Syllabus and Scheme of Examination

for

B.Sc. (Mathematics Honours)

Fakir Mohan University, Balasore

Under

Choice Based Credit System (CBCS)

(Applicable from the Academic Session 2016-17 onwards)

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Semester

Core

Course(14)

100X14=1400

Ability Enhancement

Compulsory Course(AECC)(2)

50X2=100

Skill Enhancement

Course(SEC)(2)

50X2=100

Elective:

Discipline Specific DSC

Course(4)

(related to core subject)

100X4=400

Generic Elective(GE)(4)

(Not related to core courses;

2 different subjects of 2 papers

each)

100X4=400

C1

C2

C3

C4

C5

C6

C7

C8

C9

C10

C11 DSC-1

C12 DSC-2

C13 DSC-3

C14 DSC-4-Project work

CBCS (B.Sc. Honours) from 2016-17

GE-2B (Paper-II)

AECC-II

Environmental Science

50 marks

GE-1B (Paper-II)

SEC-1

Soft Skill

50 marks

GE-2A (Paper-I)

Total:1400+100+100+400+400=2400 marks

VI

III

IV

AECC-I

(English Communication/MIL)

50 marks

SEC-2

Course specific

skill course

50 marks

I

II

V

GE-1A (Paper-I)

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Core Courses (C)

(Credit: 06 each, Total Marks: 100)

C-A to C-D 1. C-1A: Calculus and Analytical Solid Geometry

2. C-1B: Differential Equations

3. C-1C: Real Analysis

4. C-1D: Algebra

Discipline Specific Elective Courses (DSE)

(Credit: 06 each, Total Marks: 100)

DSE-A and DSE-B

DSE-A (Any one of the following)

1. Linear Algebra

2. Mechanics

3. Matrices

DSE-B (Any one of the following)

1. Numerical Methods

2. Complex Analysis

3. Linear Programming

Skill Enhancement Courses (SEC)

(Credit:02, Total Marks: 50)

SEC-I to SEC-IV

SEC-I

1. Communicative English and Writing Skill-Compulsory.

SEC-II (Any one of the following)

1. Vector Calculus

2. Discrete Mathematics

3. Boolean Algebra

SEC-III (Any one of the following)

1. Probability and Statistics

2. Mathematical Modelling

3. Financial Mathematics

SEC-IV (Any one of the following)

1. Logic and Sets

2. Transportation and Game Theory

3. Number Theory

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COURSE STRUCTURE

B.A./ B.Sc.(Honours)-Mathematics Core Courses:6 credit each, Max. Marks:100

Ability Enhancement Compulsory Courses (AECC):2 credit each, Max. Marks:50

Skill Enhancement Courses (SEC):2 credit each, Max. Marks:50

Discipline Specific Elective (DSE):6 credit each, Max. Marks:100

Generic Electives (GE):6 credit each, Max. Marks:100

For papers with practical component: Theory: 75(Mid-Sem:15+End Sem: 60)Marks,

Practical(End Sem):25 Marks.

For papers with no practical/practical component: Theory 100(Mid-Sem.:20+End

Sem.:80) Marks

For papers with 50 Marks: Mid-Sem.:10 Marks + End Sem.:40 Marks.

Semester-I

Core Courses

(C)

Ability

Enhancement

Compulsory

Courses

(AECC)

Skill

Enhancement

Courses

(SEC)

Discipline Specific

Elective

(DSE)

Generic Electives

(GE)

C-1.1: Calculus-I(P)

C-1.2: Algebra-I

MIL/Alt. English X X GE-I

Semester-II

Core Courses

(C)

Ability

Enhancement

Compulsory Courses

(AECC)

Skill

Enhancement

Courses

(SEC)

Discipline

Specific

Elective

(DSE)

Generic

Electives

(GE)

C-2.1: Real Analysis

(Analysis-I)

C-2.2: Differential Equations(P)

Environmental

Science

X GE-II

Semester-III

Core Courses

(C)

Ability

Enhancement

Compulsory Courses

(AECC)

Skill

Enhancement

Courses

(SEC)

Discipline

Specific

Elective

(DSE)

Generic

Electives

(GE)

C-3.1: Theory of Real Functions

(Analysis-II)

C-3.2: Group Theory

(Algebra-II)

C-3.3: Partial Differential Equations and

Systems of Ordinary Differential Equations

(P)

X SEC-I

X GE-III

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Semester-IV

Core Courses

(C)

Ability

Enhancement

Compulsory Courses

(AECC)

Skill

Enhancement

Courses

(SEC)

Discipline

Specific

Elective

(DSE)

Generic

Electives

(GE)

C-4.1: Numerical Methods(P)

C-4.2: Riemann Integration and Series of

Functions

(Analysis-III)

C-4.3: Ring Theory and Linear Algebra-I

(Algebra-III)

X SEC-II

X GE-IV

Semester-V Core Courses

(C)

Ability

Enhancement

Compulsory Courses

(AECC)

Skill

Enhancement

Courses

(SEC)

Discipline

Specific

Elective

(DSE)

Generic

Electives

(GE)

C-5.1: Multivariate Calculus

(Calculus-II)

C-5.2: Probability and Statistics

X X DSE-I

DSE-II

X

Semester-VI

Core Courses

(C)

Ability

Enhancement

Compulsory Courses

(AECC)

Skill

Enhancement

Courses

(SEC)

Discipline

Specific

Elective

(DSE)

Generic

Electives

(GE)

C-6.1: Metric Spaces and Complex Analysis

(Analysis-IV)

C-6.2: Linear Programming

X X DSE-III

DSE-IV

X

Core Papers(C)

(Credit:06 each, 04 Theory +02 Practical, Total Marks:100)

1. MTH-I: Calculus-I(P)

2. MTH-II: Algebra-I 3. MTH-III: Real Analysis(Analysis-I)

4. MTH-IV: Differential Equations (P) 5. MTH-V: Theory of Real Functions(Analysis-II)

6. MTH-VI: Group Theory (Algebra-II)

7. MTH-VII: Partial Differential Equations and Systems of Ordinary Differential Equations (P)

8. MTH-VIII: Numerical Methods (P)

9. MTH-IX: Riemann Integration and Series of Functions (Analysis-III)

10. MTH-X: Ring Theory and Linear Algebra-I(Algebra-III)

11. MTH-XI: Multivariate Calculus(Calculus-II)

12. MTH-XII: Probability and Statistics

13. MTH-XIII: Metric Spaces & Complex Analysis(Analysis-IV)

14. MTH-XIV: Linear Programming

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Discipline Specific Elective Papers (DSE)

(Credit: 06 each, Total Marks;100), 04 Papers, DSE-I to IV.

DSE-I

Programming in C++(P)

DSE-II

(Any one of the following)

1. Discrete Mathematics

2. Boolean Algebra and Automata Theory

3. Mathematical Modelling

4. Number Theory

DSE-III

(Any one of the following)

1. Differential Geometry

2. Mechanics

3. Mathematical Finance

4. Ring Theory and Linear Algebra-II

DSE-IV

Project/Dissertation

Project work:75 Marks,+Viva-Voce:25 Marks.

Skill Enhancement Courses (SEC)

(Credit: 02 each, Total Marks:50):SEC-I to SEC-II

1. Communicative English & English Writing Skill (Compulsory)

2. Any one of the following:

(a) Computer Graphics

(b) Logic and Sets

(c) Combinatorial Mathematics

(d) Information Security

Generic Electives/Interdisciplinary (4 papers)

Two papers each from two allied disciplines)

GE-I to GE-IV(Credit: 06 each)

Generic Electives Courses (GE) (Minor-Mathematics) for

AlliedDisciplines:(Credit: 06 each, Total Marks:100)

1. Calculus and Ordinary Differential Equations

2. Linear Algebra and Abstract Algebra

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CORE COURSES

B.Sc. (Honours)-Mathematics

Semester-I

MATH.U-C-1.1: Calculus-I

(Total Marks: 100)

Part-I (Marks: 75)

(Theory: 60Marks+Mid-Sem: 15Marks)

Unit-I

Hyperbolic functions, higher order derivatives, Leibnizruleand its applications to problems of the type eax+bsinx, eax+bcosx, (ax+b)nsinx ,(ax+b)ncosx, concavity and inflection points, asymptotes Curve tracing in Cartesian coordinates, tracing in polar coordinate sofstandard curves, LHospitalsrule, applications in business, economics and life sciences, Unit-II

Reduction for mulae, Derivations and illustrations of reduction formulae of the type ∫ sinnxdx, ∫ cosnxdx,∫ tannxdx,∫ secnxdx,∫(logx)ndx,∫sinnxcosnxdx Volumes by slicing, disks and washers methods, volumes by cylindrical shells, parametric equations, parameterizing a curve, arc length, arc length of parametric curves, area of surface of revolution. Unit-III Techniques of sketching conics,reflection properties of conics, rotation of axe sand second degree equations, classification in to conicsusing the discriminant, polare quations of conics. Sphere, Cone, Cylinder, Central Conicoids. Unit-IV

Triple product, introduction to vector functions, operations with vector-valued functions, limits and

Continuity of vector functions, differentiation and integration of vector functions, tangent and normal Components of acceleration. Part-II (Practical,Marks:25)

List of Practicals (Using any software)

Practical/ Lab work to be performed on a Computer.

