Tata McGraw-Hill, 1989.

2) 2) Functional Analysis – George Bachman Lawrence Narici

Academic Press International, New York, 1996

THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009

(Re- Accredited with 'A' Grade by NAAC)

Department of Mathematics

(From 2011 – 2012 batch onwards)

Course : M.Phil. Code No. :

Semester : I No. of hours allotted : 9

Paper : In-depth study No. of credits :

Title of the Paper : Advanced Graph Theory


Course objective:

  • To provide an introduction to the topics of Domination and Magic Labeling

  • To give a focused look on one particular problem so that the students beginning research can see how new mathematics comes into existence



Unit - I

Domination in Graphs: Dominating sets in graphs – Bounds on the domination number in terms of order, size, degree, diameter and girth – Product graphs and Vizing’s conjecture.


Unit – II

Conditions on dominating sets: Introduction – Independent dominating sets – Total dominating sets – Connected dominating sets.

Unit - III

Preliminaries: Magic Squares – Latin Squares – Magic Rectangles – Labelings – Magic Labeling – Some Applications of Magic Labelings


Unit - IV

Edge-magic Total Labelings: Basic ideas – Cycles – Complete bipartite graphs – Trees


Unit - V

Vertex-magic Total Labelings: Basic ideas – Regular graphs – Cycles and Paths – Graphs with vertices of degree one


Text Books:

1. Fundamentals of domination in graphs

- T. W. Haynes, S. T. Hedetniemi and Peter J. Slater

Marcel Dekker Inc, New York, 1998.

2. Magic Graphs - W. D. Wallis, Birkhauser Boston, 2001



Unit

Book

Chapter/Section

I

1

1.2, 2.1 – 2.4, 2.6

II

1

6.1 – 6.4

III

2

1(Full)

IV

2

2.1, 2.4, 2.5, 2.7

V

2

3.1, 3.2, 3.2, 3.6



Reference Books : 1) Theory of domination in graphs - V. R. Kulli,

Vishwa International Publications, Gulbarga, 2010

2) Super Edge-Antimagic Graphs-A Wealth of Problems and Some Solutions

- Martin Baca and Mirka Miller, Brown Walker Press, USA, 2008

THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009

(Re- Accredited with 'A' Grade by NAAC)

Department of Mathematics

(From 2011 – 2012 batch onwards)

Course : M.Phil. Code No. :

Semester : I No. of hours allotted : 9

Paper : Elective (In-depth study) No. of credits :

Title of the Paper : Ordinary Differential Equations and Stability Theory


Course objective: To bring together the qualitative theory of differential equations systematically at an introductory level.

Unit - I Systems of Linear Differential Equations : Introduction – Systems of first order equations – Existence and Uniqueness theorem – Fundamental matrix – Non-homogeneous linear systems – Linear systems with constant co-efficients – Linear systems with Periodic co-efficients.

Unit - II Existence and Uniqueness of Solutions : Introduction – Preliminaries – Successive approximations – Picard’s theorem – Non-uniqueness of solutions – Continuation and dependence on initial conditions – Existence of Solutions in the large – Existence and uniqueness of solutions of systems.

Unit - III Oscillations of Second Order Equations: Fundamental results – Sturm’s comparison theorem – Elementary linear oscillations – Comparison theorem Hille-Wintner – Oscillations of x’’ + a(t) x = 0 - Elementary nonlinear oscillations.

Unit - IV Boundary Value Problems: Introduction – Sturm-Liouville problem – Green’s functions – Non-existence of solutions – Picard’s theorem.

Unit - V

Behaviour of Solutions of Linear Differential Equations : Introduction – nth order equations – Elementary critical points – Critical points of nonlinear systems – Linear systems with constant co-efficients – Linear systems with variable co-efficients – Second order linear differential equations.


Text Book: Ordinary Differential Equations and Stability theory

- S. G. Deo and V. Raghavendra,

Tata McGraw-Hill Publishing Company Limited, New Delhi, First Reprint, 1987



Unit

Chapter/Section

I

Chapter 4

II

Chapter 5

III

Chapter 6

IV

Chapter 7

V

Chapter 8



Reference Books : 1. Stability theory of Differential Equations – Richard Bellman,

McGraw-Hill Book Company, Inc, 1953.

2. Ordinary Differential Equations and Stability Theory: An Introduction

- David A. Sanchez, Dover Publications, Inc., New York, 1968.


THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009

(Re- Accredited with 'A' Grade by NAAC)

Department of Mathematics

(From 2011 – 2012 batch onwards)

Course : M.Phil. Code No. :

Semester : I No. of hours allotted : 9

Paper : Elective (In-depth study) No. of credits :

Title of the Paper : Computational Complexity


Course objective: To understand complexity in computation

Unit - I

Turing Machines: The standard Turing Machine – Combining Turing Machines for Complicated Tasks - Turing’s Thesis.


Unit - II

Other Models of Turing Machines: Monor Variations on the Turing Machine Theme – Turing Machines with More Complex Storage.


Unit - III

Hierarchy of Formal Languages and Automata: Recursive and Recursively Enumerable Languages – Unrestricted Grammars – Context-Sensitive Grammars and Languages – The Chomsky Hierarchy.


Unit - IV

Limits of Algorithmic Computation: Some Problems that cannot be solved by Turing Machines – Undecidable Problems for Recursively Enumerable Laguages – The Post Correspondance Problem – Undecidable Problems for Context-Free Languages – A question of efficiency.

Unit – V

An Overview of Computational Complexity: Efficiency of computation – Turing Machine Models and Complexity – Language Families and Complexity Classes – The Complexity Classes P and NP – Some NP Problems – Polynomial-Time Reduction – NP-Completeness and an Open Question.


Text Book: An Introduction to Formal Languages and Automata – Peter Linz,

Jones and Bartlett Publishers, Fourth Edition, 2006


Unit

Chapter/Section

I

9

II

10

III

11

IV

12

V

14



Reference book: Fundamentals of Computer Algorithms

- Ellis Horowitz, Sartaj Sahani,Sanguthevar Rajasekaran, Galgotia, 2007


Certificate

and

Diploma

Courses

THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009

(Re- Accredited with 'A' Grade by NAAC)

Department of Mathematics

(From 2011 – 2014 batch onwards)

Course : Certificate course Code No. :

Semester : III No. of hours allotted :40

Paper : No. of credits : 02

Title of the Paper : Astronomy


Course objective: To study the solar systems and Astronomical observations


Unit - I (8 Hours)

Celestial sphere – Diuranal motion, celestial axis and equator – Celestial Horizon – Zenith and Nadir – Transit – Due east and due west


Unit – II (8 Hours)

Zones of Earth – Trace the variation in the duration of day and night – duration of perpectual day in the place of latitude - Analytical condition for perpetual day


Unit - III (8 Hours)

Terrestrial latitudes and longitudes – Change of latitude and longitude –The reduction of latitude – The radius of curvature of earth at a station of Geographical latitude


Unit - IV (8 Hours)

Kepler’s Law of planetary motion - Longitude of Perigee - Eccentricity of the earth orbit around the Sun – Newton’s deductions from Kepler’s law – Fix the position of a planet in its elliptic orbit


Unit - V (8 Hours)

Equation of time – seasons – calendar – conversion of time


Text Book: Astronomy - S. Kumaravelu and Susila Kumaravelu,

Jeeva computers, 2009



Unit

Chapter/Section

I

2(40 - 43, 53, 54)

II

3(87, 88, 89, 90)

III

3(91, 92, 96, 100)

IV

7(168, 173, 175, 176, 180)

V

11(11.3, 11.5, 11.6,11.7)



Reference Book:

Dynamic Astronomy – Robert T Dixon, Prentice Hall - Gale, 6th Edition, 1992


THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009

(Re- Accredited with 'A' Grade by NAAC)

Department of Mathematics

(From 2011 – 2012 batch onwards)

Course : Diploma Course Code No. :

Semester :III(M.Sc.,) No. of hours allotted : Paper : No. of credits :

Title of the Paper : Statistics


Course Objective: To introduce the statistical techniques Correlation, Regression and some of the statistical tools t – test, F- test and Chi-square test

Note: Derivations and Proofs of the theorems are not included. Only problems are to be dealt with.

Unit – I (10 Hours)

Correlation: Introduction – Meaning of Correlation – Scatter Diagram – Karl Pearson’s Coefficient of correlation – Calculation of the correlation coefficient for a bivariate frequency distribution – Probable Error of correlation coefficient – Rank correlation.


Unit – II (10 Hours)

Linear and Curvilinear Regression: Introduction – Linear Regression – Curvilinear regression – Regression curves.


Unit – III (14 Hours)

Large Sample Theory: Introduction – Types of Sampling – Parameter and Statistic – Tests of Significance – Procedure for testing of hypothesis – Test of significance for large samples – Sampling attributes – Sampling variables.


Unit – IV (14 Hours)

Exact Sampling Distributions - I (Chi – square Distribution): Introduction – M.G.F. of Chi –square distribution – Some theorems on Chi – square distribution (Statements only) – Linear transformation – Applications of Chi – square distribution.


