THEORY
Fibre study
(a) Classification of fibres – study of properties common to protein,
cellulose, mineral and thermoplastic fibres.
(b) Manufacture, uses and properties of Cotton, Jute, Viscose Rayon, Wool, Silk, Nylon, Terylene and Acrylic.
2. Yarn processing – Steps involved in processing cotton yarns – classification of yarns based on direction of twist, count – simple and novelty yarns.
3. Weaving  parts of a loom, basic weaving operation, study of weaves – Basic weaves and figured weaves.
4. Fabric finishing – Purpose and uses of various finishes – singeing, scouring, bleaching, tentering, calendering, sizing, weighting, mercerising, napping, sanforising, crease proofing.
Dyeing and printing
Classification of dyes  Natural and Synthetic – Direct, Basic, Acid, Mordant, Naphthol, Reactive and Vat dyes – Methods of Dyeing  Stock, Top, Yarn and Piece dyeing.
Styles of Printing – Direct, Discharge and Resist method. Methods of printing – Hand methods  Batik, Tie & Dye, Block, Screen Printing; Machine Methods  Roller printing, Screen Printing, Duplex Printing, Transfer Printing and Photo Printing.
REFERENCES
1. Durga Deulkar, (1951). A guide to household textiles and laundry work. Atmaram and Sons, New Delhi.
2. Hess, (1961). Textile fibres and their use. Lippincot Co., New York.
3. Irwin, (1957). Clothing for Moderns. The Macmillan Company, New York.
4. Joseph, M.L., (1977). Introductory Textile Science. Rinehart & Winston.
New York. 3^{rd} Editionl
5. Norma, Hollen & Saddler (1973). Textiles. The Macmillan Co. New York.
6. Potter & Corbman, (1985).Fibre to Fabric. Mc Graw Hill Book Co. New
York.
7. Trotman, E.R. (1994). Dyeing and Chemical Technology of Textile fibres.
6^{th }Edition, B.I. Publications Pvt. Ltd., New Delhi.
8. Wingate, (1976). Textile Fabrics and their selection. Prentice Hall Inc.,
New Jersey.
SEMESTER – VI
ELECTIVE II  CLOTHING CONSTRUCTION
Theory: 4 hours
Practicals: 2 hours
OBJECTIVES:
To help the students to
Study the principles of laundering and use this knowledge in care of Textiles.
Select clothing appropriate for various family members.
Learn the techniques involved in Garment Construction.
THEORY:
Techniques of clothing construction
Selection, use and care of sewing machine and sewing tools.
Study of basic hand stitchestemporary and permanent.
Seams and seam finishes.
Methods of introducing fullness into a fabricdarts,tucks,pleats and gathers.
Principles of Pattern Making, Fabric Preparation, Pattern Layout and Garment Cutting
Steps in preparing the basic bodice, sleeve and skirt pattern for children and adult women based on body measurements.
Steps in fabric preparation.
Pattern Layout.
Methods of transferring pattern markings on to a fabric.
Care of Textiles Principles of laundering and storing cotton, wool, silk, rayon and synthetic fabrics study on selection of suitable soaps, bleaches, whitening and stiffening agents.
Family clothing planPrinciples of preparing clothing budget and wardrobe planningselection and buying of fabrics and readymades based on art principles, personal characteristics and other factors.
Application of computer aided designing in textiles.
PRACTICALS:
Fullness  Darts, Tucks, Pleats, Gathers, Frills, Ruffles and Smocking.
Fasteners – Button and Buttonhole, Loops, Press, Buttons, Hooks and Eyes and Eyelets.
Decorative stitches.
Fabric painting
Construction of Salwar Kameez.
REFERENCES:
1. Allyne Bane, 1980, “Creative Sewing”, McGraw & Hill Book Company.
2. Durga Deulkar, 1951, “A guide to household textiles and laundry work”,
Atmaram and sons. New Delhi.
3. Graves Ryan. “Complete Encyclopedia for Stitchery”
4. Hess, 1961, “Textile fibers and their use”, Lippincot Co., New York.
5. Juveka, “Easy Cutting”.
6. Joseph, “Introductory Textile Science”, Rinehart & Winston Inc., New York.
7. Irwin, 1957, “Clothing for Moderns”, The Macmillan Company,
New York.
8. Irwin, “Practical Dress Design”.
9. Lewis, Bowar, Kettunen, 1976, “Clothing Construction and Wardrobe Planning”.
The Macmillan Company. New York.
10. Marry Mathews, 1996, “Practical Clothing Construction Part I and Part II”, cosmic press.
11 Norma, Hollen, Saddler, 1973, “Textiles”, The Macmillan Company, New York.
12. Wingate, 1976, “Textile Fabrics and their selection”, Prentice Hall Inc. New Jersey.
ELECTIVE III  FAMILY STUDIES
[Common Syllabus for B.Sc. (I.D.) and B.Sc. (Clinical Nutrition)]
Theory: 5 hrs/week
OBJECTIVES
To enable students to
1. Help students to gain maturity to face the demands of married life.
2. Take right decisions towards setting up a family
THEORY:
I. FAMILY
a. Characteristics and developmental tasks – types of family – Indian
– Traditional and Modern.

