B. Sc., DEGREE COURSE IN MATHEMATICS …srnmcollege.net/event_img/604cd0ae19529ee5178f676e...Tamil...

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)

B. Sc., DEGREE COURSE

IN

MATHEMATICS

SYLLABUS AND REGULATIONS

UNDER

CHOICE BASED CREDIT SYSTEM (CBCS)

(Those who joined in 2016-2017 and after)


Objectives

1. To equip the students with specific knowledge and skills in Mathematics.

2. To organize the instruction on the lines of professional courses by adopting participative methods of

learning.

3. To assist the learners in finding employment opportunities in government,

Multinational Companies, business and industry.

Eligibility for admission

Candidates seeking admission to the B.Sc., (Mathematics) Degree Course must have passed the

Higher Secondary Examination (with Mathematics and Physics as subjects) of the Government of

Tamil Nadu, or any other examination equivalent thereto approved by the Government of Tamil Nadu.

Duration of the course The duration of the course shall be three academic years comprising six semesters

with two semesters in each academic year.

Course of Study The main subjects of study for B.Sc., Mathematics Degree course consist of the

following (For the course pattern, refer Table 1)

Part I : Tamil

Part II : English

Part III : 1. Core Subjects

2. Electives

3. Allied Subjects

Part IV :

1. Non Major Elective Subjects

2. Skill based subjects

3. Environmental Studies

4. Value Education.

Part V : Extension Activities.

Part I and II

Tamil and English Language Courses are 4 each in number.

Part III

The number of Core Courses shall be 14 and Elective Subjects shall be 4. Allied

Subjects 6.

Part IV

The number of Non Major Elective Courses shall be 2 and that of Skill based

Subjects 6. Environmental Studies and Value Education Course are 1 each in number.

Part V

These should be carried out outside the class hours. All the students shall have to enroll for NSS /

NCC / Sports & Games or any other service organization in the College and shall have to put in minimum

hours of attendance to be prescribed by the College. A candidate shall be awarded a maximum of 1 credit

for Compulsory Extension Service.


Credits The term „credit‟ refers to the weightage given to a course, usually in relation to the instructional

hours assigned to it. The total credits required for completing B.Sc.(Mathematics) degree course is

140. The particulars of credits for individual components and courses are presented in 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 2 extra credits will be added in his/her total credit to the degree, even

otherwise, it won‟t affect the completion of degree.

2. The paper is common to all UG Programmes.

3. The title of this paper is “Model Paper for Competitive Examinations”

4. Examination for this paper will be held at the end of the 6th

semester examinations.

5. There is no internal examination and only external examination for this paper.

6. Maximum marks for this paper is 100.

Scheme of Examination

Presented on Table 2.

Evaluation

The performance of a 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 teacher as well as by an end semester examination which will be a written type

examination of 3 hours duration for parts I, II, and III , and of 2 hours duration for part IV and will be

consolidated at the end of the course. The ratio of the marks to be allotted to continuous internal assessment

and to end semester examination is 25: 75 (i.e. Internal 25 marks and External 75 marks ) for theory paper

and 40 : 60 ( i.e., Internal 40 marks and External 60 marks) for practical.

The components for continuous internal assessment for theory are:

Two tests and their average ---15 marks

Seminar/Group Discussion --- 5 marks

Assignment --- 5 marks

Total --25 Marks

and for practical are:

Observation and Record Note ---15 marks

Model practical test ---25 marks

Total ---40 Marks


Question Paper Pattern (Parts I, II, and III )

Duration of Semester Examination: 3 hours Theory: Part A

Ten Questions (Multiple choice) ( No choice)10 x 1 = 10 marks

Two Questions from each Unit

Part B

Five Questions (either or type) 5 x 7 = 35 marks

One Question from each Unit

Part C

Three Questions out of five 3 x 10 = 30 marks

One Question from each unit

Total 75 Marks

Question Paper Pattern (For Part IV only)

Duration of Semester Examination: 2 hours

Theory :

Section-A

THREE Questions (either or type) 3 x 10 = 30 marks

(One Question from each unit)

Section-B

THREE questions out of FIVE 3 x 15 = 45 marks

(Atleast one question from each unit)

Total: 75 Marks

Practical:

Question Paper Pattern ( Parts III and IV) 3 x 20 = 60 marks

Duration of Semester Examination: 3 hours

Question Paper Pattern (Internal) same as in External

Note: No unit shall be omitted; not more than two questions from a single unit

Passing Minimum

1. 40% of the aggregate (Internal + External).

2. No separate pass minimum for the Internal.

3. 27 marks out of 75 is the pass minimum for the External theory examinations.

4. 21 marks out of 60 is the pass minimum for the External practical examinations.


B.Sc. Mathematics

Table 1 : Course pattern

(Those who are joining in 2016 – 2017 and after)

Study I II III IV V VI Total Total No of Total

Component Sem. Sem. Sem. Sem. Sem. Sem. Hrs Credit Course Marks

Part – I 6(3) 6(3) 6(3) 6(3) - - 24 12 4 400 Tamil

Part – II 6(3) 6(3) 6(3) 6(3) - - 24 12 4 400 English

Part- III

Core

Subjects

5(4) 5(5) 5(5) 5(5) 5(4) 5(4) 70 60 14 1400

5(4) 5(5)

5(4)

5(4)

5(4)

5(4)

5(4)

5(4)

Elective -

- 5(4) 5(4) 4(4) 4(3) 18 15 4 400 Subjects

Allied

Subjects-I (T) 4(4) 4(4) - - - - 8 8 2 200

Allied - - 4(4) 4(4) - - 8 8 2 200 Subjects-II (T)

Allied

Subjects-II (P) - - 2(0) 2(2) - - 4 2 1 100

Part- IV

Non Major 2(2) 2(2) 4 4 2 200

Electives

Skill Based 2(2) 2(2) 2(2) 2(2) 12 12 6 600

Subjects - - 2(2) 2(2)

Environmental - - - - 2(2) - 2 2 1 100

Studies

Value - - - - - 2(2) 2 2 1 100

Education

Part- V

Extension - - - 1 (1) - - - 1 - -

Activities

Total 30(20) 30(24) 30(21) 30(24) 30(26) 30(25) 180 140 42 4200

Extra Credits

Paper

2

Grand Total 142


Allied: Ancillary

Mathematics 6(4) 3(3)

3(3) - - - - - 12 10


B.Sc. Mathematics

FIRST SEMESTER

Course

Components

Subjects Subject

Code

Inst

/week/

Hrs

Credits Exam

Hrs.

Max.Marks Total

Int

Marks

Ext.

Marks

Part-I Tamil

Paper-I U16LAT11 6 3 3 25 75 100

Part-II English

Paper-I U16LAE11 6 3 3 25 75 100

Part-III Paper-I

Calculus U16MAC11 5 4 3 25 75 100

Part-III

Core

Subjects

Paper-II

Theory of

Equations

U16MAC12 5 4 3 25 75 100

Allied

Subject I

Physics

Paper-I

Theory U16PHA11 4 4 3 25 75 100

Part-IV Skill

Based

Subject

Paper-I

Principles of

Mathematics

U16MAS11 2 2 2 25 75 100

Total 20 22 600


SECOND SEMESTER

Course

Components

Subjects Subject

Code

Inst

/week/

Hrs

Credits Exam

Hrs.

Max.Marks Total

Int

Marks

Ext.

Marks

Part-I Tamil

Paper-II U16LAT21 6 3 3 25 75 100

Part-II English

Paper-II U16LAE21 6 3 3 25 75 100

Part-III

Core

Subjects

Paper-III

Analytical

Geometry of

3 Dimensions

U16MAC21 5 5 3 25 75 100

Paper IV

Trigonometry

and Vector

Calculus

U16MAC22 5 5 3 25 75 100

Allied

Subject I

Physics

Paper-II

Theory U16PHA21 4 4 3 25 75 100

Practical

Paper-II U16PHA2P1 2 2 3 40 60 100

Part-IV

Skill Paper

Data

Interpretation U16MAS21 2 2 2 25 75 100

Total 30 24 700


THIRD SEMESTER

Course

Components

Subjects Subject Code Inst

/week/

Hrs

Credits Exam

Hrs.

Max.Marks Total

Int Ext

Part-I Tamil

Paper-III U16LAT31 6 3 3 25 75 100

Part-II English

Paper-III U16LAE31 6 3 3 25 75 100

Part-IV

Core

Subjects

Paper IV

Differential

Equations

U16MAC31 5 5 3 25 75 100

Elective

Subject

Elective:

(a) Classical

Algebra

(b) Statics

U16MAE31

U16MAE32

4

4

3

25

75

100

Allied

Subject II

Computer

Application

Paper-I

Programming

in C

U16MAA31 4 4 3 25 75 100

C Practical 2 - - Examination will be

held in Semester IV

Part IV

Non-Major

Elective

NME-I

Fundamentals of

Mathematics

U16MAN31 2 2 2 25 75 100

Total 30 21 600


FOURTH SEMESTER

Course

Components


/week/

Hrs

Credits Exam

Hrs.

