Thiagarajar college (autonomous), madurai – 9




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THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 9

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

DEPARTMENT OF MATHEMATICS

B.Sc. MATHEMATICS


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

Tamil / Other Language

6

3

90

25

75

100

P211

English

6

3

90

25

75

100

MM11

Differential Calculus

5

4

75

25

75

100

MM12

Statistics

5

4

75

25

75

100

MM13

Algebra

4

4

60

25

75

100

ESM11

SBE – I

2

2

30

15

35

50

ES

Environmental studies

2

2

30

15

35

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

Tamil / Other Language

6

3

90

25

75

100

P221

English

6

3

90

25

75

100

MM21

Integral Calculus

5

4

75

25

75

100

MM22

Differential Equations and

Applications

5

4

75

25

75

100

MM23

Sequences, series and Trigonometry

4

4

60

25

75

100

ESM21

SBE – II

2

2

30

15

35

50

VE

Value Education

2

2

30

15

35

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

P131

Tamil / Other Language

6

3

90

25

75

100

P231

English

6

3

90

25

75

100

MM31

Modern Analysis

5

4

75

25

75

100

AM31(P)

Allied Physics

6

4

90

25

75

100

EMM31

Elective - I

5

5

75

25

75

100

ENM31

NME : Mathematical Aptitude for Competitive Examinations

2

2

30

15

35

50

Total

30

21















Semester – IV



Code No.

Subject

Contact

Hrs /

Week

Credits

Total No

of Hrs

Allotted

Max.

Marks

CA

Max.

Marks

SE

Total

P141

Tamil / Other Language

6

3

90

25

75

100

P241

English

6

3

90

25

75

100

MM41

Modern Algebra

5

4

75

25

75

100

AM41(P)

Allied Physics

4

4

60

25

75

100

AML41(P)

Allied Physics – Practical

2

2

30

40

60

100

EMM41

Elective – II

5

5

75

25

75

100

ENM41

NME : Mathematical Logic

2

2

30

15

35

50

Total

30

23















Semester – V



Code No.

Subject

Contact

Hrs /

Week

Credits

Total No

of Hrs

Allotted

Max.

Marks

CA

Max.

Marks

SE

Total

MM51

Mechanics

5

4

75

25

75

100

MM52

Operations Research – I

5

4

75

25

75

100

MM53

C – Programming

5

4

75

25

75

100

AM51(C)

Allied Chemistry

6

4

90

25

75

100

EMM51

Elective – III

5

5

75

25

75

100

ESM51

SBE – III

2

2

30

15

35

50

ESM52

SBE – IV

2

2

30

15

35

50

Self study paper

History of Mathematics




















Total

30

25















Semester – VI



Code No.

Subject

Contact

Hrs /

Week

Credits

Total No

of Hrs

Allotted

Max.

Marks

CA

Max.

Marks

SE

Total

MM61

Complex Analysis

6

4

90

25

75

100

MM62

Operations Research – II

5

4

75

25

75

100

MM63

Graph Theory

4

4

60

25

75

100

MM64

Numerical Methods

5

4

75

25

75

100

AM61(C)

Allied Chemistry

4

4

60

25

75

100

AML61(C)

Allied Chemistry – Practical

2

2

30

40

60

100

ESM61

SBE – V

2

2

30

15

35

50

ESM62

SBE – VI

2

2

30

15

35

50




Part V




1













Total

30

27















List of Non Major Elective papers (NME) (2 Hours /week)

1) Mathematical Aptitude for competitive Examinations (For semester – III)

2) Mathematical Logic (For semester – IV)


List of Elective papers (5 Hours / week)

(One elective paper to be chosen in each of III, IV and V semester)

1) Analytical Geometry of 3D and Vector Calculus

2) Financial Accounting and Costing

3) Stochastic Processes

4) Data Structures

5) Fuzzy sets

6) Computer Algorithms

7) Data Mining

8) Mathematical Modelling


List of Skill Based Elective papers (SBE) (2 Hours / week)