1. Plotting the graph soft the function seax+b,log(ax+b),1/(ax+b),sin(ax+b),cos(ax+b),|ax+b| and to illustrate the effect of a and both the graph. 2. Plotting the graphs of the polynomialofdegree 4 and 5, the derivative graph, the second derivative graph and comparing them. 3. Sketching parametric curves (Eg. Trochoid, cycloid, epicycloids, hypocycloid). 4. Tracing of conics in cartesian coordinates/ polar coordinates. 5. Sketching ellipsoid, hyper boloid of one and two sheets, ellipticcone, elliptic, paraboloid, hyperbolic paraboloid using Cartesian coordinates. 6. Matrix operation (addition, multiplication, inverse, transpose). Books Recommended:

1. M. J. Strauss, G. L.BradleyandK.J.Smith,Calculus,3rd Ed., Dorling Kindersley (India) P. Ltd. (Pearson Education), Delhi, 2007.Chapters:4 (4.3,4.4,4.5 & 4.7), 9(9.4),

10(10.1-10.4).

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2. H.Anton,I.BivensandS.Davis,Calculus,7thEd.,JohnWileyandSons(Asia)P.Ltd., Singapore, 2002.Chapters:6,(6.2-6.5),7(7.8),8(8.2-8.3,Pages:532-

538),11(11.1),13(13.5) 3. Analytical Geometry of Quadratic Surfaces, B.P.Acharya and D. C. Sahu, Kalyani

Publishers, New Delhi, Ludhiana. 4. Elements of vector calculus by Sarana & Prasad+878

Books for Reference:

1. G.B.ThomasandR.L.Finney, Calculus,9th Ed., Pearson Education, Delhi, 2005.

2. R. Courantand F. John, Introduction to Calculus and Analysis (Volumes I & II), Springer-Verlag, New York, Inc., 1989.

3. Text Book of Calculus, Part-II- Shantinarayan, S.Chand &Co., 4. Text Book of Calculus, Part-III-Shantinarayan, S.Chand &Co., 5. Shanti Narayan and P.K.Mittal-Analytical Solid Geometry,

S.Chand&CompanyPvt.Ltd.,New Delhi.

MATHMATICS- SEMESTER- 1

C-1.2: Algebra-I

Total Marks: 100

Theory: 80 Marks + Mid- Sem: 20Marks

5Lectures, 1 Tutorial (perweekperstudent)

Unit-I

Polar representation of complex numbers, n-throots of unity, DeMoivres the oremforration alindices

and it sapplications.

Unit-II

Equivalence relations, Functions, Composition of functions, Invertible functions, One to one

correspondence and cardinality of a set, Well- ordering property of positive integers, Division

algorithm, Divisibility and Euclidean algorithm, Congruence relation between integers, Principles of

Mathematical Induction, statement of Fundamental the oremofArithmetic.

Unit-III

Systems of linear equations, row reduction and echelon forms, vector equations, the matrix equation

Ax=b, solution sets of linear systems, applications of linear systems, linear independence.

Unit-IV

Introduction to linear transformations, matrix of a linear transformation, inverse of a matrix,

characterizations of invertible matrices

Sub spaces of Rn, dimension of sub spaces of Rn and rank of a matrix, Eigenvalues, EigenVectors and

Characteristic Equation of a matrix.

BooksRecommended:

1. L.V.Ahlfors,ComplexAnalysis,McGraw-Hill(InternationalStudentEdn.)

2. TituAndreescuandDorinAndrica,ComplexNumbersfromAtoZ,Birkhauser,2006.Chapter:2

3. Edgar G. Goodaire and Michael M. Parmenter, Discrete Mathematics with Graph Theory,

3rdEd., Pearson Education (Singapore) P. Ltd., Indian Reprint, 2005. Chapters:2 (2.4), 3,4 (4.1-

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4.1.6,4.2-4.2.11,4.4(4.1-4.4.8),4.3-4.3.9,5(5.1-5.1.4).

4. David C.Lay, Linear Algebraand its Applications, 3rdEd., Pearson Education Asia, Indian

Reprint

5. V. Krishanmurthy, V. P. Mainra & J. B. Arara – An Introduction of Linear Algebra Chapters:

1(1.1-1.9), 2(2.1-2.3,2.8,2.9), 5(5.1,5.2)

Semester-II

C-2.1:RealAnalysis(Analysis-I)

TotalMarks:100

Theory:80Marks+Mid-Sem:20Marks

5Lectures,1Tutorial(perweekperstudent)

Unit-I

ReviewofAlgebraicandOrderPropertiesofR,NeighborhoodofapointinR,Ideaofcountablesets,unco

untablesetsanduncountabilityofR.Boundedabovesets,Boundedbelowsets,BoundedSets,Unbound

edsets,SupremaandInfima.

Unit-II

TheCompletenessPropertyofR,TheArchimedeanProperty,DensityofRational(andIrrational)num

bersinR,Intervals.Limitpointsofaset,Isolatedpoints,IllustrationsofBolzano-

Weierstrasstheoremforsets.

Unit-III

Sequences,Boundedsequence,Convergentsequence,Limitofasequence.Limit Theorems,

MonotoneSequences,MonotoneConvergenceTheorem.Subsequences,DivergenceCriteria,Monoto

neSubsequenceTheorem(statementonly),BolzanoWeierstrassTheoremforSequences.Cauchysequ

ence,CauchysConvergenceCriterion.

Unit-IV

Infiniteseries,convergenceanddivergenceofinfiniteseries,CauchyCriterion,Testsforconvergence:Co

mparison test, Limit Comparison test, Ratio Test

Unit-V

Cauchys n-

throottest,Integraltest,Alternatingseries,Leibniztest,AbsoluteandConditionalconvergence.

BookRecommended:

1.G.DasandS.Pattanayak,FundamentalsofMathematicsAnalysis,TMHPub-

lishingCo.,Chapters:2(2.1to2.4,2.5to2.7),3(3.1-3.5),4(4.1to4.7,4.10,4.11,4.12,4.13).

BooksforReferences:

9 | P a g e

1.R.G.BartleandD.R.Sherbert,IntroductiontoRealAnalysis,3rdEd.,JohnWileyandSons(Asia)Pvt.

Ltd., Singapore, 2002.

2.GeraldG.Bilodeau , Paul R.Thie,G.E.Keough,AnIntroductiontoAnalysis,2nd

Ed.,Jones&Bartlett,2010.

3.BrianS.Thomson,Andrew.M.BrucknerandJudithB.Bruckner,ElementaryRealAnalysis,Prentice

Hall,2001.

4.S.K.Berberian,AFirstCourseinRealAnalysis,SpringerVerlag,NewYork,1994.

5.S.C.MallikandS.Arora-MathematicalAnalysis,NewAgeInternationalPublications.

6.D.SmasundaramandB.Choudhury-

AFirstCourseinMathematicalAnalysis,NarosaPublishingHouse.

7.S.L.GuptaandNishaRani-RealAnalysis,VikasPublishingHousePvt.Ltd.,NewDelhi.

8. R.B. Dash & D.D. Dalai – A Course on Mathematical analysis, Kalyani Publisher

C-2.2:DifferentialEquations

(TotalMarks:100)

Part-I(Marks:75)

Theory:60Marks+Mid-Sem:15Marks

04Lectures(perweekperstudent)

Unit-I

Differentialequationsandmathematicalmodels.FirstorderandfirstdegreeODE(variablesseparable,

homogeneous, exact,andlinear).Equationsoffirst

orderbutofhigherdegree.Applicationsoffirstorderdifferentialequations(Growth,DecayandChemical

Reactions,Heatflow,Oxygendebt,Economics).

Unit-II

Secondorderlinearequations(homogeneousandnon-

homogeneous)withconstantcoefficients,second

orderequationswithvariablecoefficients,variationofparameters,methodofundeterminedcoefficients

Unit-III

Equationsreducibletolinearequationswithconstantcoefficients,Euler’sequation.Applicationsofseco

ndorderdifferentialequations.

Unit-IV

Powerseriessolutionsofsecondorderdifferentialequations.

Unit-V

Laplacetransformsanditsapplicationstosolutionsofdifferentialequations.

Part-II(Practical:Marks:25)

ListofPracticals(UsinganySoftware)

Practical/LabworktobeperformedonaComputer.