Functions of family – Family in India – Factors influencing the
Indian Family.
II. MARRIAGE AND FAMILY AS BASIC INSTITUTION

Motives of Marriage

Functions of Marriage
III. Importance of physical, mental health, emotional maturity, personality development in marriage – Factors affecting Marriage relationship – Religion, social, economic status, career and money.
IV. ADJUSTMENT IN MARRIAGE – Adjustment towards male, sex, finance, society, inlaw.
V. FAMILY LIFE CYCLE – Stage – beginning family, expanding family, contracting family – adjustment in different stages.
VI. CRISIS IN THE FAMILY  Critical Family situation, alcoholism, widowhood etc. – their effects on children.
VII. Maternal and paternal deprivation and their effect on the child growth and development.
VIII. Parental attitudes and their influence on children – styles of parenting.
IX. Small family norms – concept, advantages and limitations.
PRACTICALS
1. Study on qualities preferred by Adolescents in their life partner.
2. Survey on inlaw relationships.
3. Survey on different types of family.
REFERENCES
1. Christensen, H.T. (1964). Handbook of Marriage and the Family – Rand
Mc Nally Co.
2. Christensen, H.T. and Johnson, K.P. (1971) – Marriage and the Family –
Ronald Press Co, 3rd Edition.
3. Desouza, A (1973). Women in contemporary India – Manohar Book
Service.
4. Duvall, E.M. (1977) – Marriage and Family development, J.B. Lippincott Company, Philadelphia.
5. Goode, W.J. (1965) – The Family. Prentice Hall of India.
6. Kapadia, K.M. (1972) – Marriage and Family in India – Oxford University Press, Bombay.
7. Landis F. and Landis M.D. (1935) – Personal Adjustments in Marriage and Family living – Prentice Hall Inc. of New York.
8. Laudir J.T. and Landis M.D. (1978) Marriage and Family – Prentice Hall Inc. of New York., 6^{th} edition.
9. Stinnet, N and Walters, J (1977) Relationships in Marriage and Family – Macmillan Publishing.
10. Sussman, M.D. (1953) – Source Book on Marriage and Family – Houghton Mifflin Co, New York.
11. B.Sc. DEGREE COURSE IN MATHEMATICS
SYLLABUS
CORE SUBJECT : PAPER – V
DIFFERENTIAL EQUATIONS AND LAPLACE TRANSFORMS
Credits  4 Instructional Hours – 4
First order but of higher degree equations – solvable for p, solvable for x, solvable for y, clairaut’s form – simple problems.
Second order differential equations with constant coefficients with particular integrals for e^{ax}, x^{m}, e^{ax }sinmx, e^{ax }cosmx
Second order differential equations with variable coefficients ;
Method of variation of parameters; Total differential equations, simple problems.
Partial Differential equations :
Formation of P.D.E by eliminating arbitrary constants and arbitrary functions; complete integral; Singular integral ; general integral; Charpit’s method and standard types f(p,q)=0, f(x,p,q)=0, f(y,p,q)=0, f(z,p,q)=0, f(x,p)= f(y,q); Clairaut’s form and Lagrange’s equations Pp+Qq=R – simple problems.
Laplace transform; inverse Laplace transform(usual types); applications of Laplace transform to solution of first and second order linear differential equations (constant coefficients) and simultaneous linear differential equations – simple problems.
Reference Books :

Engineering Mathematics volume 3 : M.K. Venkataraman(National Publishing Co.)

Engineering Mathematics Volume 3 : P.Kandasamy and others(S.Chand and Co.)

Integral Calculus and differential equations : Dipak Chatterjee (Tata McGraw Hill Publishing Company Ltd.)

Advanced Engineering Mathematics : Erwin Kreyszig (John Wiley and sons New York 1999)

Calculus : Narayanan and others (S.Viswanathan Publishers)

Differential Equations and Integral Transforms : Dr.S.Sudha (Emerald Publishers)
Core Subject  Paper VI
COORDINATE GEOMETRY OF 3 DIMENSIONS AND PROBABILITY
Credits  4 Instructional Hours – 5
Planes and Lines : Planes and Lines  Reduction to symmetric form of a line given by a pair of planes; conditions for 2 lines to be coplanar and the equation of the plane containing the lines; length and equation of the shortest distance between 2 skew lines; image of a point and a line w. r. t. a plane, bisector planes.
Sphere :
Equation of a sphere ; general equation ; section of a sphere by a plane ; tangent plane ; radical plane ; coaxal system of spheres; orthogonal spheres.
Probability :
Probability space; total probability ; multiplication law on probability; conditional probability ; independent events; Baye’s Theorm.
Random variables; discrete and continuous ; distribution functions ; expected value ; moments; moment generating function; probability generating function.
Reference Books :

Differential Equations, Fourier series and Analytical Solid Geometry : P.R.Vittal (Margham Publishers)

Engineering Mathematics volume 3 : M.K. Venkataraman(National Publishing Co.)

Engineering Mathematics volume 3 : P.Kandasamy and others(S.Chand and Co.)

Advanced Engineering Mathematics : Stanley Grossman and William R.Devit(Harper and Row publishers)

Fundamentals of Mathematical Statistics : S.C.Gupta and V.K. Kapoor (S.Chand and Co.)

Mathematical Statistics and Probability by P.R.Vittal (Margham Publishers)
Core Subject  Paper – VII
VECTOR CALCULUS, FOURIER SERIES AND FOURIER TRANSFORMS
Credits  4 Instructional Hours – 5
Vector Differentiation :
Gradient , divergence, curl, directional derivative, unit normal to a surface.
Vector integration: line, surface and volume integrals; theorems of Gauss, Stokes and Green. (without proof) – simple problems.
Fourier Series: Expansions of periodic function of period 2π ; expansion of even and odd functions; half range series.
Fourier Transform: Infinite Fourier transform (Complex form, no derivation); sine and cosine transforms; simple properties of Fourier Transforms; Convolution theorem; Parseval’s identity.
Reference Books :

Engineering Mathematics Volume 3 : M. K. Venkataraman (National Publishing Co.)