Max.Marks Total

Int Ext

Part-I Tamil

Paper-IV

U16LAT41 6 3 3 25 75 100

Part-II English

Paper-IV

U16LAE41 6 3 3 25 75 100

Part-III

Core

Subjects

Paper-VI

Sequences and

Series

U16MAC41 5 5 3 25 75 100

Elective

Subject

Elective:

(a) Dynamics

(b) Number

Theory

U16MAE41

U16MAE42

5 4 3 25 75 100

Allied

Subject II

Computer

Application

Paper-II

Object Oriented

Programming

with C++

U16MAA41 4 4 3 25 75 100

Paper-III

C++ Practical

U16MAA4P1 2 2 3 40 60 100

Part IV

Non-Major

Elective

Paper-II

Optimization

Techniques

U16MAN41 2 2 2 25 75 100

Extension

Activities

U16CNA41


FIFTH SEMESTER

Course

Components

Subjects Subject

Code

Inst

/week

/Hrs

Credits Exam

Hrs.

Max.Marks Total

Int Ext

Part-III

Core

Subjects

Paper-VII

Modern

Algebra

U16MAC51 5 4 3 25 75 100

Paper-VIII

Real Analysis U16MAC52 5 4 3 25 75 100

Paper-IX

Statistics U16MAC53 5 4 3 25 75 100

Paper-X

Linear

Programming

U16MAC54 5 4 4 25 75 100

Elective

Subject

Elective:

(a) Numerical

Methods

(b) Discrete

Mathematics

U16MAE51

U16MAE52

4

4

3

25

75

100

Part IV

Skill based

Subject

Paper III

MS-Office

Practical

U16MAS5P1 2 2 3 40 60 100

Paper IV

Summation of

Series

U16MAS51 2 2 2 25 75 100

Environmental

Studies U16CNE51 2 2 2 25 75 100


SIXTH SEMESTER

Course

Components


/week/

Hrs

Credits Exam

Hrs.

Max.Marks Total

Int Ext

Part-III

Core

Subjects

Paper-Xi

Theory of

Vector Spaces

U16MAC61 5 4 3 25 75 100

Paper XII

Complex

Analysis

U16MAC62 5 4 3 25 75 100

Paper XIII

Graph Theory U16MAC63 5 4 3 25 75 100

Paper XIV

Operations

Research

U16MAC64 5 4 4 25 75 100

Elective

Subject

Elective:

(a)Advanced

Statistics

(b) basic Fuzzy

Set Theory

U16MAE61

U16MAE62

4

4

3

25

75

100

Part IV

Skill based

Subject

Paper V

MAT Lab

Theory

U16MAS61 2 2 3 40 60 100

Paper VI

MAT Lab

Practical

U16MAS6P1 2 2 2 25 75 100

Value Education U16CNV61 2 2 2 25 75 100

Extra Credits paper:

Model Paper for Competitive

Examination

U16CNX61 2 3 100


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: B.Sc Mathematics Subject Code :U16MAC11

Semester : I No. of Hours allotted:5/week

Part III : Core Paper I No. of Credits :4

Title of the Paper: CALCULUS

Objectives:

To give a comprehensive idea about the underlying principles of differentiation

and integration of functions.

To have a good foundation in all the concepts of variation and summation.

UNIT-I: Successive differentiation – Leibnitz Formula – Maxima and Minima of two

variables.

UNIT-II: Subtangent and Subnormal – Polar coordinates – Angle between the radius vector

and the tangent – Slope of the tangent – Angle of intersection of two curves – Polar sub

tangent and Polar subnormal – Length of an arc.

UNIT-III: Envelopes – Curvatures – Circle, radius and centre of curvature – Evolutes.

UNIT-IV: Polar coordinates – Radius of curvature in Polar coordinates – p-r equation –

pedal equation of curves – Definite Integrals and their properties.

UNIT-V:

Reduction Formulae for sinnx , cos

nx, tan

nx, cosec

nx,sec

nx, sin

nx.cos

mx–Bernoulli‟s

formula – Double and Triple integrals –(changing the order of integration is excluded).

Text Books

Text Book-I

Title of the Book : Calculus Volume I

Name(s) of the author : S. Narayanan & T.K.Manicavachagom Pillay

Publisher : S. Vioswanathan Pvt. Ltd.,

Edition / Year : 2006


Text Book-2:

Title of the Book : Calculus Volume II

Name(s) of the author : S. Narayanan & T.K.Manicavachagom Pillay

Publisher : S. Vioswanathan Pvt. Ltd.,


Unit-I: (From Text Book-1)

Chapter III(Sections 1.1 to 1.6, 2.1 and 2.2)

Chapter VIII( Sections 4 and 4.1)

Unit-II: (From Text Book-1)

Chapter IX( Sections 2 and 4.1 to 4.6)

Unit-III: (From Text Book-1)

Chapter X(Sections 1.1 to 1.4, 2.1 to 2.4)

Unit-IV: (From Text Book-1)

Chapter X(Sections 2.6 and 2.7 )

(From Text Book-2)

Chapter 1( Section 11)

Unit-V: (From Text Book-2)

Chapter 1(Sections 13.3 to 13.9, 15.1)

Chapter 5(Sections 2.1 and 2.2, 4)

Reference Book:

Title of the Book : Calculus

Name(s) of the author : Dr. S. Arumugam and A.T. Isaac.

Publisher : New Gamma Publishing House,

Edition / Year : July 2011

Prepared by:

Signature :





SYLLABUS

Programme: B.Sc Mathematics Subject Code : U16MAC12

Semester : I No. of Hours allotted:5/week

Part III : Core Paper II No. of Credits :4

Title of the Paper: THEORY OF EQUATIONS

Objectives:

To impart the techniques available in the literature in solving the algebraic

equations.

To have a good foundation in the concept of Algebra.

UNIT – I Theory of Equations – Remainder Theorem - Imaginary roots – Irrational roots –

Relation between the roots and the coefficients – Symmetric functions of the roots

UNIT – II Sum of the powers of the roots of an equation – Newton‟s Theorem –

Transformation of equations – Roots multiplied by a given number

UNIT – III

Reciprocal roots – Reciprocal equations – Standard forms - To increase and

decrease the roots of a given equation by a given constant – Removal of terms and

consequent problems.

UNIT – IV Transformation in general - Descartes‟ rule of signs – Roll‟s theorem – Multiple

roots – Strum‟s theorem – Horner‟s method

UNIT – V General solution of cubic equations – Cardon‟s method --Ferrari‟s method of

solving biquadratic equations.

Text Book(s):

Text Book-I

Title of the Book : Algebra Volume I

Name(s) of the author : T.K.Manicavachagom Pillay T. Natarajan & K.S. Ganapathy

Publisher : S. Viswanathan Pvt. Ltd.,



Unit-I

Chapter 6(Sections 1 to 12)

Unit-II:

Chapter 6(Sections 13 to 15.2)

Unit-III:

Chapter 6(Sections 15.3 to 19)

Unit-IV:

Chapter 6(Sections 21 to 28, 30)

Unit-V:

Chapter 6(Sections 34, 35)

Reference Book:

Title of the Book : ALGEBRA: Theory of Equation, Theory of Numbers and

Trigonometry



Edition / Year : Edition Jan 2011

Prepared by:

Signature :



(An Autonomous Institution Re-accredited with ‘A’ Grade by NAAC)



SYLLABUS

Programme: B.Sc Mathematics Subject Code : U16MAS11

Semester : I No. of Hours allotted: 2/week

Part IV : Skill Based Subject Paper I No. of Credits : 2

Title of the Paper: PRINCIPLES OF MATHEMATICS

Objectives:

To enable the student to have a good foundation in the basic concepts of Mathematics.

To promote the analytical thinking in the minds of young mathematicians

Unit-I Sets-Relations- functions

Unit-II Number system-Infimum and Supremum-Permutations and Combinations

Unit-III Mathematical Induction- Recurrence relations

Text Book: Materials prepared by the Department of Mathematics

Reference Book:

Title of the Book : Discrete Mathematics

Name(s) of the author : Dr. M.K. Venkataraman and others.

Publisher : The National Publishing Company,

Edition / Year : January 2011.

Prepared by:

Signature :





SYLLABUS

Programme: B.Sc Mathematics Subject Code : U16MAC21

Semester : II No. of Hours allotted: 5/week

Part III : Core Paper III No. of Credits : 5

Title of the Paper: ANALYTICAL GEOMETRY OF 3 DIMENSIONS

Objectives:

To get a clear idea about Geometrical figures namely sphere, cone and cylinder.

To lay good foundation in Geometry.

UNIT – I Distance between two points direction ratio and direction casing of a joining two points-

equation of a straight line joining two points. Equations of a straight line in slope – incorrect form.

UNIT – II The plane, Angle between two planes – Length of the perpendicular – Bisecting

plane – Distance between two planes.

UNIT – III The Straight line –symmetric form – Image of a point and Image of a line on a

plane – The plane and the straight line – Angle between a plane and a straight line.