10 | P a g e

1. Plotting of second order solution offamily ofdifferentialequations.

2. Growthmodel(exponentialcaseonly).

3. Decaymodel(exponentialcaseonly).

4. Oxygendebtmodel.

5. Economicmodel.

BookRecommended:

1.J.SinhaRoyandS.Padhy,ACourseofOrdinaryandPartialDifferentialEquations,KalyaniPublisher

s,NewDelhi.Chapters:1,2(2.1to2.7),3,4(4.1to4.7),5,7(7.1-

7.4),9(9.1,9.2,9.3,9.4,9.5,9.10,9.11,9.13).

BooksforReferences:

1.MartinBraun,DifferentialEquationsandtheirApplications,SpringerInternational.

2.M.D.Raisinghania-AdvancedDifferentialEquations,S.Chand &CompanyLtd.,NewDelhi.

3.G.DennisZill-AFirstCourseinDifferentialEquationswithModellingApplications,Cengage

Learning India Pvt.Ltd.

4.S.L.Ross,DifferentialEquations,JohnWiley&Sons,India,2004

Semester-III

C-3.1:TheoryofRealFunctions(Analysis-II)

TotalMarks:100

Theory:80Marks+Mid-Sem:20Marks

5Lectures,1Tutorial(perweekperstudent)

Unit-I

Limitsoffunctions(Ɛ -δapproach),sequentialcriterionforlimits,divergencecriteria.Limit theorems,

onesidedlimits.Infinitelimitsandlimitsatinfinity.Continuousfunctions,sequentialcriterionforcontin

uity and discontinuity.

Unit-II

Algebraofcontinuousfunctions.Continuousfunctionsonaninterval,intermediatevaluetheorem,lo

cationofrootstheorem,preservationofintervals theorem.Uniformcontinuity,non-

uniformcontinuitycriteria,uniformcontinuitytheorem.

Unit-III

Differentiabilityofafunctionatapointandinaninterval,Caratheodorystheorem,algebraofdifferentiabl

efunctions.

Relativeextrema,interiorextremumtheorem.Rollestheorem,Meanvaluetheorem,intermediatevalue

propertyofderivatives.

Unit-IV

Darbouxstheorem.Applicationsofmeanvaluetheoremtoinequalitiesandapproximation of

polynomials, Taylors theorem to inequalities.

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Unit-V

Cauchysmeanvaluetheorem.TaylorstheoremwithLagrangesformofremainder,Taylorstheoremwi

th Cauchys form of remainder, application of Taylors theorem to convex functions, relative

extrema.TaylorsseriesandMaclaurinsseriesexpansionsofexponentialandtrigonometricfunctions,ln(

1+x),1/(ax+b)and(1+x)n.

BookRecommended:

1. G.DasandS.Pattanayak, Fundamentals of Mathematics Analysis, TMH Pub-lishing

Co.,Chapters:6(6.1-6.8),7(7.1-7.7),

2. R.B Dash & D.K Dalai – A Course on Mathematical Analysis, Kalyani Publisher

BooksforReferences:

1.R.BartleandD.R.Sherbert,IntroductiontoRealAnalysis,JohnWileyandSons,2003.

2.K.A.Ross,ElementaryAnalysis:TheTheoryofCalculus,Springer,2004.

3.A.Mattuck,IntroductiontoAnalysis,PrenticeHall,1999.

4.S.R.GhorpadeandB.V.Limaye,ACourseinCalculusandRealAnalysis,Springer,2006.

C-3.2:GroupTheory(Algebra-II)

TotalMarks:100

Theory:80Marks+Mid-Sem:20Marks

5Lectures,1Tutorial(perweekperstudent)

Unit-I

Symmetriesofasquare,Dihedralgroups,definitionandexamplesofgroupsincludingpermutationgroup

sandquaterniongroups(illustrationthroughmatrices),elementarypropertiesofgroups.Subgroupsan

dexamplesofsubgroups

Unit-II

Centralizer,normalizer,centerofagroup,productoftwosubgroups,

Propertiesofcyclicgroups,classificationofsubgroupsofcyclicgroups.

Unit-III

Cyclenotationforpermutations, properties of permutations, even and odd permutations,

alternating group, properties of cosets,

LagrangestheoremandconsequencesincludingFermatsLittletheorem.

Unit-IV

Externaldirectproductofafinitenumberofgroups,normalsubgroups,factorgroups,Cauchystheoremf

orfiniteabeliangroups.

Unit-V

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Grouphomomorphisms,propertiesofhomomorphisms,Cayleystheorem,propertiesofisomorphisms,F

irst,SecondandThirdisomorphismtheorems.

BookRecommended:

1.JosephA.Gallian,ContemporaryAbstractAlgebra(4thEdn.),NarosaPublishingHouse,NewDelh

i.

BooksforReferences:

1.JohnB.Fraleigh, A First Course in Abstract Algebra, 7th Ed., Pearson, 2002.

2.M.Artin, Abstract Algebra, 2nd Ed., Pearson, 2011.

3.JosephJ.Rotman, AnIntroductiontotheTheoryofGroups,4thEd.,SpringerVerlag,1995.

4.I.N.Herstein, Topics in Algebra, Wiley Eastern Limited, India, 1975.

Ch 2 (2.1 to 2.7, 2.9,2.10,2.13)

C-3.3:PartialDifferentialEquationsandSystemsofOrdinaryDifferentialEquations

(TotalMarks:100)

Part-I(Marks:75)

Theory:60Marks+Mid-Sem:15Marks

04Lectures(perweekperstudent)

Unit-I

Systemsoflineardifferentialequations,typesoflinearsystems,differentialoperators,anoperatormetho

dforlinearsystemswithconstantcoefficients,BasicTheoryoflinearsystemsinnormalform,homoge

neous linear systems with constant coefficients(Two Equations in two unknown functions).

Unit-II

Simultaneouslinearfirstorderequationsinthreevariables,methodsofsolution,Pfaffiandifferentiale

quations,methodsofsolutionsofPfaffiandifferentialequationsinthreevariables.

Unit-III

Formation of first order partial differential equations, Linear and non-linear partial differential

equationsoffirstorder,specialtypesoffirst-

orderequations,Solutionsofpartialdifferentialequationsoffirstordersatisfyinggivenconditions.

Unit-IV

Linearpartialdifferentialequationswithconstantcoefficients,Equationsreducibletolinearpartialdiff

erentialequationswithconstantcoefficients,Partialdifferentialequationswithvariablecoefficients,S

eparationofvariables,Non-linearequationofthesecondorder.

Unit-IV

Laplaceequation,SolutionofLaplaceequationbyseparationofvariables,Onedimensionalwaveequatio

13 | P a g e

n, Solution of the wave equation(method of separation of variables), Diffusion equation,

Solution ofone-dimensionaldiffusionequation,methodofseparationofvariables.

Part-II(Practical:Marks:25)

ListofPracticals(UsinganySoftware)

Practical/LabworktobeperformedonaComputer.

1.Tofindthegeneralsolutionofthenon-homogeneoussystemoftheform:

dxdy

dtdt

withgivenconditions.

2.PlottingtheintegralsurfacesofagivenfirstorderPDEwithinitialdata.

3.Solutionofwaveequation-c2=0 for the following associated conditions:

(a)u(x,0)=φ(x),ut(x,0)=ψ(x),x ∈R,t >0.(b)u(x,0)=φ(x),ut(x,0)=ψ(x),ux(0,t)= 0,x∈(0,∞),

t>0.(c)u(x,0)=φ(x),ut(x,0)=ψ(x),u(0,t)=0,x∈(0,∞),

t>0.(d)u(x,0)=φ(x),ut(x,0)=ψ(x),u(0,t)=0,u(1,t)=0,0<x<l,t>0.

4.Solutionofwaveequation-k2=0 for the following associated conditions:

(a)u(x,0)=φ(x),u(0,t)=a,u(l,t)=b,0<x<l,t>0.

(b) u(x,0)=φ(x),x ∈R,0<t<T.

(c) u(x,0)=φ(x),u(0,t)=a,x ∈(0,∞),t ≥0.

BookRecommended:

1.J.SinhaRoyandS.Padhy,ACourseonOrdinaryandPartialDifferentialEquations,Kalyani

Publishers,NewDelhi,Ludhiana,2012.

Chapters:11,12,13(13.1-13.7),15(15.1,15.5),16(16.1,16.1.1), 17(17.1, 17.2, 17.3).

Ch. 8 (8.1 to 8.4)

BooksforReferences:

1.Tyn Myint-UandLokenathDebnath,LinearPartialDifferentialEquationsforScientistsandEn-

gineers, 4th edition, Springer, Indian reprint, 2006.

2.S.L.Ross,Differentialequations,3rdEd.,JohnWileyandSons,India,2004.