Engineering Mathematics Volume 3 : P. Kandasamy and others (S. Chand and Co.)

Vector Analysis : Murray Spiegel (Schaum Publishing company, New York)

Vector Analysis : P. Duraipandian and Laxmi Duraipandian (Emerald Publishers).
Core Subject – Paper VIII
STATICS
Credits – 4 Instructional hours : 4
Forces: Types of forces, Magnitude and direction of the resultant of the forces acting on a particle, Lami’s Theorem, equilibrium of a particle under several coplanar forces, parallel forces, moments, couplessimple problems.
Friction: Laws of friction, angle of friction, equilibrium of a body on a rough inclined plane acted on by several forces, centre of gravity of simple uniform bodies, triangular lamina, rods forming a triangle, trapezium, centre of gravity of a circular arc, elliptic quadrant, solid and hollow hemisphere, solid and hollow cone, catenarysimple problems.
Reference Book:

Mechanics – P. Duraipandian and others, S. Chand & Co.

Statics – K. Viswanatha naik and M. S. Kasi, Emerald Publishers.

Statics – S. Narayanan and others, S. Chand and Co.

Statics – A. V. Dharmapadam, S. Viswanathan and Co.
Core Subject – PAPER IX
ALGEBRAIC STRUCTURES I
Credits – 4 Instructional hours : 6
Groups: Subgroups, cyclic groups and properties of cyclic groups – simple problems; Lagrange’s Theorem; Normal subgroups; Homomorphism; Automorphism ; Cayley’s Theorem, Permutation groups.
Rings: Definition and examples, Integral domain, homomorphism of rings, Ideals and quotient Rings, Prime ideal and maximum ideal; the field and quotients of an integral domain, Euclidean Rings.
Reference Book:
Contents and treatment as in “Topic in Algebra” – I. N. Hesteien, Wiley Eastern Ltd.
Chapter 2 : Section – 2.1 , 2.2 , 2.3 , 2.4 , 2.5 , 2.6 , 2.7 (Omit Sections 1 and 2)
2.8 , 2.9 , 2.10
Chapter 3 : Section – 3.1 , 3.2 , 3.3 , 3.4 , 3.5 , 3.6 , 3.7.
Core Subject – PAPERX
REAL ANALYSIS I
Credits – 4 Instructional hours : 6
Sets and Functions : Sets and elements; Operations on sets; functions; real valued functions; equivalence; countability; real numbers; least upper bounds.
Sequences of Real Numbers: Definition of a sequence and subsequence; limit of a sequence; convergent sequences; divergent sequences; bounded sequences; monotone sequences; operations on convergent sequences; operations on divergent sequences; limit superior and limit inferior; Cauchy sequences.
Series of Real Numbers : Convergence and divergence; series with nonnegative numbers; alternating series; conditional convergence and absolute convergence; tests for absolute convergence; series whose terms form a nonincreasing sequence; the class I^{2}.
Limits and metric spaces : Limit of a function on a real line; metric spaces; limits in metric spaces.
Reference Book :

Treatment as in “Methods of Real Analysis” : Richard R. Goldberg (Oxford and IBH Publishing Co.)

Chapter 1 – (full), Chapter 2 – Sections 2.1 to 2.10
3. Chapter 3 – Section 3.1 to 3.4, 3.6 , 3.7 , 3.10 , Chapter 4 – full.
Core Subject – PAPER XI
DYNAMICS
Credits – 4 Instructional hours : 6
Kinematics : kinematics of a particle, velocity, acceleration, relative velocity, angular velocity, Newton’s laws of motion, equation of motion, rectilinear motion under constant acceleration, simple harmonic motion.
Projectiles : Time of flight, horizontal range, range in an inclined plane. Impulse and impulsive motion, collision of two smooth spheres, direct and oblique impactsimple problems.
Central forces : Central orbit as plane curve, pr equation of a central orbit, finding law of force and speed for a given central orbit, finding the central orbit for a given law of force.
Moment of inertia : Moment of inertia of simple bodies, theorems of parallel and perpendicular axes, moment of inertia of triangular lamina, circular lamina, circular ring, right circular cone, sphere (hollow and solid).
Reference Books :

Mechanics – P. Duraipandian and others, S. Chand and Co.

Dynamics – K. Viswanatha Naik and M. S. Kasi, Emerald Publishers.

Dynamics – A. V. Dharmapadam, S. Viswanathan Publishers.
Core Subject – PAPER XII
PROGRAMMING LANGUAGE ‘C’ WITH MATHEMATICAL
PRACTICALS
THEORY
Credits – 4 Instructional hours : 6
IntroductionConstants Variables DatatypesOperatorsPrecedence of operators – Library functions –Input statements Output statementsEscape sequencesFormatted outputs – Storage classes – Command line arguments – Preprocessor directives.
Control statements – if statement – if else statement – nested if statement – switch case statement – conditional operator – go to statement –while statement – do while statement – for statement – nested for – continue –exit – break.
Arrays – one dimensional arrays – declarations – initialization of arrays – two dimensional arrays – multidimensional arrays – pointers – functions – function definition – function declaration – calling a function – call by reference  call by value.
Categories of functions – nesting of functions – recursion – function with arrays – strings – arithmetic operators on characters – comparing strings – string handling functions.
Structure – structure definition – structure initialization – union – enumerations – user defined data types(typedef) – files – open – close  input – output – operations on files.
Reference Books :

Programming in ANSI C 2^{nd} edition, E. Balaguruswamy, TataMcgraw Hill Publishing Company.