1) C - Programming – Practical

2) Numerical Methods – Practical

3) Graph Theory – Practical

4) Theory of Numbers

5) Theory of Matrices

6) Statistical Test of Significance

7) Z and Fourier Transforms

8) Theory of Lattices

9) Data Structures - Practical

10) Personality Development


Self study paper:

History of Mathematics


A) Consolidation of Contact Hours and Credits : UG



Semester

Contact Hrs / Week

Credits

I

30

22

II

30

22

III

30

21

IV

30

23

V

30

25

VI

30

26

Part V




01

Total

180

140



B) Curriculum Credits : Part wise

Part – I 12 Credits

Part – II 12 Credits

Part – III

Core 60 Credits

Allied 20 Credits

Elective 15 Credits 95 Credits

Part – IV

NME (2 x 2) 04 Credits

SBE (6 x 2) 12 Credits

VE 02 Credits

ES 02 Credits 20 Credits

Part – V 01 Credits

140 Credits

THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009

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

Department of Mathematics

(From 2011 – 2014 batch onwards)

Course : B.Sc. Code No. : MM11

Semester : I No. of hours allotted : 5

Paper : Core 1 No. of credits : 4

Title of the Paper : Differential Calculus


Course objective:

To develop problem solving skills and study the applications of differential calculus


Unit - I (18 Hours)

Continuous functions – Algebra of continuous functions – Types of discontinuities – Properties of continuous functions - Differentiability - Algebra of derivatives – Derivatives of standard functions - The Chain rule for differentiation - Differentiation of inverse function - nth derivative of some standard functions.


Unit - II (15 Hours)

Leibnitz's theorem for nth derivative of a product - Partial derivatives – Homogeneous functions and Euler’s theorem.


Unit - III (15 Hours)

Multiple points of a curve - Asymptotes - Method of finding asymptotes for the curve y = f(x) - Method of finding asymptotes for the curve f(x, y)= 0.


Unit - IV (12 Hours)

Curvature - Evolute - Envelope.


Unit - V (15 Hours)

Maxima and minima of functions of two variables - Lagrange's method of Undermined multipliers.


Text Books :

1) Calculus, Arumugam and Issac,

New Gamma publishing House, Edition 1995

2) Calculus – Volume I, S. Narayanan, T.K. Manicka Vasagam Pillay,

S. Viswanathan Pvt. Ltd., Edition 1997



Unit

Book

Chapter/section

I

1

2.1 – 2.5, 3.1 – 3.5, 3.12

II

1

3.13 – 3.15

III

1

10.2, 11.1 – 11.2

IV

1

8 and 9(Full)

V

2

8.4, 8.5



Reference Book :

Differential Calculus, Shanti Narayan,

S. Chand and Company Ltd., 14th Edition, Reprint 2002


THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009

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

Department of Mathematics

(From 2011 – 2014 batch onwards)

Course : B.Sc. Code No. : MM12

Semester : I No. of hours allotted : 5

Paper : Core 2 No. of credits : 4

Title of the Paper : Statistics


Course objective: To acquire various skills about basic statistical concepts and to know fitting statistical data in various distributions.

Unit - I (15 Hours) Measures of Dispersion : Introduction – Measures of Dispersion. Moments Skewness and Kurtosis : Introduction – Moments – Skewness and Kurtosis.


Unit - II (15 Hours) Correlation and Regression : Introduction – Correlation – Rank Correlation – Regression – Correlation Coefficient for a Bivariate Frequency Distribution.

Unit - III (15 Hours) Random Variables : Introduction – Random Variables – Discrete Random Variable – Continuous Random Variable – Mathematical Expectations – Mathematical Expectation of Continuous Random Variable – Moment Generating Function – Characteristic Function.

Unit - IV (15 Hours) Some Special Distributions : Introduction – Binomial Distribution – Poisson Distribution – Normal Distribution – Some More Continuous Distributions (Gamma Distribution, Chi – Square Distribution, Student’s t-Distribution, Snedecor’s F-Distribution, Fischer’s Z-Distribution).

Unit - V (15 Hours) Tests of Significance (Small Samples) : Introduction – Test of Significance Based on t – Distribution – Test of Significance Based on F-Test.