Semester-IV

C-4.1:NumericalMethods

(TotalMarks:100)

Part-I(Marks:75)

=a1x+b1y+f1(t),=a2x+b2y+f2(t)

∂ 2u∂ 2u

∂t2 ∂x2

∂u∂ 2u

∂t∂x2

14 | P a g e

Theory:60Marks+Mid-Sem:15Marks

04Lectures(perweekperstudent) (Using Scientific Calculator)

Unit-I

Algorithms,Convergence,Errors:Relative,Absolute,Roundoff,Truncation.TranscendentalandPoly

nomialequations:Bisectionmethod,Newtonsmethod,Secantmethod.Rateofconvergenceofthesem

ethods.

Unit-II

Systemoflinearalgebraicequations:GaussianEliminationandGaussJordanmethods.GaussJacobimet

hod,GaussSeidelmethodandtheirconvergenceanalysis.

Unit-III

Interpolation:LagrangeandNewtonsmethods.Errorbounds.Finitedifferenceoperators.Gregoryforwa

rdandbackwarddifference interpolation.

Unit-IV

NumericalIntegration:Trapezoidalrule,Simpsonsrule,Simpsons3/8thrule,BoolesRule.Midpointrule

,CompositeTrapezoidalrule,CompositeSimpsonsrule.

Unit-V

OrdinaryDifferentialEquations:Eulersmethod.Runge-Kutta methods of orders two and four.

Part-II(Practical:Marks:25)

ListofPracticals(UsinganySoftware)

Practical/LabworktobeperformedonaComputer.

1.Calculatethesum1/1+1/2+1/3+1/4+----------+1/N.

2.To find the absolute value of an integer.

3.Enter100integersintoanarrayandsorttheminanascendingorder.

4.BisectionMethod.

5.NewtonRaphsonMethod.

6.SecantMethod.

7.RegulaiFalsiMethod.

8.LUdecompositionMethod.

9.Gauss-JacobiMethod.

10.SORMethodorGauss-SiedelMethod.

11.Lagrange Interpolation or Newton Interpolation.

12.Simpsonsrule.

15 | P a g e

Note:ForanyoftheCAS(Computeraidedsoftware)Datatypes-

simpledatatypes,floatingdatatypes,character data types, arithmetic operators and operator

precedence, variables and constant

declarations,expressions,input/output,relationaloperators,logicaloperatorsandlogicalexpression

s,controlstatementsandloopstatements,Arraysshouldbeintroducedtothestudents.

BookRecommended:

1.B.P.AcharyaandR.N.Das,ACourseonNumericalAnalysis,KalyaniPublishers,NewDelhi,Ludhiana.

Chapters:1,2(2.1to2.4,2.6,2.8,2.9),3(3.1to3.4,3.6to3.8,3.10),4(4.1,4.2),5(5.1,5.2,5.3),6(6.1,6.

2,6.3,6.10,6.11),7(7.1,7.2,7.3,7.4&7.7).

2.BrianBradie,AFriendlyIntroductiontoNumericalAnalysis,PearsonEducation,India,2007.

BooksforReferences:

1.M.K.Jain,S.R.K.IyengarandR.K.Jain,NumericalMethodsforScientificandEngineeringComput

ation,6thEd.,NewageInternationalPublisher,India,2007.

2.C.F.GeraldandP.O.Wheatley,AppliedNumericalAnalysis,PearsonEducation,India,2008.

3.UriM.AscherandChenGreif,AFirstCourseinNumericalMethods,7thEd.,PHILearningPrivateLi

mited,2013.

4.JohnH.MathewsandKurtisD.Fink,NumericalMethodsusingMatlab,4thEd.,PHILearningPrivat

eLimited,2012.

16 | P a g e

C-4.2:RiemannIntegrationandSeriesofFunctions(Analysis-III)

TotalMarks:100

Theory:80Marks+Mid-Sem:20Marks

5Lectures,1Tutorial(perweekperstudent)

Unit-I

Riemannintegration; inequalitiesofupperandlowersums;

Riemannconditionsofintegrability.RiemannsumanddefinitionofRiemannintegralthroughRiemannsu

ms;equivalenceoftwodefinitions;Riemannintegrability of monotone and

continuousfunctions,Properties

oftheRiemannintegral;definitionandintegrabilityofpiecewisecontinuousandmonotonefunctions.I

ntermediateValuetheoremforIntegrals;FundamentaltheoremsofCalculus.

Unit-II

Improperintegrals;ConvergenceofBetaandGammafunctions.

Unit-III

Pointwiseanduniformconvergenceofsequenceoffunctions.Theorems on continuity, derivability

andintegrabilityofthelimitfunctionofasequenceoffunctions.

Unit-IV

Seriesoffunctions;Theoremsonthecontinuityandderivabilityofthesumfunctionofaseriesoffunction

s;CauchycriterionforuniformconvergenceandWeierstrassM-Test.

Unit-V

LimitsuperiorandLimitinferior.Powerseries,radiusofconvergence,CauchyHadamardTheorem,Diffe

rentiationandintegrationofpowerseries;AbelsTheorem;WeierstrassApproximationTheorem.

BookRecommended:

1. G.DasandS.Pattanayak-FundamentalsofMathematicsAnalysis, TMHPublishingCo.,

Chapters:8(8.1 to 8.6), 9 (9.1 to 9.8)

BooksforReferences:

1.K.A.Ross,ElementaryAnalysis,TheTheoryofCalculus,UndergraduateTextsinMathematics,Sprin

ger (SIE), Indian reprint, 2004.

2.R.G.BartleD.R.Sherbert,IntroductiontoRealAnalysis,3rdEd.,JohnWileyandSons(Asia)Pvt.Ltd

.,Singapore,2002.

3.CharlesG.Denlinger, Elements of Real Analysis, Jones & Bartlett (Student Edition), 2011.

4.S.C.MallikandS.Arora-Mathematical Analysis, New Age International Ltd., New Delhi.

5.Shanti Narayan and M.D.Raisinghania-ElementsofRealAnalysis,S.Chand&Co.Pvt.Ltd.

C-4.3:RingTheoryandLinearAlgebra-I(Analysis-III)

17 | P a g e

TotalMarks:100

Theory:80Marks+Mid-Sem:20Marks

5Lectures,1Tutorial(perweekperstudent)

Unit-I

Definitionandexamplesofrings,propertiesofrings,subrings,integraldomainsandfields,characteristic

ofaring.Ideal,idealgeneratedbyasubsetofaring,factorrings,operationsonideals,primeandmaximalid

eals.

Unit-II

Ringhomomorphisms,propertiesofringhomomorphisms,IsomorphismtheoremsI,IIandIII,fieldofquot

ients.

Unit-III

Vectorspaces,subspaces,algebraofsubspaces,quotientspaces,linearcombinationofvectors,linearsp

an,linearindependence,basisanddimension,dimensionofsubspaces.

Unit-IV

Lineartransformations,nullspace,range,rankand nullity of a linear transformation, matrix

representation of a linear transformation, algebra of linear transformations.

Unit-V

Isomorphisms, Isomorphism theorems,invertibility and isomorphisms, change of coordinate

matrix.

BookRecommended:

1.JosephA.Gallian,ContemporaryAbstractAlgebra(4thEdn.),NarosaPublishingHouse,NewDelhi

.Chapters:12,13,14,15.

2.StephenH.Friedberg,ArnoldJ.Insel,LawrenceE.Spence,LinearAlgebra,4thEd.,Prentice

HallofIndiaPvt.Ltd.,NewDelhi,2004.Chapters:1 (1.2-1.6), 2(2.1-2.5).

BooksforReferences:

1.JohnB.Fraleigh, A First Course in Abstract Algebra, 7th Ed., Pearson, 2002.

2.M.Artin, Abstract Algebra, 2nd Ed., Pearson, 2011.

3.S.Lang, Introduction to Linear Algebra, 2nd Ed., Springer, 2005.

4.Gilbert Strang, Linear Algebra and its Applications, Cengage Learning India Pvt.Ltd.

5.S.Kumaresan,LinearAlgebra-AGeometricApproach,PrenticeHallofIndia,1999.

6.KennethHoffman,RayAldenKunze,LinearAlgebra,2ndEd.,Prentice-HallofIndiaPvt.Ltd.,1971.

7.I.N.Herstein-Topics in Algebra, Wiley Eastern Pvt.Ltd.

18 | P a g e

Semester-V

C-5.1:MultivariateCalculus(Calculus-II)

TotalMarks:100

Theory:80Marks+Mid-Sem:20Marks

5Lectures,1Tutorial(perweekperstudent)

Unit-I

Functionsofseveralvariables,limitandcontinuityoffunctionsoftwovariablesPartialdifferentiation,t

otaldifferentiabilityanddifferentiability,sufficientconditionfordifferentiability.Chainruleforoneandt

woindependentparameters

Unit-II

Directionalderivatives,thegradient,maximalandnormalpropertyofthegradient,tangentplanes.Extr

emaoffunctionsoftwovariables,methodofLagrangemultipliers,constrained optimization

problems, Definition of vector field, divergence and curl

Unit-III

Extrema of functions of two variables, method of Lagrange multipliers, constrained

optimization problems,Definitionofvector field, divergence and curl.