Venugopal, programming in C

Gottfied, B.S. : programming with C , Schaum’s outline series, TMH 2001
Practicals
Writing ‘C’ programs for the following :

To convert centigrade to Fahrenheit

To find the area, circumference of a circle

To convert days to months and days

To solve quadratic equations

To find sum of n numbers

To find the largest and smallest numbers

To evaluate the sine series, cosine series

To evaluate the power series

To generate Pascal’s triangle, Floyd’s triangle

To add and subtract two matrices

To multiply two matrices

To evaluate Fibonacci series using functions

To evaluate compound interest using functions

To add complex numbers using functions

To use string functions
SEMESTER VI
CORE SUBJECT – PAPER XIII
ALGEBRAIC STRUCTURESII
Credits – 4 Instructional hours : 6
Vector Spaces : Definition and examples, linear dependence and independence, dual spaces, inner product spaces.
Linear Transformations : Algebra of linear transformations, characteristic roots, matrices, canonical forms, triangular forms.
Treatment and content as in “Topics in Algebra” – I. N. HersteinWiley Eastern Ltd.
Chapter 4 – Sections 4.1 to 4.4
Chapter 6 – Sections 6.1 to 6.4
Reference Books:

University Algebra – N. S. Gopalakrishnan – New Age International Publications, Wiley Eastern Ltd.

First course in Algebra – John B. Fraleigh, Addison Wesley.

Text Book of Algebra – R. Balakrishna and N. Ramabadran, Vikas publishing Co.

Algebra – S. Arumugam, New Gamma publishing house, Palayamkottai.
CORE SUBJECT XIV
REAL ANALYSIS II
Credits – 4 Instructional hours : 6
Continuous functions on Metric Spaces: Functions continuous at a point on the real line, reformulation, functions continuous on a metric space, open sets, closed sets, discontinuous functions on the real line.
Connectedness Completeness and compactness: More about open sets, connected sets, bounded sets and totally bounded sets, complete metric spaces, compact metric spaces, continuous functions on a compact metric space, continuity of inverse functions, uniform continuity.
Calculus : Sets of measure zero, definition of the Riemann integral, existence of the Riemann integral (statement only) properties of Riemann integral, derivatives, Rolle’s theorem, Law of mean, Fundamental theorems of calculus, Taylor’s theorem.
Sequences and Series of Functions.
Pointwise convergence of sequences of functions, uniform convergence of sequences of functions.
Treatment as in “Methods of Real Analysis” Richard R. Goldberg (Oxford and IBH Publishing Co)
Chapter 5 and 6 full, Chapter 7, section 7.1 to 7.8, Chapter 8, section 8.5 only, Chapter 9, sections 9.1 and 9.2 0nly
^{
}
^{
}^{ } CORE SUBJECT – PAPER – XV
COMPLEX ANALYSIS
Credits – 4 Instructional hours : 6
Complex numbers : Point at infinity , Stereographic projection
Anlaytic functions : Functions of a complex variable , mappings, limits , theorems of limits without proof, continuity, derivatives, differentiation formula , CauchyRiemann equations , sufficient conditions CauchyRiemann equations in polar form, analytic functions, harmonic functions.
Mappings by elementary functions: linear functions, the function 1/z,linear fractional transformations , the functions w=z^{n}, w=e^{z}, special linear fractional transformations.
Integrals : definite integrals, contours , line integrals, CauchyGoursat theorem(without proof), Cauchy integral formula, derivatives of analytic functions, maximum moduli of functions.
Series : convergence of sequences and series (theorems without proof),Taylor’s series, Laurent’s series, zero’s of analytic functions.
Residues and poles : residues, the residue theorem, the principal part of functions, poles, evaluation of improper real integrals, improper integrals, integrals involving trigonometric functions, definite integrals of trigonometric functions
Content and Treatment as in “Complex Variables and Applications” – Ruel V. Churchill, James W. Brown and Roger F.VerheyMcGrawhill International student edition.
Reference Books :

Theory and problems of Complex Variables – Murray R.Spiegel ,Schaum outline series

Complex Analysis – P.Duraipandian

Introducation to Complex Analysis S. Ponnuswamy , Narosa Publishers 1993
Elective Subjects may be chosen from the following list.
List of Elective subjects.

Operations Research – I

Graph Theory – I

Special Functions – I

Astronomy  I

Operations Research – II (prerequisite Operations Research –I)

Graph Theory – II(prerequisite Graph theory – I)

Special Functions – II(prerequisite Special Functions – I)

Astronomy – II (prerequisite Astronomy – I)