UNIT – IV Coplanar lines – Shortest distance between two lines – Skew lines

UNIT – V The Sphere – Equation of a sphere – Equation of the tangent plane – Simple

problems


Text Book:

Title of the Book : Analytical Geometry of Three dimensions

Name(s) of the author : T. K. Manicavachagom Pillay & T. Natarajan

Publisher : S. Viswanathan Printers.,

Edition / Year : Revised Edition – 1996, Reprint 2001.

Unit – I Chapter I(all sections)

Unit-II

Chapter II( All Sections)

Unit-III

Chapter III (Sections 1 to 6)

Unit-IV

Chapter III (Sections 7 and 8)

Unit-V:

Chapter IV ( All Sections)

Reference Book:

Title of the Book : Analytical Geometry 3D and Vector Calculus




Prepared by:

Signature :



SATTUR – 626 203.

Department of Mathematics (For those who are joining in 2016 – 2017 and after)

SYLLABUS


Semester : II No. of Hours allotted:5/week

Part III : Core Paper IV No. of Credits :5

Title of the Paper: TRIGONOMETRY AND VECTOR CALCULUS

Objectives:

To enrich with the knowledge of trigonometric functions.

To have a good foundation in vector calculus.

UNIT – I De Moivre‟s Theorem (statement only) – Expansion of sin nθ, cos nθ & tan nθ –

Power series of sin θ, cos θ & tan θ(statements only) – Expansion of

sinnθ, cos

nθ and sin

nθcos

mθ.

UNIT – II Hyperbolic functions - Inverse Hyperbolic functions – Logarithm of a complex

number – Gregory series – Calculation of the value of π.

UNIT – III Vector differentiation – Gradient, Divergence, Curl and their Properties - Simple

problems.

UNIT – IV Vector integration – Line integrals, Surface Integrals, Volume Integrals

UNIT – V Gauss divergence theorem, Green‟s theorem and Stokes theorem (statements

without proof) – applications

Text Book:

Title of the Book : Trigonometry

Name(s) of the author : T.K.Manicavachagom Pillay & T. Narayanan

dition / Year : Revised Edition – 1998, Reprint 2003.

Unit-I: (From Text Book-1)

Chapter II(Section 3 only).

Chapter III(Sections 1 to 3 up to page 66, 4 and 5).


Unit-II: (From Text Book-1)

Chapter IV(Sections 1 and 2).

Chapter V(Section 5)

Chapter VI ( Sections 3.1 only)

Unit-III: (From Text Book-2)

Chapter IV(Sections 1, 2, 6 to 12).

Unit-IV: (From Text Book-2)

Chapter VI(Sections 1 to 5).

Unit-V: (From Text Book-2)

Chapter VI(Sections 6 to 9 ).

Text Book 2:

Title of the Book : Analytical Geometry 3D and Vector Calculus




Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS

Programme: B.Sc Mathematics Subject Code :U16MAS21

Semester : II No. of Hours allotted:5/week

Part III : Skill Paper II No. of Credits :2

Title of the Paper: DATA INTERPRETATION

Objectives:

To develop the skills in interpreting various forms of data.

To enrich the ability to solve various business and industrial problems.

UNIT – I Tabulation

UNIT–II Bar graphs

UNIT–III Pie charts – Line graphs

Text Book:

Title of the Book : Quantitative Aptitude for Competitive Examination

Name(s) of the author : R.S. Agarwal,

Publisher : S. Chand and Company Ltd.,

Edition / Year : 2011.

Unit-I

Chapter 36 (All Sections).

Unit-II:


Unit-III:

Chapter 38 (All Sections) and



Reference Book:

Title of the Book :An Advanced Approach to Data interpretation for Competitive

Examinations,

Name(s) of the author : R.S. Agarwal

Publisher : S.Chand and Co Publications.

Edition / Year : Ist Edition Reprint 2012.

Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS


Semester : III No. of Hours allotted:5/week

Part III : Core Paper IV No. of Credits :5

Title of the Paper: DIFFERENTIAL EQUATIONS

Objectives:

To enrich with the knowledge of Applied Mathematics.

To have a good foundation on Differential Equations.

UNIT – I Exact differential equations – Equations of the first order but of higher degree –

Equations solvable for y – Equations solvable for x and p - Clairaut‟s form – Equations

that do not contain x, y explicitly – Equations homogeneous in x and y .

UNIT-II

Linear equations with constant coefficients -Linear equations with variable

coefficients – Equations reducible to the linear homogeneous equations – Simultaneous

linear differential equations with constant coefficients.

UNIT-III

Linear equations of the second order – Reduction to the normal form – Change of the

independent variables – Variation of parameters.

UNIT-IV

Partial differential equations of the first order – Derivation of partial

differential equations – Lagrange‟s method of solving the linear equations– Standard

forms – Equations reducible to the standard forms.

UNIT-V

Laplace Transforms – Theorems – Problems – Evaluation of integrals – inverse

Laplace Transforms – Results – Solving ordinary differential equation with constant

coefficient and variable coefficients – Solving simultaneous linear equations using

Laplace Transforms.


Text Book:

Title of the Book : Differential Equations and its Applications

Name(s) of the author : S. Narayanan & T.K. Manickavachagom Pillay


Edition / Year : Revised Edition - 2012.

Unit-I

Chapter II(Sections 6.1 to 6.4)

Chapter IV(Sections 1, 2, 3, 4)

Unit-II:

Chapter V(Sections 1 to 6, )

Chapter VI(Sections 6 )

Unit-III:

Chapter VIII(Sections 1 to 4)

Unit-IV:

Chapter XII(Sections 1 to 5)

Unit-V:

Chapter IX( All Sections )

Reference Book:

Title of the Book : Differential Equations and its Applications



Edition / Year : November 2011

Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS

Programme: B.Sc Mathematics Subject Code : U16MAE31

Semester : III No. of Hours allotted: 5/week

Part III : Elective Paper I(a) No. of Credits :4

Title of the Paper: CLASSICAL ALGEBRA

To enrich with the knowledge of summation of infinite terms

To have a good foundation in classical algebra.

UNIT – I The Binomial Theorem for positive integral index (without proof)-general term – greatest

coefficient in the expansion of (1 + x)𝑛 –Summation of series involving Binomial coefficients –

Mulltinomial Theorem(without proof) – Vandermonde‟s Theorem.

UNIT-II

Binomial Theorem for rational index(without proof) – Some important particular cases of the

binomial expansions – Numerically greatest term in (1 + x)𝑛– coefficient of x𝑛 in expansion of

rational function – application of binomial theorem to the summation of series – sum of coefficients –

Approximate values..

UNIT-III

Exponential limit – Exponential Theorem – summation – Logarithmic series – Modification of

logarithmic series – summation using logarithmic series – Euler‟s constant – application of

exponential and logarithmic series in limit and approximation – miscellaneous examples.

UNIT-IV

Summation of series – application of partial fractions – seires of products involving successive

terms of AP .

UNIT-V

Sum of series with arbitrary terms – summation by difference series – recurring series – the

generating function – to find the sum to n terms of a given recurring series.


Text Book:


Name(s) of the author : T.K. Manickavachagom Pillay & Others


Edition / Year : Edition- 2010.

Unit-I


Unit-II:

Chapter 3(Sections 5 to 12,14)

Unit-III:

Chapter 4(Sections 1 to 3, 5 -9)

Unit-IV:


Unit-V:


Reference Book:

Title of the Book : Higher Algebra

Name(s) of the author : Hall and Knight

Publisher : Reem Publication (p) ltd, New Delhi


Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS

Programme: B.Sc Mathematics Subject Code :U16MAE32


Part III : Elective PaperI(b) No. of Credits :4

Title of the Paper: STATICS

Objectives:

To enrich the knowledge of applied Mathematics

To have a good foundation in Principles of Statics.

UNIT – I Forces acting at a point - Resultant and components - Parallelogram law of a forces -

Triangle law of forces - Converse of Triangle law of forces - Lami‟s theorem.

UNIT-II

Resolution of a force – Theorems of resolved parts - Resultant of any number of coplanar

forces -Condition of equilibrium.

UNIT-III

Parallel forces - Resultant of two like and unlike parallel forces – Conditions of equilibrium

of three coplanar parallel forces – Centre of two parallel forces - Moment of a force - Varigon‟s

theorem – Generalised Theorem of Moments.

UNIT-IV

Equilibrium of Three forces acting on a rigid body: Rigid body subjected to any three forces –

Three coplanar forces – Conditions of equilibrium – Two Trigonometrical Theorems – Some artifices.

UNIT-V

Friction: Statical, Dynamical and Limiting Friction – Laws of Friction –Equilibrium of a

particle on a rough inclined plane – Problems on friction.


Text Book:

Title of the Book : Statics

Name(s) of the author : M.K. Venkataraman,

Publisher : Agasthiyar,

Edition / Year : 11th

Edition, July 2012.

Unit-I


Unit-II:


Unit-III:


Unit-IV:


Unit-V:


Reference Book:

Title of the Book : Golden Statics

Name(s) of the author : N.P. Bali .

Publisher : Lakshmi Publications,

Edition / Year :

Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS

Programme: B.Sc Mathematics Subject Code :U16MAA31


Part III : Allied Subject II-Paper-I(T) No. of Credits :4

Title of the Paper: PROGRAMMING IN C

Objectives:

To enrich with the knowledge of Procedure Oriented Programming Language.