Test Based on Chi-Square Distribution: Introduction – Chi-Square Test for Population Variance – Chi-Square Test to test the goodness of fit.


Text Book

Statistics - S. Arumugam and A. Thangapandi Isaac,

New Gamma Publishing House, June 2007



Unit

Chapter/section

I

3(3.0 & 3.1), 4(4.0 to 4.2)

II

6(6.0 to 6.4)

III

12(12.0 to 12.6)

IV

13(13.0 to 13.4)

V

15(15.0 to 15.2), 16(16.0 to 16.2)



Reference Books : 1. Fundamentals of Mathematical Statistics

- S. C. Gupta and V.K. Kapoor, Sultan Chand & Sons, 9th Edition.

2. Statistical methods - Dr. S. P. Gupta

- Sultan Chand and Sons, 25th thoroughly revised and enlarged edition, New Delhi – 110 002

THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009

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

Department of Mathematics

(From 2011 – 2014 batch onwards)

Course : B.Sc. Code No. : MM13

Semester : I No. of hours allotted : 4

Paper : Core 3 No. of credits : 4

Title of the Paper : Algebra


Course objective:

  • To study various methods of solving equations.

  • To study what are inequalities and what are their importance in Mathematics.


Unit –I (12 Hours)

BINOMIAL THEOREM : Binomial theorem for a rational index – Some important particular cases of binomial expansion – sign of terms of a binomial expansion – Numerically greatest term – Expansion by splitting the term by Partial fractions – Application to Summation of series


Unit- II (12 Hours)

EXPONENTIAL AND LOGARITHMIC SERIES : Exponential limit – Exponential theorem – summation of series – Expansion in two ways – Logarithmic series theorem – Modification of log series – Differents forms – Euler’s constant - summation of series

Unit – III (12 Hours)

THEORY OF EQUATIONS : ransformations of equations – Construction of new equations from the given ones, Reciprocal equations, Descartes rule of signs and Multiple roots

Unit – IV (12 Hours)

CONTINUED FRACTIONS : Definitions – Recurring continued fractions – law of formation of the successive convergents – Properties of convergents


Unit – V (12 Hours)

INEQUALITIES : Inequalities – Elementary properties – Arithmetic mean – Geometric mean – Weierstrass inequality – Cauchy inequality


Text Books:

1. Algebra - Vol – 1 T.K.M Pillay and others, S. Viswanathan (printers and publishers), 2008

2. Algebra –Vol – 2 T.K.M Pillay and others, S. Viswanathan (printers and publishers), 2008



Unit

Book

Chapter/section

I

1

3(3.5 - 3.10)

II

1

4(4.1 to 4.9)

III

1

6(6.15, 6.16, 6.24, 6.26)

IV

2

3(1 - 4, 5.1 - 5.8)

V

2

4(1 – 12)



Reference Book: Algebra - S. Arumugam and Issac, New Gamma publications, 1995


THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009

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

Department of Mathematics

(From 2011 – 2014 batch onwards)

Course : B.Sc. Code No. : MM21

Semester : II No. of hours allotted : 5

Paper : Core 4 No. of credits : 4

Title of the Paper : Integral Calculus


Course objective: To develop problem solving skills in Calculus and study the applications of integral calculus


Unit - I (18 Hours)

Integration by parts - Bernouilli's formula - Reduction formula - Improper integrals - Some tests for convergence of improper integrals - Evaluation of some improper integrals.


Unit - II (18 Hours)

Double integral - Evaluation of double integral - Triple integral - Jacobians - Change of variables in double and triple integrals.


Unit - III (12 Hours)

Beta and Gamma functions - Properties and results involving Beta and Gamma functions.


Unit - IV (15 Hours)

Area as double integral - Volume as triple integral - Area of surface.


Unit - V (12 Hours)

Centre of mass - Moment of inertia.