Discrete Mathematics

Elementary Number Theory
OPERATIONS RESEARCH – I
Credits – 5 Instructional hours : 6
Linear programming – formulation – graphical solution – simplex method
BigM method – Twophase methodduality primaldual relation – dual simplex method – revised simplex method – Sensitivity analysis.
Transportation problem – assignment problem.
Sequencing problem – n jobs through 2 machines – n jobs through 3 machines – two jobs through m machines – n jobs through m machines
Books for reference :
1.Gauss S.I. Linear programming , McGrawHill Book Company.
2.Gupta P.K. and Hira D.S. Problems in Operations Research , S.Chand & Co.
3. Kanti Swaroop, Gupta P.K and Manmohan , problems in operations Research,
Sultan Chand & Sons
4. Ravindran A., Phillips D.T. and Solberg J.J., Operations research, John wiley
& Sons.
5. Taha H.A. Operation Research, Macmillan pub. Company, New York.
6. Linear Programming, transporation, assignment game by Dr.Paria, Books and
Allied(p) Ltd.,1999.
GRAPH THEORY –I
Credits – 5 Instructional hours : 6
Graphs, subgraphs, degree of a vertex, isomorphism of graphs, independent sets
and coverings, intersection graphs and line graphs, adjacency and incidence
matrices, operations on graphs, degree sequences and graphic sequences –
simple problems.
Connectedness, walks, trails,paths, components, bridge, block, connectivity – simple problems. Eulerian and Hamiltonian graphs, trees – simple problems
Content and treatment as in Invitation to Graph Theory by S.Arumugam and S.Ramachandran, New Gamma Publishing House, Palayamkottai
Chapters 1, 2(omit 2.5),3,4,5,6.
Reference books:
1. A first book at graph theory by John Clark and Derek Allan Holton, Allied publishers
2. Graph Theory by S.Kumaravelu and susheela Kumaravelu,Publishers authors C/o 182
Chidambara Nagar, Nagarkoil
SPECIAL FUNCTIONS – I
Credits – 5 Instructional hours : 6
Simultaneous linear differential equation – particular solution of variation of parameter – Numerical methods for solving ordinary differential equations – Use of Taylor series – Adams methodRungekutta method  Picards methods – Extrapolation with differences.
Series solution of differential equations – properties of power series – singular points of linear second order differential equation – the method of Frobenius – Bessel Functions – Properties of Bessel Functions – Differential equation satisfied by Bessel Functions – Legender Functions.
Book for study:
Advanced Calculus of Application, F. B. Hilder brandt
(Section: 1.8, 1.9,3.1 to 3.4,4.1 to 4.8, 4.10, 4.12)
Book for reference:

Differential Equations and Calculus of Variations – L. Els golts

Differential Equations – Diwan and Agashe.

Numerical Analysis – Sea borough
^{ }ASTRONOMY – I
Credits – 5 Instructional hours : 6
Spherical trigonometry – Celestial sphere and Diurnal motion – The Earth. Zones of earth, variations of Day and night, Dip and Tuei light – Astronomical Refraction – Geocentric ParallaxKeplers laws, Newton’s deductions and Anomalies – The solar system.
Treatment and Content : “Astronomy” by S. Kumara velu and Susheela Kumaravelu.
OPERATIONS RESEARCH  II
Credits – 5 Instructional hours : 6
PERT and CPM : project network diagram – Critical path (crashing excluded) – PERT computations.
Queuing theory – Basic concepts – Steady state analysis of M/M/1 and M/M/systems with infinite and finite capacities.
Inventory models : Basic concepts  EOQ models : (a) Uniform demand rate infinite production rate with no shortages (b) Uniform demand rate Finite production rate with no shortages – Classical newspaper boy problem with discrete demand – purchase inventory model with one price break.
Game theory : Twoperson Zerosum game with saddle point – without saddle point – dominance – solving 2 x n or m x 2 game by graphical method.
Integer programming : Branch and bound method.
Books for References :

Gauss S. I., Linear Programming, Mcgrawhill Book Company.

Gupta P. K. and Hira D. S., problems in operations research, S. Chand & Co.

Kanti Swaroop, Gupta P. K. and Manmohan, Problems in Operations Research, Sultan Chand & Sons.

Ravindran A., Philips D. T. and Solberg J. J., Operations Research, John Wiley & Sons.

Taha H. A., Operations Research, Macmilliam Publishing Company, New York.
GRAPH THEORY – II
Credits – 5 Instructional hours : 6
Planarity: Definition and properties, characterization of planar graphs, colourabiliry, chromatic number and index, the five colour theorem, four colour problem, chromatic polynomials directed graphs : Definition and basic properties, paths and connectedness, digraphs and matrices, tournaments, some application connector problem, shortest path problem, one way traffic system; traveling sales man problem.
Tretement as in Invitation to Graph Theory by S. Arumugam and S. Ramachandran, Chapters 7 (omit 7.3), Chapters : 8, 9, 10.1 to 10.5.
Matching : Maximum matching, augmenting path, Bergi’s theorem, Hall’s theorem, Marriage problem, matching and covering: Kongi’s minimax theorem, odd and even components, Tuttes theorem.
Chapter 14 in Graph Theory by S. Kumaravelu and Susheela Kumaravelu.
SPECIAL FUNCTIONS – II
Credits – 5 Instructional hours : 6
Partial Differential equations – Definition and example.
Transverse vibration of a string – solution of wave equations by separation of variables – displacement expressed in Fourier series.
One dimensional heat flow – Heat equation and its solution.
Two dimensional heat flow (steady state only)
Laplace equation in two dimensions and its solutions.
Temperature distribution in rectangular plates.
Laplace’s equation in polar coordinates and its solution.
Temperature distribution in circular annulus.
Laplace transform method of solving partial differential equation.
Books for Reference:

Advanced Calculus for application – F. B. Hilder Brandt.

Differential Equations – Diwan and Agashe.

Mathematics for Engineers and Physicists –Louis Rpes

Mathematics for Engineers – Sckolnikoff.