Unit-IV

Doubleintegrationoverrectangularregion,doubleintegrationovernon-

rectangularregion,Doubleintegralsinpolarco-

ordinates,Tripleintegrals,Tripleintegraloveraparallelepipedandsolidregions.Volume by triple

integrals, cylindrical and spherical co-

ordinates.Changeofvariablesindoubleintegralsandtripleintegrals.

Unit-V

Line integrals, Applications of line integrals:Mass and Work.Fundamental theorem for line

integrals,conservativevectorfields,independenceofpath.Greenstheorem,surfaceintegrals,integralso

verparametricallydefinedsurfaces.Stokestheorem,TheDivergencetheorem.

BooksRecommended:

1.M.J.Strauss,G.L.BradleyandK.J.Smith,Calculus,3rd Ed., Dorling Kindersley (India)

Pvt.Ltd.(PearsonEducation),Delhi,2007.Chapters:11(11.1(Pages:541-543),11.2-

11.6,11.7(Pages:598-605),11.8(Pages:610-614)),12(12.1,-12.3,12.4(Pages:652-

660),12.5,12.6),13(13.2,13.3,13.4(Pages:712-716),13.5(Pages:723-726;729-

730),13.6(Pages:733-737),13.7(Pages:742-745)).

BooksforReference:

1.G.B.ThomasandR.L.Finney,Calculus,9thEd.,PearsonEducation,Delhi,2005.

2.E.Marsden,A.J.Tromba and A.Weinstein, Basic Multivariable Calculus, Springer (SIE),

Indianreprint, 2005.

3.SantoshK.Sengar-AdvancedCalculus,CengageLearningIndiaPvt.Ltd.

C-5.2:ProbabilityandStatistics

TotalMarks:100

Theory:80Marks+Mid-Sem:20Marks

19 | P a g e

5Lectures,1Tutorial(perweekperstudent)

Unit-I

Samplespace,probabilityaxioms,realrandomvariables(discreteandcontinuous),cumulativedistributi

onfunction,probabilitymass/densityfunctions

Unit-II

Mathematicalexpectation,moments,momentgeneratingfunction,characteristicfunction.

Unit-III

Discretedistributions:uniform,binomial,Poisson,geometric,negativebinomial,continuousdistribu

tions:uniform,normal,exponential.Jointcumulativedistributionfunctionanditsproperties,jointprob

ability density functions, marginal and conditional distributions.

Unit-IV

Expectationoffunctionoftworandomvariables,conditionalexpectations,independentrandomvari

ables, bivariate normal distribution, correlation coefficient, joint moment generating function

(jmgf) andcalculation of covariance (from jmgf), linear regression for two variables.

Unit-V

Chebyshevs inequality, statement and interpretation of (weak) law of large numbers and

strong law

oflargenumbers,CentralLimittheoremforindependentandidenticallydistributedrandomvariableswi

thfinitevariance,MarkovChains,Chapman-Kolmogorovequations,classificationofstates.

BooksRecommended:

1.RobertV.Hogg,JosephW.McKeanandAllenT.Craig,IntroductiontoMathematicalStatistics,Pears

onEducation,Asia,2007.Chapters:1(1.1,1.3.1.5-1.9),2(2.1,2.3-2.5).

2.IrwinMillerandMaryleesMiller,JohnE.Freund,MathematicalStatisticswithApplications,7thEd.,P

earsonEducation,Asia,2006.Chapters:4,5(5.1-5.5,5.7),6(6.2,6.3,6.5-6.7),14(14.1,14.2)

3.SheldonRoss,IntroductiontoProbabilityModels,9thEd.,AcademicPress,IndianReprint,2007.

Chapters:2(2.7),4(4.1-4.3).

BooksforReferences:

1.AlexanderM.Mood,FranklinA.GraybillandDuaneC.Boes,IntroductiontotheTheoryofStatistics,3

rdEd.,TataMcGraw-Hill,Reprint2007.

2.S.C.GuptaandV.K.Kapoor-Fundamentals of Mathematical Statistics,

S.ChandandCompanyPvt.Ltd.,NewDelhi.

3.S.Ross-AFirstCourseinProbability,PearsonEducation.

Semester-VI

C-6.1:MetricSpacesandComplexAnalysis(Analysis-IV)

TotalMarks:100

20 | P a g e

Theory:80Marks+Mid-Sem:20Marks

5Lectures,1Tutorial(perweekperstudent)

Unit-I

Metricspaces:definitionandexamples.Sequencesinmetricspaces,Cauchysequences.CompleteMetric

Spaces.Openandclosedballs,neighbourhood,openset,interiorofaset.Limitpointofaset,closedset,di

ameterofaset,Cantorstheorem.

Unit-II

Subspaces,densesets,separablespaces.Continuousmappings, sequential criterion and other

characterizations of continuity.Uniformcontinuity.Homeomorphism, Contraction mappings,

Banach Fixed point Theorem.Connectedness,connectedsubsetsofR.

Unit-III

Propertiesofcomplexnumbers,regionsinthecomplexplane,functionsofcomplexvariable,mappings.D

erivatives,differentiationformulas,Cauchy-

Riemannequations,sufficientconditionsfordifferentiability.

Unit-IV

Analytic functions, examples of analytic functions, exponential function, Logarithmic function,

trigonometricfunction,derivativesoffunctions,definiteintegralsoffunctions.Contours,Contourintegr

alsanditsexamples,upperboundsformoduliofcontourintegrals.Cauchy-

Goursattheorem,Cauchyintegralformula.

Unit-V

Liouvilles theorem and the fundamental theorem of

algebra.Convergenceofsequencesandseries,Taylorseriesanditsexamples.Laurentseriesanditsexam

ples,absoluteanduniformconvergenceofpowerseries.

BooksRecommended:

1.P.K.Jain and K.Ahmad,MetricSpaces,NarosaPublishingHouse,NewDelhi.Chapters:2(1-9),3(1-

4),4(1-4),6(1-2),7(1only).

2.JamesWardBrownandRuelV.Churchill, Complex Variables and Applications, 8th Ed.,

McGrawHillInternationalEdition,2009.Chapters:1(11only),2(12,13),2(15-

22,24,25),3(29,30,34)4(37-41,43-46,50-53),5(55-60,62,63,66).

BooksforReferences:

1.SatishShiraliandHarikishanL.Vasudeva,MetricSpaces,SpringerVerlag,London,2006.

2.S.Kumaresan,TopologyofMetricSpaces,2ndEd.,NarosaPublishingHouse,2011.

3.S.Ponnusamy-FoundationsofComplexAnalysis,AlphaScienceInternationalLtd.

4.J.B.Conway-Functionsofonecomplexvariable,Springer.

5.N.Das- Complex Function Theory, Allied Publishers Pvt.Ltd.,Mumbai.

C-6.2:LinearProgramming

TotalMarks:100

Theory:80Marks+Mid-Sem:20Marks

21 | P a g e

5Lectures,1Tutorial(perweekperstudent)

Unit-I ( Scientific Calculator may be allowed)

Introduction to linear programming problem, Theory of simplex method, optimality and

unboundedness,thesimplexalgorithm,simplexmethodintableauformat,introductiontoartificialvar

iables,twophasemethod, BigM method and their comparison.

Unit-II

Duality, formulation of the dual problem, primal-dual relationships, economic interpretation of

the dual.

Unit-III

Transportationproblem

anditsmathematicalformulation,northwestcornermethodleastcostmethodandVogelapproximati

onmethodfordeterminationofstartingbasicsolution,algorithmforsolvingtransportation problem

Unit-IV

Assignmentproblem and

itsmathematicalformulation,Hungarianmethodforsolvingassignmentproblem.

Unit-V

Gametheory:formulationoftwopersonzerosumgames,solvingtwopersonzerosumgames,gameswith

mixedstrategies,graphicalsolutionprocedure,linearprogrammingsolutionofgames.

RecommendedBooks:

1.MokhtarS.Bazaraa,JohnJ.Jarvis and HanifD.Sherali,

LinearProgrammingandNetworkFlows,2ndEd.,JohnWileyandSons,India,2004.Chapters:3(3.2-

3.3,3.5-3.8),4(4.1-4.4),6(6.1-6.3).

2.F.S.HillierandG.J.Lieberman, Introduction to Operations Research, 9th Ed., Tata McGraw

Hill,Singapore,2009.Chapter:14

3.HamdyA.Taha,OperationsResearch,AnIntroduction,8thEd.,PrenticeHallIndia,2006.Chapter:5(

5.1,5.3,5.4).