To have a good foundation on Programming in C.

UNIT – I Overview of C ( not for exam ) - Introduction to C – The character set in C – Keywords

and Identifiers – Constants – Variables – Data Types – Declaration – Defining Symbolic Constants –

Operators – Arithmetic Expressions – Type Conversions in Expressions.

UNIT-II

Managing Input and Output Operations – Formatted Input – Formatted Output – Decision

Making and Branching – IF – Switch – Conditional – GOTO Statements – Decision Making

and Looping – WHILE – DO – FOR Statements.

UNIT-III

Arrays – One Dimensional Arrays – Two Dimensional Arrays – Character Arrays and Strings –

Reading Strings from Terminals – String Handling Functions.

UNIT-IV

User defined Functions – Elements of User-Defined Functions – Nesting of

Functions – Recursion

UNIT-V

Structures and Unions: Definitions – Processing a Structure – Structure and functions – Self

referential Structures – Bit fields – Unions – Enumerations. File Management in C: Opening and

Closing of Data files – Creating a Data file – Processing a data file – Unformatted data file –Command

Line Arguments.

One Program question (B or C) from each unit.


Text Book:

Title of the Book : Programming in ANSI C

Name(s) of the author : E.Balagurusamy

Publisher : Tata McGraw Hills,

Edition / Year : Fourth Edition, 2007.

Unit-I

Chapter 1( All Sections, not for exam),

Chapter 2( All Sections), and

Chapter 3( All Sections).

Unit-II:

Chapter 4( All Sections),

Chapter 5( All Sections), and

Chapter 6( All Sections ).

Unit-III:

Chapter 7( All Sections ) and

Chapter 8 ( All Sections).

Unit-IV:

Chapter 9( Sections 9.1 to 9.13, 9.15 to 9.19 )

Unit-V:

Chapter 10 ( All Sections ) and

Chapter 12 ( All Sections).

Reference Book:

Title of the Book : Programming with C.

Name(s) of the author : Byron Gottfried.

Publisher : Tata McGraw Hill.

Edition / Year : Second Edition 1998, Reprint 2001.

Prepared by:

Signature :




SATTUR – 626 203.


SYLLABUS

Programme: B.Sc Mathematics Subject Code :U16MAN31


Part IV : Non Major Elective I No. of Credits :2

Title of the Paper: FUNDAMENTALS OF MATHEMATICS

Objectives:

To lay the foundation in the basic principles of Mathematics for other major students

To equip the students with Knowledge and skills in cracking the mathematical problems in competitive

examinations.

UNIT – I Ratio and Proportion – Arithmetic Progression – Geometric Progression-Examples.

UNIT – II Quadratic Equations – Partial Fractions – Differentiation – ( u ± v) , uv and u/v

forms only – Examples

UNIT – III Matrices – Addition and Multiplication of two matrices, Solutions to

simultaneous equations – 2 equations two unknowns-Examples.

Text Book:

Title of the Book : Business Mathematics

Name(s) of the author : G.K.Renganath, C.S. Sampangiram, Y. Rajaram

Publisher : Himalaya Publishing House,


Edition, Reprint 2006.

Unit-I

Chapter 9 (Sections 9.1 to 9.6) and

Chapter 6 (Sections 6.1 to 6.3).

Unit-II:

Chapter 4 (Section 4.4)

Chapter 5 (Sections 5.1, 5.2) and

Chapter 11 (Sections 11.11 and 11.12).

Unit-III:

Chapter 8 (Sections 8.1 to 8.4)

Chapter 4 (Section 4.6).

Reference Book:

Title of the Book : Business Mathematics

Name(s) of the author : M. Wilson.

Publisher : Himalaya Publishing House Pvt. Ltd,

Edition / Year : 3rd

Revised Edition, 2008, Reprint 2010

Prepared by:

Signature :




SATTUR – 626 203.


SYLLABUS


Semester : IV No. of Hours allotted: 5/week

Part III : Core Paper III No. of Credits : 5

Title of the Paper: SEQUENCES AND SERIES

Objectives:

To impart the knowledge of sequences and summation of series

To have a good foundation in real sequences and series

To develop the skill of computation with real sequences and series

UNIT – I Sequences – Bounded - Monotonic – Convergent – Divergent and Oscillating

sequences – Algebra of limits.

UNIT – II Behaviour of monotonic sequences – Some Theorems on limits – Cauchy‟s first

limit theorem – Cesaro‟s theorem – Cauchy‟s second limit theorem - Subsequences and

Cauchy sequences.

UNIT – III Series of positive terms – Infinite series – Theorems – Cauchy‟s general principle

of convergence – Comparison test – Harmonic series.

UNIT – IV Kummer‟s test – D‟Alembert‟s ratio test – Raabe‟s test – De Morgan and

Bertrand,s test – Gauss‟s test ( only statements to all the above five tests, no proof) –

Applications to simple problems – Cauchy‟s root test – Cauchy‟s condensation test –

Cauchy‟s integral.

UNIT – V Series of arbitrary terms – Alternating series – Leibnitz‟s test – Absolute convergence – Test for

convergence – Dirichlet‟s test – Abel‟s test – Multiplication of series – Abel‟s theorem – Merten‟s theorem.

Text Book:

Title of the Book : Sequences and Series

Name(s) of the author : S. Arumugam and A. Thangapandi Isaac

Publisher : New Gamma Publishing House, Palayamkottai

Edition / Year : Edition July 2010.


Unit-I

Chapter 3(Sections 3.0 to 3.6)

Unit-II:

Chapter 3(Sections 3.7 to 3.9, 3.11)

Unit-III:

Chapter 4(Sections 4.1, 4.2)

Unit-IV:


Unit-V:


Reference Book:


Name(s) of the author : S. Narayanan and T.K.Manicavachagom Pillay

Publisher : S. Viswanathan Pvt. Ltd,


Edition, 2006.

Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS


Semester : IV No. of Hours allotted: 5/week

Part III : Elective PaperII – (a) No. of Credits : 4

Title of the paper : DYNAMICS

Objectives :

To enrich with the knowledge of applied mathematics

To have a good foundation in Dynamics.

UNIT-I

Projectiles – Path of a projectile – Maximum height –Time taken by a particle –

Time of flight – Horizontal Range – Simple problems.

UNIT-II

Range on a inclined plane - Impact – Laws of Impact – Impact in a fixed smooth

plane.

UNIT-III

Direct and Oblique impact.

UNIT-IV

Simple Harmonic Motions – Equation of motion – Composition of two S.H.M‟s.

UNIT-V

Central orbits – Components of velocities and accelerations along and

perpendicular to radius vector – Differential equation of a central orbit – Pedal equations.

Text Book:

Title of the Book : DYNAMICS

Name(s) of the author : Dr. M.K.Venkatraman,

Publisher

Edition / Year : Agasthiyar , 12thEdition, Jul 2006

Unit-I


Unit-II:

Chapter 6(Sections 6.12 to 6.16) and


Unit-III:


Unit-IV:


Unit-V:



Reference Book:

Title of the Book : Golden Dynamics

Name(s) of the author : N. P. Bali

Publisher

Edition / Year : Lakshmi Publications, New Delhi , 2002

Prepared by:

Signature :



(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 : B. Sc., Mathematics Subject Code :U16MAE42

Semester : IV No. of Hours allotted: 5 / Week

Part III : Elective PaperII- (b) No. of Credits : 4

Title of the paper: NUMBER THEORY

Objectives

To make student aware of the laws bounded by the numbers

To make student familiar with the computation of congruences

Unit-I

Early Number theory- The division Algorithm-The g.c.d-The Euclidean algorithm

Unit-II

The fundamental Theorem of arithmetic- The sieve of Eratosthenes –The Goldbach Conjecture

Unit-III

Basic properties of Congruences-Binary and decimal Representations of Integers- linear congruences-

The Chinese remainder theorem

Unit-IV

Fermat‟s Little theorem and psudoprimes-Wilson‟s theorem

Unit-V

The sum and number of divisors-The mobious inversion formula- The greatest integer function

Text book:

Title of the Paper : “Elementary Number Theory”:

Name of the Author(s) : David M.Burton

Publishers : TATA McGraw-Hill Ltd

Edition : 6th

edition

Unit-I : Chapter 2.1 to 2.4

Unit-II : Chapter 3.1 to 3.3

Unit-III : Chapter 4.2 to 4.4

Unit-IV : Chapter 5.2 to 5.3

Unit-V : Chapter 6.1 to 6.3


Reference Book:

Reference Books -1

Title of the Book : An Intoruction to Theory of Numbers

Name of the Authors : Niven and Zuckermann

Publishers : Wiley Eastern Ltd

Edition/Year : 13rd Edition / 1972

Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS

Programme: B.Sc Mathematics Subject Code :U16MAA41

Semester : IV No. of Hours allotted:5/week

Part III : Allied Subject II-Paper II(T) No. of Credits :4

Title of the Paper: OBJECT ORIENTED PROGRAMMING WITH C++

Objectives:s

To enrich with the knowledge of OOPs

To have a good foundation in C++ Programming.