Alaigal – T. R. Balakrishnan, Tamil Nadu Test book society.
ASTRONOMY – II
Credits – 5 Instructional hours : 6
Equation of time, seasons, calendar and conversion of time – Heliocentric parallax, Annual parallax and aberration – procession and nutation – the moonEclipsesPlanetary motion.
Treatment and Content : “Astronomy” by S. Kumaravelu & Susheela Kumaravelu.
DISCRETE MATHEMATICS
Credits – 5 Instructional hours : 6
^{ }
Integers, sets, integers, divisibility of integers, mathematical induction, representation of positive integers.
Boolean algebra and its applications.
Recurrence relation and generating functions
Introduction to graph theory.
Contents and treatment as in introduction to Discrete Mathematics, 2^{nd} edition, 2002 by M. K. Sen and B. C. Chakraborthy Books and Allied private Ltd., Kolkata.
Chapter 1, Chapter 6 (omit 6.4 and 6.6), Chapter 7 and 8.
Reference Books:

Discrete mathematics for computer scientists and mathematicians by J. L. Mertt, Abraham Kendel and T. P. Baker prenticehall, India.

Discrete mathematics for computer scientists by John TrussAddision Wesley.

Elements of Discrete Mathematics, C. L. Liu, New York McgrawHill, 1977.

Discrete mathematical structures with applications to computer science, J. T. Tremblay and R. P. Manohar, New York, Mcgrawhill, 1975.

Discrete mathematical structures, Bernard Kolman, Robert C. Busby, Shron Ross, 3^{rd} edition, 1998, Prentice hall of India, New Delhi.
ELEMENTARY NUMBER THEORY
Credits – 5 Instructional hours : 6
An introduction top the Theory of Numbers (Vth edition) by Ivan Niven, Herbert S. Zuckarman and Hugh L. Montgometry John Wiley & Sons, Inc.2001.
Chapter 1 : Divisibility
Chapter 2 : 2.1 Congruences
2.2 Solution of Congruences
2.3 Chinese Remaining Theorem
2.8 From Page 97 to 104 (cor 2.42, Th 2.43 and cor 2.44 are
omitted)
2.10 Number Theory from an Algebric view point.
2.11 Groups, rings and fields.
Chapter 3 : 3.1 Quadratic Residues
3.2 Quadratic reciprocity
3.3 The Jacobi Symbol
Chapter 4 : 4.1 Greatest Integer Function
4.2 Arithmetic function
4.3 The Mobius Inversion formula
4.5 Combinational Number Theory (4.4 is omitted)
Chapter 5 : 5.1 The equation ax+by=c
5.2 Simultaneous Linear Equations
5.3 Pythagorean Triples
5.4 Assorted examples
(only simple problem should be asked)
Books for reference:

Elementary theory of numbers, cy. Hsiung, Allied publishers, 1995.

Elementary Number Theory, Allyn and Bacon Inc., Boston, 1980.

Introduction to Analytic Number Theory, Tom. M. Apostol, Narosa Publishing House, New Delhi, 1989.
The Allied Subjects may be chosen from the following List.
List of Allied subjects.

Physics – I

Chemistry – I

Calculus of finite differences and Numerical Analysis –I

Mathematical Statistics – I

Financial Accounting  I

Physics – II (prerequisite Physics – I)

Chemistry – II (prerequisite Chemistry – I)

Calculus of finite differences and Numerical Analysis –II (prerequisite Calculus of finite differences and Numerical Analysis –I )

Mathematical Statistics – II (prerequisite Mathematical Statistics – I)

Financial Accounting – II (prerequisite Financial Accounting – I)

Cost Accounting

Management Accounting
NOTE: Syllabus for Financial Accounting – I and II can be obtained from Board of Studies for Commerc
Calculus of finite differences and Numerical Analysis – I (5 Credits )
Solutions of algebraic and transcendental equations, Bisection method, Iteration method, Regulafalsi method, NewtonRaphsons method.
Solution of Simultaneous linear equations: Guasselimination method, GuassJordan method, GuassSiedel method, Crout’s method.
Finite differences: E operators and relation between them, Differences of a polynomial, factorial polynomials, differences of zero, summation series.
Interpolation with equal intervals: Newton’s forward and backward interpolation formulae. Central differences formulaeGauss forward and backward formulae, Sterling’s formula and Bessel’s formula.
Interpolation with unequal intervals: Divided differences and Newton’s divided differences formula for interpolation and Lagrange’s formula for interpolation.
Inverse Interpolation – Lagrange’s method, Reversion of series method.
Reference Books:

Calculus of finite differences and Numerical analysis by GuptaMalik, Krishna Prakastan Mandir, Meerut.

Numerical methods in Science and Engineering by M. K. Venkataraman, National publishing house, Chennai.

Numerical Analysis by B. D. Gupta, Konark publishing.

Calculus of finite differences and Numerical Analysis by Sexena, S. Chand & Co.
Calculus of finite differences and Numerical Analysis – II (5 Credits)
Numerical differentiation: Derivatives using Newton’s forward and backward difference formulae, Derivatives using Sterling’s formula, Derivative using divided difference formula, Maxima and Minima using the above formulae.
Numerical integration: General quadrature formula, Trapezoidal rule, Simpson’s onethird rule, Simpson’s threeeighth rule, Weddle’s rule, EulerMaclaurin Summation formula, Sterling’s formula for n!.
Difference equations: Linear homogenous and nonhomogenous difference equation with constant coefficients, particular integrals for a^u x^m , x^m, sinkx, coskx.
Numerical solution of ordinary difference equations (I order only)
Taylor’s series method, Picard’s method, Euler’s method, Modified Euler’s method, Rungekutta method fourth order only, Predictorcorrector methodMilne’s method and AdamsBashforth method.
Reference Books:

Calculus of finite differences and Numerical Analysis by GuptaMalik, Krishna prakastan Mandir, Meerut.