BooksforReference:

1.G.Hadley,LinearProgramming,NarosaPublishingHouse,NewDelhi,2002.

2.Kanti Swarup, P.K.GuptaandManMohan-OperationsResearch,S.ChandandCo.Pvt.Ltd.

3.N.V.R. Naidu,G. RajendraandT. KrishnaRao-OperationsResearch,I.K.

InternationalPublishingHousePvt.Ltd., New Delhi, Bangalore.

4.R.Veerachamy and V.RaviKumar-OperationsResearch-I.K.InternationalPublishingHouse

Pvt.Ltd., New Delhi, Bangalore.

5.P.K.GuptaandD.S.Hira-OperationsResearch,S.ChandandCompanyPvt.Ltd.,NewDelhi

22 | P a g e

DisciplineSpecificEcectives(DES)

DSE-1

ProgramminginC++(Compulsory)

Part-I(Marks:75)

(Theory:60Marks+Mid-Sem:15Marks)

Introductiontostructuredprogramming:datatypes-

simpledatatypes,floatingdatatypes,characterdatatypes,stringdatatypes,arithmeticoperatorsando

peratorsprecedence,variablesandconstantdeclarations,expressions,inputusingtheextractionopera

tor¿¿andcin,outputusingtheinsertionoperator¡¡andcout,preprocessordirectives,increment(++)a

nddecrement(–

)operations,creatingaC++program,input/output,relationaloperators,logicaloperatorsandlogical

expressions,ifandif-elsestatement,switchandbreakstatements.for,whileanddo-

whileloopsandcontinuestatement,nestedcontrolstatement,valuereturningfunctions,valueversusre

ferenceparameters,localandglobalvariables,onedimensionalarray,twodimensionalarray,pointerdat

aandpointervariables.

BookRecommended:

1.D.S.Malik: C++ Programming Language, Edition-2009, Course Technology, Cengage

Learning,IndiaEdition.Chapters:2(Pages:37-95),3(Pages:96-129),4(Pages:134-

178),5(Pages:181-236),6,7(Pages:287-304),9(pages:357-390),14(Pages:594-600).

BooksforReferences:

1.E.Balaguruswami:ObjectorientedprogrammingwithC++,fifthedition,TataMcGrawHillEducatio

nPvt.Ltd.

2.R.JohnsonbaughandM.Kalin-Applications Programming in ANSI C, Pearson Education.

3.S.B.Lippman and J.Lajoie, C++ Primer,3rdEd.,AddisonWesley,2000.

4.Bjarne Stroustrup , The C++ Programming Language, 3rd Ed., Addison Welsley.

Part-II(Practical,Marks:25)

ListofPracticals(Usinganysoftware)

Practical/LabworktobeperformedonaComputer.

1.CalculatetheSumoftheseries++..+for any positive integer N.

2.Writeauserdefinedfunctiontofindtheabsolutevalueofanintegeranduseittoevaluatethe

function(-1)n/|n|,forn=-2,-1,0,1,2.

3.Calculate the factorial of anynaturalnumber.

4.Readfloatingnumbersandcomputetwoaverages:theaverageofnegativenumbersandtheaverageof

positivenumbers.

1111

123N

23 | P a g e

5.Writeaprogramthat

promptstheusertoinputapositiveinteger.Itshouldthenoutputamessageindicatingwhetherthenumb

erisaprimenumber.

6.Writeaprogramthatpromptstheusertoinputthevalueofa,bandcinvolvedintheequationax2+bx+c

=0andoutputsthetypeoftherootsoftheequation.Alsotheprogramshouldoutputsalltherootsoftheeq

uation.

7.writeaprogramthatgeneratesrandomintegerbetween0and99.GiventhatfirsttwoFibonaccinumber

sare0and1,generateallFibonaccinumberslessthanorequaltogeneratednumber

8.Writeaprogramthatdoesthefollowing:

a.Promptstheusertoinputfivedecimalnumbers.

b.Printsthefivedecimalnumbers.

c.Convertseachdecimalnumbertothenearestinteger.

d.Addsthesefiveintegers.

e.Printsthesumandaverageofthem.

9.Write a program that uses whileloops to perform the following steps:

a.Prompttheusertoinputtwointegers:firstNumandsecondNum(firstNumshoulbelessthansecond

Num).

b.OutputalloddandevennumbersbetweenfirstNumandsecondNum.

c.OutputthesumofallevennumbersbetweenfirstNumandsecondNum.

d.Output the sum of the square of the odd numbers firs tNumand second Num.

e.OutputalluppercaseletterscorrespondingtothenumbersbetweenfirstNumandsecondNum,

if any.

10.Write a programthat prompts the user to input

fivedecimalnumbers.Theprogramshouldthenadd the five decimal numbers, convert the sum to

the nearest integer, and print the result.

11.Writeaprogramthatpromptstheusertoenterthelengthsofthreesidesofatriangleandthenoutputs

amessageindicatingwhetherthetriangleisarighttriangleorascalenetriangle.

12.Writeavaluereturningfunctionsmallertodeterminethesmallestnumberfrom a set of

numbers.Usethisfunctiontodeterminethesmallestnumberfromasetof10numbers.

13.Writeafunctionthattakesasaparameteraninteger(asalongvalue)andreturnsthenumberofodd,

even,andzerodigits.Alsowriteaprogramtotestyourfunction.

14.Enter100 integers into an array and short them in an ascending/ descending order and

print thelargest/smallestintegers.

15.Enter10 integers into an array and then search for a particular integer in the array.

16.Multiplication/Additionoftwomatricesusingtwodimensionalarrays.

17.Usingarrays,readthevectorsofthefollowingtype:A=(12345678),

B=(02340156)andcomputetheproductandadditionofthesevectors.

18.Readfromatextfileandwritetoatextfile.

19.Writeafunction,reverseDigit,thattakesanintegerasaparameterandreturnsthenumberwithitsdigi

tsreversed.For example, the value of function reverse

Digit12345is54321andthevalueofreverseDigit-532is-235.

24 | P a g e

DSE-II

TotalMarks:100

Theory:80Marks+Mid-Sem:20Marks

5Lectures,1Tutorial(perweekperstudent.

(Anyoneofthefollowing)

1-DiscreteMathematics

Unit-I

Logic,proportionalequivalence,predicatesandquantifiers,nestedquantifiers,methodsofproof,relatio

nsandtheirproperties,n-

aryrelationsandtheirapplications,Booleanfunctionsandtheirrepresentation.

Unit-II

Thebasiccounting,thePigeon-holeprinciple,GeneralizedPermutationsandCombinations,

Recurrencerelations,Countingusingrecurrencerelations,

Unit-III

Solvinglinearhomogeneousrecurrencerelationswithconstantcoefficients,Generatingfunctions,Solvi

ngrecurrencerelationsusinggeneratingfunctions.

Unit-IV

Partiallyorderedsets,Hassediagramofpartiallyorderedsets,mapsbetweenorderedsets,dualityprincipl

e,Latticesasorderedsets,Latticesasalgebraicstructures,sublattices,Booleanalgebraanditsproperties

.

Unit-IV

Graphs:Basicconceptsandgraphterminology,representinggraphsandgraphisomorphism.Distancein

a graph, Cut-vertices and Cut-edges, Connectivity, Euler and Hamiltonian path.

BookRecommended:

1.KennethH.Rosen,DiscreteMathematicsandApplications,TataMcGrawHillPublications,Chapters

:1(1.1to1.5),4(4.1,4.2,4.5),6(6.1,6.2,6.5,6.6),7(7.1,7.2),8,10(10.1,10.2).

BooksforReferences:

1.BA.DaveyandH.A.Priestley, Introduction to Lattices and Order, Cambridge University

Press,Cambridge,1990.

2.EdgarG.GoodaireandMichaelM.Parmenter,DiscreteMathematicswithGraphTheory(2ndEdition

), Pearson Education (Singapore) Pte.Ltd.,IndianReprint2003.

3.RudolfLidlandGnterPilz,AppliedAbstractAlgebra(2ndEdition),UndergraduateTextsinMathem

atics, Springer (SIE), Indian reprint, 2004.

4.D.S.Malik-Discrete Mathematics: Theory & Applications, Cengage Learning India Pvt.Ltd.

5.KevinFerland-DiscreteMathematicalStructures,CengageLearningIndiaPvt.Ltd.

25 | P a g e

2-MathematicalModelling

Unit-I

SimplesituationsrequiringMathematicalmodelling.Thetechniqueof Mathematical modelling,

Mathematicalmodellingthroughdifferentialequations,lineargrowthanddecaymodels,non-

lineargrowthanddecaymodels,compartmentmodels,Mathematicalmodellingofgeometricalproblem

sthroughordinarydifferential equations of first order.