UNIT-I Principles of OOP – Software evolution – basic concepts of OOP – benefits of

OOP – Object Oriented Languages – C++ tokens – keywords - identifiers – variables – operators – manipulators

– expressions and control structures in C++.

UNIT-II Functions in C++ - Main function – Function prototyping – Default arguments Call by reference – return

by reference – function overloading – Recursion and inline functions.

UNIT-III Classes and objects – Constructors and Destructors.

UNIT-IV Operator overloading and type conversions.

UNIT-V Inheritance – Various types of inheritance and managing I/O operations.

One Program question ( either B or C ) from each unit.

Text Book:

Title of the Book : Object Oriented Programming in C++

Name(s) of the author : E. Balagurusamy,

Publisher : TATA McGraw Hills,


Edition, 2010.

Unit-I


Chapter 3(Sections 3.2 to 3.4, 3.10, 3.13, 3.17, 3.19, 3.24)

Unit-II:

Chapter 4(Sections 4.2 to 4.5, 4.9, 4.10)

Unit-III:


Chapter 6(All Sections)

Unit-IV:



Unit-V:



Reference Book:

Title of the Book : Programming with C++

Name(s) of the author : D. Ravichandran

Publisher : Tata McGraw Hill Pub. Company Ltd.,

Edition / Year : 1996, Reprint 2001.

Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS

Programme: B.Sc Mathematics Subject Code :U16MAA4P1

Semester : IV No. of Hours allotted:5/week

Part III : Allied Subject II PaperIII(Practical) No. of Credits :2

Title of the Paper: C / C++ and Object Oriented Programming with C++

Objectives:

To enrich with the practical knowledge of OOPs

To have a good foundation in C++ Programming.

A.C / C++ Programs:

1. Write a program to find the variance and standard deviation for given set of values in C.

2. Write a program to sort names in alphabetical order in C / C++.

3. Write a program to solve quadratic equation in C/ C++.

4. Write a program to display the Pascal‟s triangle in C / C++.

5. Write a program to find the factorial of a number using recurrence function in C

6. Write a program to calculate the Simple interest in C++.

B.Object Oriented C++ Programs:

1. Write a C++ program to find biggest of two numbers using nesting of member functions.

2. Write a program for swapping of two numbers using friend function in C++.

3. Write a program for Employees details using Single Inheritance in C++.

4. Write a C++ program for unary minus operator to change the sign of the values.

5. Write a program to add two complex numbers using Operator Overloading in C++.

6. Write a program to find the biggest of three numbers using macro definitions in C++.

7. Write a program for Simple Bank Transaction in C++.

8. Write a C++ program for adding of two times using objects as functions arguments.

9. Write a program to find the multiplication of two matrices.

Prepared by:

Signature :



(An Autonomous Institution Re-accredited with „A‟ Grade by NAAC)

SATTUR – 626 203.

Department of Mathematics

(For those who are joining in 2013-2014 and after)

SYLLABUS

Programme : B. Sc., Mathematics Subject Code :U16MAN41

Semester : IV No.of Hours allotted : 2 / Week

Part IV : Non Major Elective Paper II No.of Credits : 2

Title of the Paper : OPTIMIZATION TECHNIQUES

Objectives

To impart Optimization Techniques

To Make the Students become familiar with the basic Principle of LPP

Unit-I

Mathematical formulations of L.P.P.S- Product allocation problem- Product mix

problem – Production problem – Graphical method of solving L.P.P( having

bounded solutions)

Unit-II

Simple method of solving a L.P.P – canonical form maximization problems.

Unit-III

Transportation problems – initial basic feasible solutions of north west corner Rule

– Row minima method – column minima method – least cost method – Vogel‟s

Application method – Assignment problem – solution by Hungarian method

Text Book:

Title of the Book :Operations Research

Name(s) of the author : Kanti Swarup, P.K. Gupta & Man Mohan

Publisher : Sultan Chand & Son‟s.

Edition / Year : Fifteenth Edition /2010

Unit-I:

Problems: 201,202,203,204,205)

(Problems : 301,302,303,305,306)

Unit-II:

Problems:411,413,414,415

Unit-III:

Problems: 1001,1002,1003,1004

Problems: 1101 and 1102

Prepared by:

Signature:



SATTUR – 626 203.


SYLLABUS


Semester : V No. of Hours allotted:5/week

Part III : Core Paper VII No. of Credits :4

Title of the Paper: MODERN ALGEBRA

Objectives:

To enrich with the knowledge of Abstract Algebra

To have a good foundation in Groups and Rings.

Unit-I

Groups – Definition and examples – Permutation Groups – Sn and An- Subgroups

Unit-II

Cyclic groups – Order of an element - Cosets and Lagrange‟s theorem and its

applications.

Unit-III

Normal subgroups and Quotient groups.

Unit-IV

Homomorphism and Isomorphism

Unit-V

Rings – Definitions and examples – Elementary properties of Rings –

Isomorphism – Types of Rings.


Text Book:

Title of the Book : Modern Algebra

Name(s) of the author : Dr. S. Arumugam and A.T. Isaac

Publisher : SciTech

Edition / Year : Edition 203, Reprint Nov 2011.

Unit-I


Unit-II:


Unit-III:

Chapter 3(Sections 3.9)

Unit-IV:

Chapter 3(Sections 3.10, 3.11)

Unit-V:


Reference Book(s):

Reference Book-I


Name(s) of the author : A.R.VAsista,

Publisher : Kedarnath Ramnath Publications


Reference Book-II

Title of the Book : Linear Algebra

Name(s) of the author : Krishna Moorthy and others

Publisher : East west Publications


Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS

Programme: B. Sc Mathematics Subject Code :U16MAC52


Part III : Core Paper VIII No. of Credits :4

Title of the Paper: REAL ANALYSIS

Objectives:

To give a comprehensive idea about the continuity, connectedness and compactness.

To have a good foundation in the concepts of abstract mathematics.

UNIT – I Introduction of countable and uncountable sets - Holder‟s and Minkowski‟s

Inequalities. Metric spaces-Definition and examples - Bounded sets.

UNIT – II

Open balls – Open sets- Subspaces – Interior of a set - Closed sets - Closure –

Limit point –Dense sets.

UNIT – III Completeness -definition and examples - Cantor‟s Intersection Theorem and

Baire‟s Category Theorem – Continuity.

UNIT – IV Homeomorphism - Uniform continuity (Discontinuous functions on R are not included)

Connected - definition and examples - Connected subsets of R- Connectedness and

Continuity - Intermediate Value Theorem.

UNIT – V Compactness-definition and examples – Compact subsets of real line R–

Equivalent Characterization of Compactness – Compactness and Continuity.


Text Book:

Title of the Book : Modern Analysis

Name(s) of the author : Dr. S. Arumugam, A. Thangapandi, & Isaac.

Publisher : New Gamma Publishing House


Unit-I

Chapter 1 ( Sections 1.2, 1.3, 1.4) and

Chapter 2 ( Sections 2.1 and 2.2)

Unit-II:

Chapter 2 ( Sections 2.3 to 2.10)

Unit III:

Chapter 3 ( Sections 3.1, 3.2) and

Chapter 4 (Sections 4.1)

Unit IV:

Chapter 4 (Sections 4.2, 4.3) and

Chapter 5 (Sections 5.1, 5.2, 5.3)

Unit V:

Chapter 6 (Sections 6.1, 6.2, 6.3, 6.4)

Reference Book(s):

Reference Book-I

Title of the Book : Methods of Real Analysis

Name(s) of the author : Gold berg,

Publisher : Oxford and IBH


Reference Book-II

Title of the Book : Metric Spaces

Name(s) of the author : Copson

Publisher : Cambridge Publications


Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS



Part III : Core Paper IX No. of Credits :4

Title of the Paper: STATISTICS

Objectives:

To give a foundation in statistical data analysis.

Applying the various measures of statistical parameters to real life.

UNIT – I Correlation and Regression

Correlation- Rank Correlation- Regression lines.

UNIT – II Curve Fitting & Index Numbers

Principle of Least Squares- Fitting a straight line- Fitting a second degree

parabola – Exponential curves.

Index Number - Consumer Price Index Numbers- Conversion of Chain Base

Index Number into Fixed Base Index and Conversely.

UNIT – III Analysis of Time Series Time series – Components of Time series – Measurement of trends.

UNIT – IV Theory of Attributes

Two Attributes only - Consistency of Data - Independence and Association of

Data.

UNIT – V Probability

Probability - Conditional Probability – Baye‟s Theorem.


Text Book:

Title of the Book : Statistics

Name(s) of the author : Dr.S.Arumugam and Mr. A. Thangapandi Isaac

Publisher : New Gamma Publishing Houses,

Edition / Year : Edition, Year 2009.

Unit I:

Chapter 6 (6.1, 6.2, 6.3)

Unit II:

Chapter 5(All Sections) and


Unit III:


Unit IV:

Chapter 8 (All Sections- only problems with two attributes)

Unit V:


Reference Book(s):

Reference Book-1:

Title of the Book : Elements of Mathematical Statistics

Name(s) of the author : S.C.Gupta, V.K.Kapoor,

Publisher : Sultan Chand and Sons,


Editon, 2001.

Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS



Part III : Core Paper X No. of Credits :4

Title of the Paper: LINEAR PROGRAMMING

Objectives:

To develop the skills in decision making.

Applying the decisions making problems in real life.

UNIT – I Linear Programming Problem-I

Mathematical Formulation of the problem (simple problems) – Graphical solution

Method – Some Exceptional Cases – General Linear Programming Problem – Canonical

and Standard Forms of LPP.

UNIT – II Linear Programming Problem-II

Simplex Method – Two Phase Method – Big-M Method.

UNIT – II Dual and Duality.

General Primal - Dual pair – Formulating a dual Problem – Primal - Dual pair

In Matrix Form – Duality and Simplex Method – Dual Simplex method.

UNIT – IV Transportation Problems

LP Formulation of the Transportation Problem – Existence of solution in T.P –

The Transportation Table – Solution of a Transportation Problem – Finding an initial

basic feasible solution – Transportation Algorithm MODI Method.

UNIT – V Assignment Problems

Mathematical formulation of an assignment problem – Hungarian assignment

method – The traveling salesman problem.


Text Book:

Title of the Book : Operation Research

Name(s) of the author : Kanti Swarup, P.K.Gupta, and Manmohan.,

Publisher : Sultan Chand & Sons, Reprint,


Edition, Year 2010.

Unit-I


Chapter 3 (3.2 to 3.5)

Unit II:

Chapter 4 (4.1, 4.3, 4.4)

Unit III:

Chapter 5 (5.2, 5.3, 5.4, 5.7, 5.9)

Unit IV:

Chapter 10 (10.2, 10.3, 10.5, 10.8, 10.9, 10.13)

Unit IV:

Chapter 11 (11.2, 11.3, 11.7)

Reference Book:

Title of the Book : Operations Research

Name(s) of the author : S.D.Sharma

Publisher : Kedar Nath, Ram Nath and Co.


Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS



Part III : Elective PaperIII – (a) No. of Credits :4

Title of the Paper: NUMERICAL METHODS

Objectives:

To develop the skills of solving numerical problems.

To find the applications of numerical methods.

UNIT – I

Errors in Numerical Computation - Iteration method – Bisection Method -

Newton-Raphson Method - Simultaneous Equations-Back Substitution-Gauss

Elimination Method-Gauss‟ Jordan Elimination Method-Iterative methods- Gauss Jacobi

Iteration Method – Gauss–Seidel Iteration Method.

UNIT– II

Difference Operators- Forward difference Table- Properties of the Operator -

Backward Differences – Central Difference Operator.- Other Difference Operators.

UNIT – III

Newton‟s Interpolation Formulae-Central Difference Interpolation Formulae –

Lagrange‟s Interpolation Formula -Divided Differences - Newton‟s Divided Difference

Formula.

UNIT – IV

Derivatives using Newton‟s Forward Difference Formula and Newton‟s

Backward Difference Formula – Derivatives using Central Difference Formulae.

UNIT – V

Numerical Integration- Newton – Cotes quadrature formula – Trapezoidal rule –

Simpson‟s one third rule – Simpson‟s three eight rule –Weddle‟s rule – Romberg‟s

method.


Text Book:

Title of the Book : Numerical Analysis

Name(s) of the author : Dr. S.Arumugam, A.Thangapanid Isaac, and A. Somasundram,

Publisher

Edition / Year : SCITECH Publications Pvt. Ltd., Year 2004.

Unit-1

Chapter 3 (Sections 3.1, 3.2, 3.3 and 3.5

Chapter 4 (Sections 4.1 to 4.4, 4.7, 4.8)

Unit II:

Chapter 6 (Sections 6.1 and 6.2)

Unit III:


Unit IV:


Unit V:

Chapter 8 (Section 8.5)

Reference Book:

Reference Book-1:

Title of the Book : Numerical Analysis

Name(s) of the author : T.K. Manickavasagam Pillay and Narayanan,

Publisher : Viswanathan (Printers and Publishers, Pvt. Ltd.,)


Reference Book-2:

Title of the Book : Introduction Methods of Numerical Analysis

Name(s) of the author : S.S. Sastry

Publisher

Edition / Year : Prentice Hall of India Pvt. Ltd., 2000.

Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS



Part III : Elective Paper III –(b) No. of Credits :4

Title of the Paper: DISCRETE MATHEMATICS

Objectives:

To enhance skill in discrete structures such as lattice in mathematics.

Applying discrete structures in applied mathematics.

UNIT – I : Lattices

Lattices- Hasse diagrams – Some Properties of Lattices- Duality principle –

Lattice Through Algebraic Operations.

UNIT – II : Types of Lattices

New Lattices – Lattice Homomorphisms – Product Lattice of Two Lattices -

Modular and Distributive lattices.

UNIT – III : Boolean Algebras

Boolean Algebras – Boolean Polynomials.

Unit- IV: Recurrence relations and Generating functions

Recurrence –Polynomials and Evaluations -Recurrence relations – Solutions to first

order Homogeneous linear relations- Generating functions

Unit-V : Logic :

If statements, connectives, Well formed formulae- Truth table of a Formulae- Tautology

Text Book:

Title of the Book : Discrete Mathematics

Name(s) of the author : Dr.M.K.Venkataraman, Dr.N.Sridharan and

Dr.N.Chandrasekaran

Publisher : The National Publishing Company, Chennai-1.

Edition / Year : 2000 Edition, Reprint 2001.


UnitI:

Chapter X (Sections 1, 2 )

Unit II:


Unit III:


Unit-IV:

Chapter V(Sections 1 to4, 6)

Unit-V:

Chapter IX( Sections 1to 3, 5 to 7)

Reference Book:

Title of the Book : Discrete Mathematical Structure with Application to Computer Science

Name(s) of the author : R. Manohar

Publisher

Edition / Year : Tata McGraw Hill Education, 2001.

Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS

Programme: B.Sc Mathematics Subject Code :U16MAS5P1


Part III : Skill Based PaperIII No. of Credits :2

Title of the Paper: MS OFFICE PRACTICAL

Objectives:

To enrich the practical knowledge in MS Office.

To develop the practical skills by developing the mathematical expressions

UNIT – I MS – WORD

1. Using MS – Word perform the following

a) Change the font size

b) Change the font type

c) Align the text to Left, Right, Justify, and Center

d) Underline Bold, Italics the text

e) Inserting bullets and numbers

2. Table manipulation and preparing application form.

3. Illustrating the Mail Merge concepts.

4. Using MS Equation editor or Math type to prepare mathematical expressions.

UNIT – II MS – EXCEL

5. Building a worksheet to perform correlation and regression co-efficient using

Formula and check the answer with built –in-function.

6. Mark sheet preparation using statistical functions.

7. Drawing graphs and Charts for the given data.

.


UNIT – III MS – POWER POINT

8. Preparing chart for a college environment in PowerPoint.

9. Preparing Power Point Presentation for a Mathematical concept.

10. Presentations applying slide transitions formatting.

Text Book:

Title of the Book : Microsoft Office - 97

Name(s) of the author : C. Nellaikannan

Publisher : Nels Publications


Edition 2004.

Unit-I

MS – WORD

Unit-II:

MS – Excel

Unit-III:

MS –Power Point

Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS



Part III : Skill Based PaperIV No. of Credits :2

Title of the Paper: SUMMATION OF SERIES

Objectives:

To enhance skill in summing up the various type of series.

Applying abstract concept of limits of sequences in applied mathematics.

UNIT – I : Binomial Summation

Binomial Theorem for a rational index ( Statement only) – Some Important

Particular Cases of the Binomial Expansion – Application of the Binomial Theorem to

the summation of Series – Approximate values.

UNIT – II : Exponential Summation

The Exponential Theorem (Statement only ) – Examples – Summation.

UNIT – III : Logarithmic Summation

The Logarithmic Theorem ( Statement only ) – Modification of the logarithmic

series – Sums of the certain series – Euler constant -Series 1 – ½ + 1/3 – ¼ + ∙ ∙ ∙ – Series

summed up by the logarithmic series.

Text Book:


Name(s) of the author : T.K.Manicavachagom Pillay, T.Natarajan, K.S.Ganapathy.

Publisher : S. Viswanathan (Printers and Publishers), Pvt. Ltd., Chennai.

Edition / Year : Edition 2004, Reprint 2010.


Unit-I

Chapter 3 (Sections 5, 6, 10, 14 (up to page 173))

Unit II:

Chapter 4 (Sections 2, 3)

Unit III:

Chapter 4 (Sections 5 to 9)

Reference Book:

Title of the Book : Summation of Series and Trigonometry

Name(s) of the author : Dr.S. Arumugam and A. Thangapandi Isaac

Publisher : New Gamma Publishing House, Palayamkottai,

Edition / Year : July 2003.

Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS

Programme: Common for All UG Programmes Subject Code :U16CNE51


Part III : Paper XIII No. of Credits :2

Title of the Paper: ENVIRONMENTAL SCIENCE

Objectives:

To create awareness on Environment.

UNIT – I: Earth and its Environment (10 hours)

Structure of earth and its components.