Text Book :

Calculus volume II - Arumugam and Issac,

New Gamma publishing House, Edition 1990



Unit

Chapter/section

I

2.7 – 2.8, 3.1 – 3.4

II

4.1 – 4.5

III

5(Full)

IV

6.2, 6.5, 6.6

V

6.7, 6.8



Reference Book :

Integral Calculus, Shanti Narayan,

S. Chand and Company Ltd., 9th Edition, Reprint 2002


THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009

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

Department of Mathematics

(From 2011 – 2014 batch onwards)

Course : B.Sc. Code No. : MM22

Semester : II No. of hours allotted : 5

Paper : Core 5 No. of credits : 4

Title of the Paper : Differential Equations and its Applications


Course objective:

1. To expose the students to various methods of solving different kinds of differential

equations.

2. To expose the students how to apply their knowledge in Differential Equations to other

branches of Sciences.

Unit – I (15 Hours)

Differential Equations of First Order : Differential Equation – Equations of first order and first degree – Exact differential Equations – Integrating factors – Linear equations – Bernouilli’s equations – Equations of first order and higher degree.


Unit – II (15 Hours)

Linear Equations of Higher order : Linear equations with constant coefficients – Method of finding complementary functions – Method of finding particular integral - Homogeneous linear equations – Linear equations with variable coefficients – Simultaneous linear differential equations – Total differential equations - Method of variation of parameters - Removal of first derivative.


Unit – III (15 Hours)

Laplace Transform : Laplace transform – Inverse Laplace transform – Solution of differential equation using Laplace transform.


Unit – IV (15 Hours)

Partial Differential Equations : Formation of partial differential equations – First order partial differential equations – Methods of solving first order partial differential equations – Some standard forms – Charpit’s Method.


Unit – V (15 Hours)

Applications of Differential Equations : Orthogonal trajectories – Growth and decay – Continuous compound interest – The Brachistochrone problem – Simple electric circuits – Falling bodies – Simple harmonic motion – Central forces – Planetary motion.


Text Book: Differential Equations and Applications – Arumugam & Isaac,

New Gamma Publishing House – 2008.



Unit

Chapter/section

I

1 (Section 1.1 to 1.7)

II

2(Section 2.1 to 2.7)

III

3(Section 3.1 to 3.3)

IV

4(Section 4.1 to 4.5)

V

6(Section 6.1 - 6.4, 6.6 - 6.8, 6.10, 6.11)

Reference Book

Differential Equations and its Applications– S. Narayanan and T. K. ManicavachagamPillay, S. Viswanathan (printers & publishers) Pvt. Ltd., 1996

THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009

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

Department of Mathematics

(From 2011 – 2014 batch onwards)

Course : B.Sc. Code No. : MM23

Semester : II No. of hours allotted : 4

Paper : Core 6 No. of credits : 4

Title of the Paper : Sequences, Series and Trigonometry


Course objective: 1.To introduce the convergency and divergency of sequences and series

2.To introduce the trigonometric functions


Unit - I (12 Hours)

Sequences – Bounded sequences – monotonic sequences – convergent sequences - divergent and oscillating sequences – Algebra of limits.


Unit - II (12 Hours)

Behaviour of Monotonic Sequences - Some theorems on limits – Subsequenes – Limit points – Cauchy sequences – The upper and lower limits of a sequence.


Unit - III (12 Hours)

Infinite Series – Comparison Test – Kummer’s Test – Root Test and Condensation Test – Integral Test.


Unit - IV (12 Hours)

Alternating series – Absolute Convergence – Tests for Convergence of Series of arbitrary terms- Rearrangement of Series – Multiplication of series – Power series.


Unit - V (12 Hours)

Expression for sin nθ, cos nθ, tan nθ, sinn θ, cosn θ – Expansion of sin θ , cos θ, tan θ in powers of θ - Hyperbolic functions - - Inverse Hypeerbolic functions


Text Books: 1) Sequences and Series - Arumugam and Issac,

New Gamma Publishing House, 1997

2) Trigonometry and Fourier Serie - Arumugam, Issac and Somasundaram,

New Gamma Publishing House, 1997



Unit

Book

Chapter/section

I

1

3.1 – 3.6

II

1

3.7 – 3.12

III

1

4.1 – 4.5

IV

1

5.1 – 5.6

V

2

1.2, 1.2, 1.3, 2.1, 2.2



Reference Books : 1. Algebra Volume I - T.K.M. Pillai, T. Natarajan and K.S. Ganapathy