Unit-II

Mathematicalmodellinginpopulationdynamics,Mathematicalmodellingofepidemicsthroughsyst

ems of ordinary differential equations of first order, compartment models through systems of

ordinarydifferentialequations,Mathematicalmodellingineconomicsthroughsystemsofordinarydif

ferentialequations of first order.

Unit-III

Mathematicalmodelsinmedicine,armsrace,battlesandinternationaltradeintermsofsystemsoford

inary differential equations, Mathematical modelling of planetary

motions,Mathematicalmodellingofcircularmotionandmotionofsatellites,mathematicalmodellingt

hroughlineardifferentialequationsofsecondorder

Unit-IV

Situation giving rise to partial differential equations models,massbalance equations:First

methodofgettingPDEmodels,momentumbalanceequations.Thesecondmethodof obtaining partial

differentialmodels,variationalprinciples,thirdfunction,fourthmethodofobtainingpartialdifferential

equationmodels

Unit-II

Models for traffic flow of a

highway.Situationthatcanbemodelledthroughgraphs,mathematicalmodelsintermsofdirectedgrap

hs,optimizationprinciplesandtechniques,Mathematicalmodellingthroughcalculusofvariations.

BooksRecommended:

1.J.N.Kapur-

MathematicalModelling,Chapters:1(1.1and1.2),2(2.1to2.4,2.6),3(3.1to3.5),4(4.1to4.3),6(6.1to

6.6),7(7.1to7.2),9(9.1and9.2).

26 | P a g e

3-NumberTheory

Unit-I

Divisibitytheoreminintegers, Primesandtheirdistributions, Fundamentaltheoremofarithmetic,

Greatestcommondivisor,Euclideanalgorithms,Modulararithmetic,LinearDiophantineequation,p

rimecountingfunction,statementofprimenumbertheorem, Goldbach conjecture.

Unit-II

Introductiontocongruences, Linear Congruences, Chinese Remaindertheorem,

Polynomialcongruences,Systemoflinearcongruences,completesetofresidues,Chineseremainderthe

orem,Fermatslittletheorem,Wilsonstheorem.

Unit-III

Numbertheoreticfunctions,sumandnumberofdivisors,totallymultiplicativefunctions,definitionand

propertiesoftheDirichletproduct

Unit-IV

TheMbiusinversionformula,thegreatestintegerfunction,Eulersphifunction,Eulerstheorem,reduce

dsetofresidues,somepropertiesofEulersphi-function.

Unit-V

Orderofanintegermodulon,primitiverootsforprimes,compositenumbershavingprimitiveroots,Eul

erscriterion,theLegendresymbolanditsproperties,quadraticreciprocity,quadraticcongruenceswithc

ompositemoduli.

BookRecommended:

1.D.M.Burton-

ElementaryNumberTheory,McGrawHill,Chapters:2(2.1to2.4),3(3.1to3.3),4(4.1to4.4),5(5.1to5.

4),6(6.1to6.3),7(7.1to7.3),8(8.1to8.2),9(9.1to9.3).

BooksforReferences:

1.K.H.Rosen-ElementaryNumberTheory&its Applications, Pearson Addition Wesley.

2.I.NivenandH.S.Zuckerman-AnIntroductiontoTheoryofNumbers,WileyEasternPvt.Ltd.

3.TomM.Apostol-IntroductiontoAnalyticNumberTheory,SpringerInternationalStudentEdn.

4.NevilleRobinns,BeginningNumberTheory(2ndEdition),NarosaPublishingHousePvt.Limited,Del

hi,2007.

4-BooleanAlgebraandAutomataTheory

27 | P a g e

Unit-I

Definition,examplesandbasicpropertiesoforderedsets,mapsbetweenorderedsets,dualityprinciple,lat

ticesasorderedsets,latticesasalgebraicstructures,sublattices,productsandhomomorphisms.Definiti

on,examplesandpropertiesofmodularanddistributivelattices

Unit-II

Booleanalgebras,Booleanpolynomials,minimalformsofBooleanpolynomials,QuinnMcCluskeym

ethod,Karnaughdiagrams,switchingcircuitsandapplicationsofswitchingcircuits.

Unit-III

Introduction:Alphabets,strings,andlanguages.FiniteAutomataandRegularLanguages:deterministi

candnon-

deterministicfiniteautomata,regularexpressions,regularlanguagesandtheirrelationshipwithfiniteaut

omata,pumpinglemmaandclosurepropertiesofregularlanguages.

Unit-IV

ContextFreeGrammarsandPushdownAutomata:Contextfreegrammars(CFG),parsetrees,ambiguiti

esingrammarsandlanguages,pushdownautomaton(PDA)andthelanguageacceptedbyPDA,determi

nisticPDA,Non-

deterministicPDA,propertiesofcontextfreelanguages;normalforms,pumpinglemma,closureproper

ties,decisionproperties.

Unit-V

TuringMachines:Turingmachineasamodelofcomputation,programmingwithaTuringmachine,va

riantsofTuringmachineandtheirequivalence.Undecidability:Recursivelyenumerableandrecursivelan

guages,undecidableproblemsaboutTuringmachines:haltingproblem,PostCorrespondenceProblem,

andundecidabilityproblemsAboutCFGs.

BooksRecommended:

1.BA.DaveyandH.A.Priestley, Introduction to Lattices and Order, Cambridge University

Press,Cambridge,1990.

2.EdgarG.GoodaireandMichaelM.Parmenter,DiscreteMathematicswithGraphTheory,(2ndEd.),

Pearson Education (Singapore) P.Ltd., Indian Reprint 2003.

3.RudolfLidlandGnterPilz,AppliedAbstractAlgebra,2ndEd.,UndergraduateTextsinMathematics

, Springer (SIE), Indian reprint, 2004.

4.J.E.Hopcroft,R.Motwani and J.D.Ullman, Introduction to Automata Theory, Languages,

andComputation,2ndEd.,Addison-Wesley,2001.

5.H.R.Lewis,C.H.Papadimitriou, C.Papadimitriou, Elements of the Theory of Computation,

2ndEd.,Prentice-Hall,NJ,1997.

6.J.A.Anderson, Automata Theory with Modern Applications, Cambridge University Press,

2006.

DSE-III

TotalMarks:100

28 | P a g e

Theory:80Marks+Mid-Sem:20Marks

5Lectures,1Tutorial(perweekperstudent.

(Anyoneofthefollowing)

1-DifferentialGeometry

Unit-I

TheoryofSpaceCurves:Spacecurves,Planercurves,Curvature,torsionandSerret-

Frenetformulae.Osculatingcircles,Osculatingcirclesandspheres.Existenceofspacecurves.Evolutesa

ndinvolutesofcurves.

Unit-II

Osculatingcircles,Osculatingcirclesandspheres.Existenceofspacecurves.Evolutesandinvolutesofcur

ves.

Unit-III

Developables:Developableassociatedwithspacecurvesandcurvesonsurfaces,Minimalsurfaces.

Unit-IV

TheoryofSurfaces:Parametriccurvesonsurfaces.Directioncoefficients.FirstandsecondFundamenta

lforms.PrincipalandGaussiancurvatures.

Unit-V

Linesofcurvature,Eulerstheorem.Rodriguesformula,ConjugateandAsymptoticlines.

BookRecommended:

1.C.E.Weatherburn,DifferentialGeometryofThreeDimensions,CambridgeUniversityPress2003.Ch

apters:1(1-4, 7,8,10), 2(13, 14, 16,17),3,4(29-31,35,37, 38).

BooksforReferences

1.T.J.Willmore, An IntroductiontoDifferentialGeometry,DoverPublications,2012.

2.S.Lang,FundamentalsofDifferentialGeometry,Springer,1999.

3.B.O’Neill,ElementaryDifferentialGeometry,2ndEd.,AcademicPress,2006.

4.A.N.Pressley-ElementaryDifferentialGeometry,Springer.

5.B.P.Acharya and R.N.Das-

FundamentalsofDifferentialGeometry,KalyaniPublishers,Ludhiana,NewDelhi.

29 | P a g e

2-Mechanics

Unit-I

Momentofaforceaboutapointandanaxis,coupleandcouplemoment,Momentofacoupleaboutalin

e,resultantofaforcesystem,distributedforcesystem,freebodydiagram,freebodyinvolvinginterior

sections, general equations of equilibrium, two point equivalent loading, problems arising

fromstructures,staticindeterminacy

Unit-II

LawsofCoulombfriction,applicationtosimpleandcomplexsurfacecontactfrictionproblems,trans

missionofpowerthroughbelts,screwjack,wedge,firstmomentofanareaandthecentroid,othercent

ers,

Unit-III

TheoremofPappus-

Guldinus,secondmomentsandtheproductofareaofaplanearea,transfertheorems,relationbetweense

condmomentsandproductsofarea,polarmomentofarea,principalaxes.