Atmosphere, Hydrosphere Lithosphere and Biosphere.

Resources-Renewable and Non renewable resources.

UNIT – II: Ecology and Ecosystem Concepts (10 hours)

Ecology: Definition- Ecosystem: Definition- Structure and function –Food

chain and food web- one example for an ecosystem.

Pollution and Global Issues: Definition, causes, effects and control measures of Air,

Water, Soil and Nuclear Pollution.

Global issues: Global warming, Green house effect and ozone layer depletion.

UNIT – III: Biodiversity and Disaster Management (10 hours)

Introduction- Definition –Value of Biodiversity.

Biodiversity of India –Hot spots of Biodiversity.

Disaster Management- Flood and drought –Earthquake and Tsunami- Cyclones and

Hurricanes-precautions, warnings, rescue and rehabilitation.

Text Book:

1. Environmental Studies N.Arumugam and Kumaresan , 2012 Saras Publication Nagercoil.


Reference Book:

1. Fundamentals of Ecology, Odum, E.P (1985 Edition) Published by W.B.Publishers,

Philadelphia.

2. Textbook of Environmental studies for under graduate course by Erach Bharucha

3. Environmental Biology – P.D.Sharma (2006) Published by Rastogi Publishers Ganapathi

Shivaji Road, Meerut, 250 002.

4. Environmental Studies J. Dharmaraj Tensy Publications Sivakasi.

:

Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS

Programme: B. Sc Mathematics Subject Code :U16MAC61

Semester : VI No. of Hours allotted:5/week

Part III : Core Subject XI No. of Credits :4

Title of the Paper: THEORY OF VECTOR SPACES

Objectives:

To give a comprehensive idea about the vector spaces and inner product spaces.

To have a good foundation in all the concepts of matrices.

UNIT-I: Vector Spaces

Definition and Examples – Subspaces – Linear Transformation –Fundamental

Theorem of Homomorphism.

UNIT-II: Linear Independence

Span of a set – Linear independence – Basis and Dimension – Rank and Nullity –

Matrix of a Linear Transformation.

UNIT-III: Inner Product Spaces

Definition and examples – Orthogonality – Orthogonal complement.

UNIT-IV: Matrices

Elementary Transformation – Rank of a Matrix – Simultaneous linear equations –

Characteristic Equations and Cayley Hamilton theorem – Eigen values and Eigen

vectors.

UNIT-V: Bilinear forms

Bilinear form – Quadratic forms – Reduction of a quadratic form to the diagonal form.

Text Book:


Name(s) of the author : Dr. S.Arumugam and Mr. A. Thangapandi Isaac,

Publisher : SciTech Publications Ltd.,

Edition / Year : Edition 2003, Reprint Nov 2011.


Unit-I


Unit-II:

Chapter 5 (Sections 5.4, 5.5, 5.6, 5.7, 5.8)

Unit-III:


Unit-IV:


Unit-V:

Chapter 8 (Sections 8.1, 8.2).

Reference Book(s):

Reference Book-I


Name(s) of the author : A.R.VAsista,

Publisher : Kedarnath Ramnath Publications


Reference Book-II

Title of the Book : Linear Algebra

Name(s) of the author : Krishna Moorthy and others,

Publisher : East west Publications


Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS



Part III : Core Paper XII No. of Credits :4

Title of the Paper: COMPLEX ANALYSIS

Objectives:

To give a comprehensive idea about the underlying principles of analytic functions.

To have a good foundation in complex integration.

UNIT – I Analytic Function

Complex Numbers (Not for the examination)- Analytic function – C.R-equations

– Sufficient conditions – Harmonic functions.

UNIT – II Transformations

Elementary Transformations – Bilinear Transformations – Cross ratio – Fixed

points –Special Bilinear Transformation which map real axis onto itself, the unit circle onto

itself and the real axis onto the unit circle.

UNIT – III Complex Integration

Definite Integrals - Cauchy‟s theorem – Cauchy‟s integral formula - Higher

derivatives – Morera‟s theorem – Cauchy‟s inequality – Lioville‟s theorem –

Fundamental theorem of algebra.

UNIT – IV Expansion of Series

Taylor‟s series– Laurent‟s series- Zero of an analytic function – Definition of

singularities.

UNIT – V Calculus of Residues

Residues – Cauchy‟s Residue Theorem -Evaluation of definite integrals.


Text Book:

Title of the Book : Complex Analysis

Name(s) of the author : Dr.S.Arumugam, A.Thangapandi Isaac and A. Somasundram,

Publisher : SciTech Publications

Edition / Year : Edition, Year 2011.

Unit-I

Chapter 2 (Sections 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8)

Unit-II:


Unit-III:


Unit-IV:


Unit-V:


Reference Book(s):

Reference Book-I


Name(s) of the author : S. Narayanan and T.K. Manickavasagam Pillay

Publisher : S. Viswanathan Printers and Publihsers

Edition / Year :

Reference Book-II


Name(s) of the author : Shanthi Narayanan,

Publisher :

Edition / Year :

Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS



Part III : Core Paper XIII No. of Credits :4

Title of the Paper: GRAPH THEORY

Objectives:

To give a comprehensive idea about the basic knowledge of graphs.

To find the applications in various graph theoretic problems.

UNIT-I : Graphs and Subgraphs

Graphs – Degrees – Subgraphs, Isomorphism, Ramsey Numbers – Independent

sets and Coverings – Intersection graphs and line graphs – Matrices of graphs –

Operations on Graphs.

UNIT-II : Degree sequences and connectedness

Degree sequences – Graphic Sequences – Walks, Trails and Paths –

Connectedness and Components – Blocks – Connectivity.

UNIT-III: Eulerian, Hamiltonian graphs and Trees

Eulerian Graphs - -Hamiltoninan Graphs - Trees – Characterization of Trees –

Centre of a Tree.

UNIT-IV : Matchings and Planarity

Matchings – Matchings in Bipartite Graphs – Planarity – Definition and

Properties – Characterization of Planar Graphs.

UNIT-V : Colourability

Chromatic number and Chromatic index - The five colour theorem –

colour problem - Chromatic Polynomials.


Text Book:

Title of the Book : Invitation to Graph Theory

Name(s) of the author : Dr. S. Arumugam and S. Ramachandran,

Publisher : SciTech Publications,

Edition / Year : 2nd

Edition, 2003, Reprint.

Unit-I

Chapter 2 (All Sections)

Unit-II:



Unit-III:



Unit-IV:

Chapters 7 (All Sections) and

Chapter 8 (Sections 8.1 and 8.2)

Unit-V:


Reference Book(s):

Reference Book-I

Title of the Book : Graph Theory

Name(s) of the author : S.A.Choudam

Publisher :

Edition / Year :

Reference Book-II

Title of the Book : Graph Theory

Name(s) of the author : R. Balakrishnan

Publisher : Springer Publications.

Edition / Year :

Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS



Part III : Core Paper XIV No. of Credits :4

Title of the Paper: OPERATIONS RESEARCH

Objectives:

To have a comprehensive idea of advanced decisions making problems.

To apply these decision making problems in real life.

UNIT – I: Sequencing Problem and Replacement Problem

Problem of Sequencing- Basic terms used in Sequencing- Processing n jobs

through Two machines.

Replacement Problem Introduction – Replacement of Equipment / Asset that

Deteriorates Gradually.

UNIT – II: Dynamic Programming

Recursive Equation Approach- Characteristics of Dynamic Programming -

Dynamic Programming Algorithm- Solutions of Discrete Dynamic Programming Problems.

UNIT – III: Game Theory

Two-Person zero- sum games- Some Basic terms- The Maximin- Minimax Principle –

Games Without Saddle Points-Mixed strategies- Graphic solution of 2xn and mx2 games -

Dominance Property- Arithmetic method for n x n games–General solution of m x n

Rectangular games (LP method)

UNIT – IV: Inventory Control

Reasons for Carrying Inventories - The Inventory Decisions- Objective of Scientific

Inventory Control-Costs associated with Inventories- Factors Affecting Inventory Control –

An Inventory Control Problem – The Concept of EOQ – Deterministic inventory problems

with No Shortages- Deterministic Inventory problem with Shortages.


UNIT –V: Queueing Theory

Queueing system- Elements of queueing system- Operating characteristics of queueing

system- Poisson queueing systems- (M/M/1) : (∞ /FIFO), (M/M/1) :(N/FIFO) (only)

Text Book:

Title of the Book : Operation Research

Name(s) of the author : Kanti Swarup, P.K.Gupta and Manmohan,

Publisher : Sultan Chand & Sons.


edition, Reprint 2010.

Unit-I

Chapter 12 (Sections 12.2, 12.3, 12.4) and

Chapter 18 (Sections 18.1, 18.2 ).

Unit II:


Unit III:


Unit IV:


Unit V:


Reference Book:

Title of the Book : Operations Research

Name(s) of the author : S.D. Sharma

Publisher : Kedar Nath, Ram Nath and Co.


Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS

Programme: B. Sc Mathematics Subject Code :U16MAE61


Part III : Elective Paper IV–(a) No. of Credits :4

Title of the Paper: ADVANCED STATISTICS

Objectives:

To have a comprehensive idea about the probability distributions and its applications.