S. Viswanathan Publishers, 2008

2. Trigonometry - S. Narayanan and T.K. Manickavachagom Pillay

S. Viswanathan Publishers, 1986


THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009

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

Department of Mathematics

(From 2011 – 2014 batch onwards)

Course : B.Sc. Code No. : MM31

Semester : III No. of hours allotted : 5

Paper : Core 7 No. of credits : 4

Title of the Paper : Modern Analysis


Course objective: To acquire knowledge in countable and uncountable sets, inequalities, Metric spaces, continuity, completeness and connectedness of metric spaces.


Unit - I (15 Hours)

Preliminaries: Sets and Functions – Countable sets – Uncountable sets – Inequalities of Holder and Minkowski.


Unit - II (15 Hours)

Metric Spaces : Definitions and Examples – Bounded Sets in a Metric Space – Open Ball in a Metric Space – Open Sets – Subspaces – Interior of a Set – Closed Sets – Closure – Limit Point – Dense Sets.


Unit - III (15 Hours)

Complete Metric Space and Continuity : Introduction – Completeness – Baire’s Category Theorem - Continuity – Homeomorphism – Uniform Continuity – Discontinuous Functions on R.


Unit – IV (15 Hours)

Connectedness: Introduction –Definition and Examples – Connected Subsets of R – Connectedness and Continuity.


Unit - V (15 Hours)

Compactness: Introduction – Compact Space – Compact Subset of R – Equivalent Characterization for Compactness – Compactness and Continuity.


Text Book: Modern Analysis - S. Arumugam and A. Thangapandi Isaac,

New Gamma Publishing House, 1997



Unit

Chapter/section

I

1(1.1 to 1.4)

II

2(2.1 to 2.10)

III

3(3.0 to 3.2), 4(4.0 to 4.4)

IV

5(5.0 to 5.3)

V

6(6.0 to 6.4)



Reference Book : Methods of Real Analysis - Goldberg,

Oxford and IBH publishing Company, 1964.


THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009

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

Department of Mathematics

(From 2011 – 2014 batch onwards)

Course : B.Sc. Code No. : MM41

Semester : IV No. of hours allotted : 5

Paper : Core 8 No. of credits : 4

Title of the Paper : Modern Algebra


Course objective: To study the theory related with theorem so that the students may cope-up with the higher studies in Algebraic systems


Unit - I (18 Hours)

Group - Elementary properties of a group - Permutation groups - Subgroups - Cyclic groups - Cosets and Lagrange's theorem.


Unit - II (15 Hours)

Normal subgroups - Isomorphism - Automorphism - Homomorphism.


Unit - III (15 Hours)

Ring - Properties of Rings - Isomorphism - Types of Rings - Characteristic of a Ring - Ideals - Quotient Rings - Maximal and Prime ideals - Homomorphism of Rings.


Unit - IV (15 Hours)

Field of quotients of an integral domain - Ordered integral domain - U.F.D. - Euclidean domain.


Unit - V (12 Hours)

Vector space - Subspace - linear transformation - Linear span - Linear independence - Basis and dimension - Inner product spaces - Orthogonality.


Text Book: Modern Algebra - S. Arumugam and A. Thangapandi Isaac

New Gamma Publishing House, 1996



Unit

Chapter/Section

I

3.1, 3.2, 3.4 – 3.6, 3.8

II

3.9 – 3.12

III

4.1 – 4.5, 4.7 – 4.10

IV

4.11 – 4.14

V

5.1 – 5.6, 6.1 – 6.2



Reference Book:

Topics in Algebra -I.N. Herstein, Wiely India Pvt. Ltd, II Edition, Reprint 2007


THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009

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

Department of Mathematics

(From 2011 – 2014 batch onwards)

Course : B.Sc. Code No. : MM51

Semester : V No. of hours allotted : 5

Paper : Core 9 No. of credits : 4

Title of the Paper : Mechanics
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