Numerical methods in Science and Engineering by M. K. Venkataraman, National publishing house, Chennai.

Numerical Analysis by B. D. Gupta, Konark publishing.

Calculus of finite differences and Numerical Analysis by Saxena, Chand & Co.
MATHEMATICAL STATISTICS – I (4 credits)
(Theory and Practicals)
UNIT – 1 : Statistics – Definition – functions – applications – complete enumeration – sampling methods – measures of central tendency – measures of dispersion – skew nesskurtosis.
UNIT – 2 : Sample space – Events, Definition of probability (Classical, Statistical & Axiomatic ) – Addition and multiplication laws of probability – Independence – Conditional probability – Bayes theorem – simple problems.
UNIT – 3 : Random Variables (Discrete and continuous), Distribution function – Expected values & moments – Moment generating function – probability generating function – Examples. Characteristic function – Uniqueness and inversion theorems (Statements and applications only) – Cumulants, Chebychev’s inequality – Simple problems.
UNIT – 4 : Concepts of bivariate distribution – Correlation : Rank correlation coefficient – Concepts of partial and multiple correlation coefficients – Regression : Method of Least squares for fitting Linear, Quadratic and exponential curves  simple problems.
UNIT – 5 : Standard distributions – Binomial, Hyper geometric, Poission, Normal and Uniform distributions – Geometric, Exponential, Gamma and Beta distributions, Interrelationship among distributions.
Books for study and reference:

Hogg R. V. & Craig A. T. 1988) : Introduction to Mathematical Statistics, Mcmillan.

Mood A. M & Graybill F. A & Boes D. G (1974) : Introduction to theory of Statistics, Mcgraw Hill.

Snedecor G. W. & Cochran W. G (1967) : Statistical Methods, Oxford and
IBH.
MATHEMATICAL STATISTICS – II (4 credits)
(Theory and Practicals)
UNIT – 1 : Sampling Theory – sampling distributions – concept of standard errorsampling distribution based on Normal distribution : t, chisquare and F distribution.
UNIT – 2 : Point estimationconcepts of unbiasedness, consistency, efficiency and sufficiencyCramer Rao inequalitymethods of estimation : Maximum likelihood, moments and minimum chisquare and their properties. (Statement only)
UNIT – 3 : Test of Significancestandard errorlarge sample tests. Exact tests based on Normal, t, chisquare and F distributions with respect to population mean/means, proportion/proportions variances and correlation coefficient. Theory of attributes – tests of independence of attributes based on contingency tables – goodness of fit tests based on Chisquare.
UNIT – 4 : Analysis of variance : One way, twoway classification – Concepts and problems, interval estimation – confidence intervals for population mean/means, proportion/proportions and variances based on Normal, t, chisquare and F.
UNIT – 5 : Tests of hypothesis : Type I and Type II errors – power of testNeyman Pearson Lemma – Likelihood ratio tests – concepts of most powerful test – (statements and results only) simple problems
.
Books for study and reference:

Hogg R. V. & Craig A. T (1998) : Introduction to Mathematical Statistics, Mcmillan.

Mood A. M & Graybill F. A & Boes D. G (1974) : Introduction to theory of Statistics.

Snedecor G. W & Cochran W. G : Statistical Methods, Oxford and IBH.

Hoel P. G. (1971) : Introduction to Mathematical Statistics, Wiley.

Wilks S. S : Elementary Statistical Analysis, Oxford and IBH.
^{ }
^{
} Practicals Based on Mathematical Statistics I and II (credits)

Construction of univariate and bivariate frequency distributions with
samples of size not exceeding 200.

Diagramatic and Graphical Representation of data and frequency
distribution.

Cumulative frequency distributionOgivesLorenz curve.

Measure of location and dispersion(absolute and relative), Skewness and
Kurtosis.

Numerical Problem involving derivation of marginal and conditional
distributions and related measures of Moments.

Fitting of Binomial, Poisson and Normal distributions and tests of
goodness of fit.

Curve fitting by the method of least squares.
(i) y=ax+b ;(ii) y=ax^2 +bx+c ;(iii) y=ae^bx ;(iv) y=ax^b

Computation of correlation coefficients and regression lines for raw and
grouped data. Rank correlation coefficient.

Asymptotic and exact test of significance with regard to population
mean, proportion, variance and coefficient of correlation.

Test for independence of attributes based on contingency table.