To have a knowledge in testing the hypothesis for small and large samples.

UNIT – I : Random Variables

Random Variables- Discrete Random Variable- Continuous Random Variable-

Mathematical Expectations- Mathematical Expectation of Continuous Random Variable-

Moment Generating Function (Except cumulant generating function)

UNIT – II : Some Special Distributions

Binomial Distribution- Poisson Distribution- Normal Distribution.

UNIT –III : Tests of Significance (Large samples)

Sampling- Sampling Distribution- Testing of Hypothesis-Procedure for Testing of

Hypothesis for Large Samples- Tests of Significance for Large Samples- Test of

Significance for Means- Test for Standard Deviation.

UNIT – IV: Tests of Significance (Small samples)

Test of Significance based on t-distribution (t-test) - Test of Significance based on

F-test- Test for Significance of an Observed Sample Correlation. Test Based on

Distribution- X2 -Test to test the Goodness of Fit.

UNIT – V : Analysis of Variance

One Criterion of Classification- Two Criteria of Classification- Three Criteria of

Classification (Latin Square Design).


Text Book:

Title of the Book : Statistics

Name(s) of the author : Dr. S. Arumugam And Mr. A. Thangapandi Isaac

Publisher : New Gamma Publishing Houses,

Edition / Year : year 2009.

Unit-I

Chapter 12 (All Sections – Except cumulant generating functions)

Unit-2


Unit-3

Chapter 14 (Sections 14.1 to 14.4, 14.5( IA, IIA, IIIA only)

Unit--4

Chapter 15 ( Sections 15.1,15.2,) and

Chapter 16 (16.2)

Unit-5


Reference Book:

Title of the Book : Fundamentals of Mathematical Statistics

Name(s) of the author : S.C.Gupta and V.K.Kapoor,

Publisher

Edition / Year : Sultan Chand and Co, New Delhi.:2003.

Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS



Part III : Elective Paper IV –(b) No. of Credits :4

Title of the Paper: FUZZY SET THEORY

Objectives:

To make aware of the student that the laws of impreciseness governing the real life.

To enrich their knowledge of fuzzy sets.

UNIT – I Basic-Fuzzy sets- diagrammatic representation of fuzzy sets- symbolic representation of

fuzzy set-Basic concepts of fuzzy sets: distance , height

Unit-II

Standard set operations on fuzzy sets: union, intersection, complement-

Laws of excluded middle –laws of contradiction-Demorgon‟s laws- Difference between fuzzy

sets and Crisp sets-

Unit-III

The extension principle –image and inverse image of fuzzy sets under crisp function-

properties --cuts of fuzzy sets-properties

Unit-IV

Arithmetic operations on intervals- Fuzzy numbers-Arithmetic operations on fuzzy

numbers-A+B, A-B, A/B, A.B

Unit-V

Binary fuzzy relations - transitive closure of binary relations function

Text Book:

Title of the Book : “Basic Fuzzy set theory”

Name(s) of the author : Prepared by the Department of Mathematics

Publisher :

Edition / Year :


Reference Book:

Title of the Book : Fuzzy sets and Fuzzy logic: Theory and Applications

Name(s) of the author : George J.Klir/Bo Yuan

Publisher

Edition / Year : Prentice Hall of India, Year of publishing: 2013

Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS



Part III : Skill Based Paper V No. of Credits :2

Title of the Paper: MATLAB - Theory

Objectives:

To enrich the Knowledge in Mathematical Softwares-MaTlab.

To enrich computer practical knowledge in various Computerized Mathematical

concepts.

UNIT – I Mathematical identities- Matrix operations.

Plot command- Graphics- Line plots- mesh-surface plots.

UNIT – II Sum of series- Taylor‟s series representation of a function Curve fitting of polynomials

and functions- fitting an equation with given data- interpolation.

UNIT – III Applications in Numerical Analysis- Solving a non linear equation- Finding maximum

and minimum of a function- Numerical integration- Ordinary differential equations.

Text Book:

Title of the Book : MATLAB – An Introduction with Application

Name(s) of the author : Amos Gilat

Publisher : Wiley India, Reprint 2007j.

Unit I:

Chapters 1, 2, 3, 5 and 9

Unit II:

Chapters 7 and 8

Unit III:

Chapter 10


Reference Book:

Title of the Book : Mastering MATLAB

Name(s) of the author : Duane Hansel man and Bruce Littlefield

Publisher : Pearson Education


Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS

Programme: B.Sc Mathematics Subject Code :U16MAS6P1


Part III : Paper IV No. of Credits :2

Title of the paper: MATLAB - Practical

Objectives:

To enrich computer practical knowledge in various mathematical concepts through

MATLAB

To develop the practical skills using arrays.

UNIT – I Programs using mathematical identities- Matrix operations. Programs using plot

command- Graphics- Line plots- mesh-surface plots.

UNIT – II Sum of series- Taylor‟s series representation of a function Curve fitting of polynomials

and functions- fitting an equation with given data- interpolation.

UNIT – III Applications in Numerical Analysis- Solving a non linear equation- Finding maximum

and minimum of a function- Numerical integration- Ordinary differential equations.

Text Book:

Title of the Book : MATLAB- An Introduction with Applications

Name(s) of the author : Amos Gilat

Publisher : Wiley India, reprint 2007


Unit I:

Chapters 1, 2, 3, 5 and 9

Unit II:

Chapters 7 and 8

Unit III

: Chapter 10

Title of the Book : Mastering MATLAB

Name(s) of the author : Duane Hansel man and Bruce Littlefield

Publisher : Pearson Education


Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS

Programme: B.Sc Mathematics Subject Code :U16CNV61


Part III : Paper VII No. of Credits :2

Title of the Paper: VALUE EDUCATION

Objectives:

To create an awareness of the vital and moral values of life.

To include value education as an integral part of the learning process

UNIT-I:

Values- Definition- Moral, Social, Spiritual values- Sources of values- Value of values-

Good manners- Character building.

Teachings and values of Hinduism, Islam and Christianity- Interfaith dialogue and Unity

of all faiths- Religious harmony.

UNIT-II:

Social Justice- Social Service- Social Service Programmes- Social Justice- Drug

addiction, Alcoholism, Smoking, Suicide- Remedial measures.

Mahatma Gandhiji, the symbol of Ahimsa- Swami Vivekananda- Message from his life-

Subramanya Bharathi- Message from his life.

UNIT-III:

Human rights- Classification- Fundamental rights- Protection of human rights- Human

rights organizations- Secularism- National Integration.

Women studies and Feminism- Role of women in society- Women and Health- Violence

against women- Legal protection for women- Women Empowerment.


Text Book

Title of the Book : VALUE EDUCATION

Name(s) of the author : K.G.S.RAMANAN

Publisher : New Century Book House, Chennai

Edition/Year : First Edition / 2016

Unit-I : Chapters 1 and 2

Unit-II : Chapters 3 and 4

Unit-III : Chapter 5 and 6

Reference Book:

Contents from websites (updated)

Prepared by:

Signature :



SATTUR – 626 203.


SYLLABUS

Programme: Common for all UG Programmes Subject Code :U16CNX61

Semester : VI No. of Credits :2

Extra Credits Paper

Title of the Paper: Model Paper for Competitive Examination

Objectives:

To create an awareness of the Competitive Examination

To make the students prepared for various Competitive Examinations

Unit I: General Knowledge

General Science – History – Geography- General Awareness.

Unit II: Current Events

Current events of the last year. (National and International).

Unit III: Aptitude

Numbers – HCF- LCM of Numbers – Decimal fractions-Simplications – square roots &

cuberoots- Sunds and indices –Percentage – Profit and loss – Ratio and Proportion.

Unit IV: Aptitude

Time and work – Times and Distance – Boats and Streams – Simple interest – Compound

interest – Area – Volume and Surface – Bankers Discount.

Unit: V: Mental Ability

Verbal Reasoning: Series Completion –Analogy – Coding – Decoding- Blood relations –

Direction Sense test- Alphabet test-Logical Ven diagrams

Non-Verbal Reasoning: Series – Classification-Mirror images-Water images.


Reference Book:

1. Advanced Objective General Knowledge – R.S.Aggarwal

2. Concise General Knowledge manual – Edgar Thorpe, Showick Thorpe

3. General Awareness and current Affairs Digest – K. Krishna Reddy

4. Manorama Year Book

5. Tata Megraw hill year Book

6. Quantitative Aptitude for Competitive Examinations by Dr. R.S.Aggarwal, S.Chand

Publications 2014.

7. A modern approach to verbal and non-verbal Reasoning by Dr. R.S. Aggarwal ,S. Chand

Publications 2011.

8. Test of Reasoning for competitive examinations - Edgar Thorpe

Prepared by:

Signature :

CHAIRMAN DEAN

B. Sc., DEGREE COURSE IN MATHEMATICS …srnmcollege.net/event_img/604cd0ae19529ee5178f676e...Tamil...

Documents

Transcript of B. Sc., DEGREE COURSE IN MATHEMATICS …srnmcollege.net/event_img/604cd0ae19529ee5178f676e...Tamil...