Unit – V (12 Hours)

Exact Sampling Distributions – II ( t , F and z distributions ) : Introduction Student’s ‘t’ Distribution - Applications of t – Distribution - Distribution of sample correlation coefficient when population correlation coefficient (Sawkin’s Method)

Text Book: Fundamentals of Mathematical Statistics - S.C. Gupta, V.K. Kapoor,

Sultan Chand & Sons, New Delhi, Eleventh Thoroughly Revised Edition, Reprint 2009


Unit

Chapter/Section

I

10(10.1 – 10.7)

II

11(11.1 – 11.4)

III

14(14.1 – 14.8)

IV

15(15.1, 15.3 – 15.6)

V

16(16.1 – 16.4)



Reference Book: Research Methodology, Methods and Techniques - C.R. Kothari

New Age International Publishers, Second Revised Edition, Reprint 2010


B.C.A.


THIAGARAJAR COLLEGE (AUTONOMOUS) MADURAI – 9.

Re-Accredited with ‘A’ Grade by NAAC

DEPARTMENT OF MATHEMATICS

BACHELOR OF COMPUTER APPLICATION

COURSE STRUCTURE (w.e.f 2011-2014 batch onwards)

Semester – I


Code

No

Subject


Contact

Hrs / Week

Credits


Total No of Hrs Allotted

Max Marks CA

Max Marks SE

Total

P111

P121

SAM11

SMM11

SMM12

SMML11


SESM11

ES

Tamil

English

Discrete Mathematics

Programming in C

Digital Principles& Applications

Lab P1:Programming In C Lab


SBE I

Environmental Studies

5

4

5

4

4

4


2


2


2

2

4

4

4

2


2


2

75

60

75

60

60

60


30


30

25

25

25

25

25

40


15


15


75

75

75

75

75

60


35


35


100

100

100

100

100

100

50


50

Total

30

22















Semester – II



Code

No

Subject


Contact

Hrs / Week

Credits


Total No. of Hrs Allotted

Max Marks CA

Max Marks SE

Total

P121

P221

SAM21

SMM21

SMM22

SMML21

SESM21

VE

Tamil

English

Operations Research

Computer Organization

COBOL Programming

Lab P2:COBOL Lab

SBE II

Value Education

5

4

5

4

4

4

2

2

2

2

4

4

4

2

2

2

75

60

75

60

60

60

30

30

25

25

25

25

25

40

15

15

75

75

75

75

75

60

35

35

100

100

100

100

100

100

50

50

Total

30

22















Semester – III


Code

No

Subject


Contact

Hrs / Week

Credits


Total No of Hrs Allotted

Max Marks CA

Max Marks SE

Total

SAM31

SMM31

SMM32

SMML31

SMML32


Elective I

SENM31

SESM31



Numerical Methods

Microprocessor & its Applications

OOPs With C++

Lab P3:C++ Lab

Lab P4:Visual Basic Lab


Mini Project

NME – I Principles of Computers

SBE III

5

4

4

4

4


5

2

2

4

4

4

2

2


4

2

2

75

60

60

60

60


75

30

30

25

25

25

25

25


40

15

15

75

75

75

75

75


60

35

35


100

100

100

100

100


100

50

50

Total

30

24















Semester – IV


Code

No

Subject


Contact

Hrs / Week

Credits


Total No of Hrs Allotted

Max Marks CA

Max Marks SE

Total

SAM41

SMM41


SMM42

SMM43

SMML41


ESM41

SENM41

SESM41

Managerial Accounting

Computer Algorithm and

Data Structures

Java Programming

Multimedia Technology

Lab P5:Java Programming Lab


Elective-II

NME-II Fundamentals of Internet

SBE IV

5


4

4

4

4


5

2

2

4


4

4

2

4


4

2

2




25


25

25

40

40


25

15

15

75


75

75

60

60


75

35

35

100


100

100

100

100


100

50

50

Total

30

26















Semester – V


Code

No

Subject


Contact

Hrs / Week

Credits


Total No of Hrs Allotted

Max Marks CA

Max Marks SE

Total

SMM51

SMM52

SMM53

SMML51

SMML52

Elective III

SESM51

Self Study

Software Engineering

Advanced Java Programming

Data Base Management Systems

Lab P6:RDBMS Lab

Lab P7: Advanced Java Lab

Major Project

SBE V

Computers and Internet Applications


4

4

4

5

5

6

2

4

4

4

2

2

5

2

60

60

60


75

75

90

30

25

25

25


25

40

40

15

75

75

75


75

60

60

35

100

100

100


100

100

100

50


Total

30

23












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