Confidence Interval based on Normal,t,Chisquare statistics.
NOTE:
Use of scientific calculator may be permitted for Mathematical Statistics Practical Examination.
Statistical and Mathematical tables are to be provided to students at the examination hall.
12. B.Sc. DEGREE COURSE IN MICROBIOLOGY
SYLLABUS
SEMESTER  III
PAPER V  MOLECULAR BIOLOGY
UNIT I
DNA structure, various forms (A, B, Z & H), Stability of nucleic acid structures; prokaryotic and eukaryotic genome organizations.
UNIT II
DNA replication, repair and recombination: Unit of replication, enzymes involved, replication origin and replication fork, fidelity of replication, extrachromosomal replicons, DNA damage and repair mechanisms.
UNIT III
RNA synthesis and processing: Transcription factors and machinery, formation of initiation complex, transcription activators and repressors, RNA polymerases, capping, elongation and termination, RNA processing, RNA editing, splicing, polyadenylation, structure and function of different types of RNA, RNA transport.
UNIT IV
Protein synthesis and processing: Ribosome, formation of initiation complex, initiation factors and their regulation, elongation and elongation factors, termination, genetic code, aminoacylation of tRNA, tRNAidentity, aminoacyl tRNA synthetase, translational proofreading, translational inhibitors, posttranslational modification of proteins.
UNIT V
Control of gene expression at transcription and translation level: Regulation of phages, viruses, prokaryotic and eukaryotic gene expression, role of chromatinin regulating gene expression and gene silencing.
PAPER VI  MAJOR PRACTICAL III
UNIT I
Estimation of DNA by diphenylamine method. Estimation of RNA by orcinol method.
UNIT II
Isolation of Plasmid DNA by Alkalysis method.
Isolation of Chromosomal DNA from Eukaryotic cells. Eg. Leaves, Human Lymphocytes.
UNIT III
Isolation of RNA from yeast.
Isolation of antibiotic resistant auxotrophic mutants.
UNIT IV
Preparation of competent cells.
UNIT V
Transformation of E.coli.
ALLIED SUBJECT II
PAPER I  BIOCHEMISTRY
UNIT I
Organization of life. Importance of water, Cell structure and organelles. Composition, Structure and function of biomolecules: Carbohydrates, Lipids, Proteins and Nucleic acids and Vitamins.
UNIT II
Principles and applications of Gelfiltration, Ion  Exchange and Affinity Chromatography; Thin Layer and Gas Chromatography; High Pressure Liquid (HPLC) Chromatography; Electrophoresis and Electrofocussing; Ultracentrifugation (velocity and buoyant density). Spectroscopic methods: UV visible and fluorescence.
UNIT III
Proteins structure, folding and function. Myoglobin, Hemoglobin, Lysozme, Ribonuclease A, Carboxypeptidase and Chymotrypsin. Principles of catalysis, enzymes and enzyme kinetics, enzyme regulation, mechanism of enzyme catalysis, isozymes.
UNIT IV
Metabolism and bioenergitics. Generation and utilization of ATP. Photo synthesis. Major metabolic pathways and their regulation.
UNIT V
Biological membrances. Transport across membranes. Signal transduction hormones and neurotransmitters.
ALLIED SUBJECT II
PAPER II  BIOCHEMISTRY PRACTICAL
UNIT I
Estimation of monosaccharides Glucose(Benedict’s) fructose, mannose. Estimation of disaccharides lactose, sucrose.
UNIT II
Qualitative analysis of starch. Qualitative analysis of arginine, cystenine, trytophan, tyrosine.
UNIT III
Estimation of chloride by Mohr’s method. Estimation of glycine by formal titration method.
UNIT IV
Estimation of iron using potassium permanganate as link solution and ferrous ammonium sulphate as standard.
UNIT V
Estimation of ascoribic acid using 2,6dichlorophenol indophenol as link solution Estimation of protein by Biuret method.
Semester  IV
paper VII  Soil AND AGRICULTURAL MICROBIOLOGY
UNIT I
Soil microbiology  quantitative and qualitative micro flora of different soilsrole of microbes in soil fertilitytests for soil fertilitysoil structure, soil formationcharacterization of soil types and importance.
UNIT II
Biogeochemical cyclesrole of micro organisms in carbon, phosphorus. sulphur and iron cycles. Methods of studying ecology of soil micro organismsmicrobial gas metabolismcarbon dioxide, hydrogen, and methane and hydrogen sulphide.
UNIT III
Microbial interactions between microorganisms, plant and soil. Rhizoplane, rhizosphere, phyllosphere, spermosphere, mycorrhizae. Microbial association with insectsgut micro flora  symbiosis between microbes and insects; organic matter decomposition.
UNIT IV
Nitrogen cycle; ammonification nitrification denitrification nitrogen fixation Biofertilizers (bacterial, cyanobacteria and azolla) and crop responsebiopesticides (bacterial, viral and fungal) saprophytes for pathogen suppression.
UNIT V
Principles of plant infection and defense mechanisms. Symptoms, Etiology, Epidemiology and Management of the following plant diseases: Mosaic disease of tobacco; Bunchy top of banana; Leaf roll of potato; Bacterial blight of paddy; Angular leaf spot of cotton, Late blight of potato; Damping off of tobacco, downy mildew of bajra; Powdery mildew of cucurbits; Head smut of sorghum; Leaf rust of coffee; Blight of maize/sorghum; Leafspot of paddy, Grassy shoot of sugar cane; Root knot of mulberry.
Paper VIII  MAJOR PRACTICAL IV
UNIT I
Methods to study soil microorganisms  Isolation and enumeration of Bacteria, Fungi, Bacteriophages, Algae, Protozoa etc., Microbiological test for fertility  Bacterial and Fungal
UNIT II
Microbiological demonstration of soil enzymes – Amylase, Protease, Lipase, Gelatinase etc.,
UNIT III
Isolation and identification of root nodule bacteria Rhizobium(symbiotic), demonstration of rhizobium in the root nodule(CS of root nodule) Isolation and identification of Azotobacter (Asymbiotic).
UNIT IV
Isolation and identification of nitrogen fixing CyanobacteriaAnabaena, Nostoc etc., Demonstration of Azolla Demonstration of antagonistic activity –bacterial and fungal.
UNIT V
Study of the following discases: Tobacco mosaic; Bacterial blight of paddy; Downy mildew of bajra; Powdery mildew of cucurbits; Head smut of sorghum; Leaf rust of coffee; Leaf spot of paddy, Red rot of sugar cane, Root knot of mulberry.
ALLIED SUBJECT II
PAPER III  BIOSTATISTICS
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