Unit-IV

Conservativeforcefield,conservationformechanicalenergy,workenergyequation,kineticenergyandw

orkkineticenergyexpressionbasedoncenterofmass,momentofmomentumequationforasingleparticle

andasystemofparticles.

Unit-V

Translationandrotationofrigidbodies,Chaslestheorem,generalrelationshipbetweentimederivatives

ofavectorfordifferentreferences,relationshipbetweenvelocitiesofaparticlefordifferentreferences,acc

elerationofparticlefordifferentreferences.

BookRecommended:

1.I.H.ShamesandG.KrishnaMohanRao,EngineeringMechanics:StaticsandDynamics,(4thEd.),Dorli

ngKindersley(India)Pvt.Ltd.(Pearson Education), Delhi, 2009.Chapters:3,4,5,6(6.1-

6.7),7,11,12(12.5,12.6),13.

BooksforReferences:

1.R.C.HibbelerandAshokGupta,EngineeringMechanics:StaticsandDynamics,11thEd.,DorlingKind

ersley(India)Pvt.Ltd.(PearsonEducation),Delhi.

2.GrantRFowles,AnalyticalMechanics,CengageLearningIndiaPvt.Ltd.

3-MathematicalFinance

Unit-I

Basicprinciples:Comparison,arbitrageandriskaversion,Interest(simpleandcompound,discreteandc

ontinuous),timevalueofmoney,inflation,netpresentvalue,internalrateofreturn(calculationbybise

ctionandNewton-

Raphsonmethods),comparisonofNPVandIRR.Bonds,bondpricesandyields,Macaulay and

modified duration, term structure of interest rates: spot and forward rates,

30 | P a g e

explanationsoftermstructure,runningpresentvalue,floating-

ratebonds,immunization,convexity,putableandcallablebonds.

Unit-II

Assetreturn,shortselling,portfolioreturn,(briefintroductiontoexpectation,variance,covariancean

dcorrelation),randomreturns, portfolio mean return and variance, diversification, portfolio

diagram,feasibleset,Markowitzmodel(reviewofLagrangemultipliersfor1and2constraints)

Unit-III

Twofundtheorem,riskfreeassets,Onefundtheorem,capitalmarketline,Sharpeindex.CapitalAssetPri

cingModel(CAPM),betasofstocksandportfolios, securitymarketline,

useofCAPMininvestmentanalysisandasapricingformula,Jensensindex.

Unit-IV

Forwardsandfutures,markingtomarket,valueofaforward/futurescontract,replicatingportfolios,fut

uresonassetswithknownincomeordividendyield,currencyfutures,hedging(short,long,cross,rolling),

optimal hedge ratio, hedging with stock index futures, interest rate futures, swaps.

Unit-V

Lognormal distribution, Lognormal model / Geometric Brownian Motion for stock prices,

Binomial

Treemodelforstockprices,parameterestimation,comparisonofthemodels.Options,Typesofoptions:

put/call,European/American,payoffofanoption,factorsaffectingoptionprices,putcallparity.

BooksRecommended:

1.DavidG.Luenberger,InvestmentScience,OxfordUniversityPress,Delhi,1998.Chapters:1,2,3,4,6,7

,8(8.5-8.8),10(except10.11,10.12),11(except11.211.8).

2.JohnC.Hull,Options,FuturesandOtherDerivatives(6thEdition),Prentice-

HallIndia,Indianreprint, 2006.Chapters:3, 5, 6, 7(except 7.10, 7.11), 8, 9.

3.SheldonRoss,AnElementaryIntroductiontoMathematicalFinance(2ndEdition),CambridgeUni

versityPress,USA,2003.Chapter:3

BooksforReferences:

1.R.C.HibbelerandAshokGupta,EngineeringMechanics:StaticsandDynamics,11thEd.,DorlingKind

ersley(India)Pvt.Ltd.(PearsonEducation),Delhi.

2.GrantRFowles,AnalyticalMechanics,CengageLearningIndiaPvt.Ltd.

4-RingTheoryandLinearAlgebra-II

Unit-I

Polynomialringsovercommutativerings,divisionalgorithmandconsequences,principalidealdomains,

factorizationofpolynomials,reducibilitytests,irreducibilitytests,Eisensteincriterion,uniquefactoriz

ationinZ[x].

Unit-II

Divisibilityinintegraldomains,irreducibles,primes,uniquefactorizationdomains,Euclideandomains

.

31 | P a g e

Unit-III

Dualspaces,dualbasis,doubledual,transposeofalineartransformationanditsmatrixinthedualbasis,a

nnihilators,Eigenspacesofalinearoperator,diagonalizability,invariantsubspacesandCayleyHamilton

theorem, the minimal polynomial for a linear operator.

Unit-IV

Innerproductspacesandnorms,Gram-

Schmidtorthogonalisationprocess,orthogonalcomplements,Bessels inequality, the adjoint of a

linear operator

Unit-V

Least Squares Approximation, minimal solutions tosystemsoflinearequations,Normalandself-

adjointoperators,OrthogonalprojectionsandSpectraltheorem.

BooksRecommended:

1.JosephA.Gallian,ContemporaryAbstractAlgebra(4thEd.),NarosaPublishingHouse,1999.Chap

ters:16,17,18.

2.StephenH.Friedberg,ArnoldJ.Insel, Lawrence E.Spence,LinearAlgebra(4thEdition),Prentice-

HallofIndiaPvt.Ltd.,NewDelhi,2004.Chapters:2(2.6 only), 5(5.1, 5.2, 5.4), 6(6.1, 6.4,

6.6),7(7.3only).

DSE-IV

ProjectWork(Compulsory)

TotalMarks:100(Project:75Marks+Viva-Voce:25Marks)

Each Student should submit a Project under the guidance of the teacher.

SkillEnhancementCourses(SEC)

(Credit:2each,TotalMarks:50)

SEC-ItoSEC-IV

SEC-I

CommunicativeEnglishandWritingSkill(Compulsory)

SEC-II

(Anyoneofthefollowing)

1-ComputerGraphics

DevelopmentofcomputerGraphics:RasterScanandRandomScangraphicsstorages,displaysprocess

32 | P a g e

orsandcharactergenerators,colourdisplaytechniques,interactiveinput/outputdevices.Points,linesa

ndcurves:Scanconversion,line-drawingalgorithms,circleandellipsegeneration,conic-

sectiongeneration,polygonfillingantialiasing.Two-

dimensionalviewing:Coordinatesystems,lineartransformations,lineandpolygon clipping

algorithms.

BooksRecommended:

1.D.Hearn and M.P.Baker-ComputerGraphics,2ndEd.,PrenticeHallofIndia,2004.

2.J.D.Foley,AvanDam,S.K.FeinerandJ.F.Hughes-

ComputerGraphics:PrincipalsandPractices,2ndEd.,Addison-Wesley,MA,1990.

3.D.F.Rogers-ProceduralElementsinComputerGraphics,2ndEd.,McGrawHillBookCompany,2001.

4.D.F.RogersandA.J.Admas-Mathematical Elements in Computer Graphics, 2nd Ed.,

McGrawHill Book Company, 1990.

2-LogicandSets

Introduction,propositions,truthtable,negation,conjunctionanddisjunction.Implications,biconditi

onalpropositions,converse,contrapositiveandinversepropositionsandprecedenceoflogicaloperators

.Propositionalequivalence:Logicalequivalences.Predicatesandquantifiers:Introduction,Quantifiers

,BindingvariablesandNegations.Sets,subsets,SetoperationsandthelawsofsettheoryandVenndiagra

ms.Examplesoffiniteandinfinitesets.Finitesetsandcountingprinciple.Empty

set,propertiesofemptyset.Standardsetoperations.Classesofsets.Powersetofaset.DifferenceandSy

mmetricdifferenceoftwosets.Setidentities,Generalizedunionandintersections.Relation:Product

set, Composition of relations, Types of relations, Partitions, Equivalence Relations with

example of

congruencemodulorelation,Partialorderingrelations,naryrelations.

BooksRecommended:

1.1.R.P.Grimaldi-DiscreteMathematicsandCombinatorialMathematics, PearsonEducation,1998.

2.P.R.Halmos-NaiveSetTheory,Springer,1974.

3.E.Kamke-TheoryofSets,DoverPublishers,1950

3-CombinartorialMathematics

Basiccountingprinciples,PermutationsandCombinations(withandwithoutrepetitions),Binomialt

heorem,Multinomialtheorem,Countingsubsets,Set-

partitions,StirlingnumbersPrincipleofInclusionandExclusion,Derangements,InversionformulaeG

eneratingfunctions:Algebraofformalpowerseries,Generatingfunctionmodels,Calculatinggenerating

functions,Exponentialgeneratingfunctions.Recurrencerelations:Recurrencerelationmodels,Dividea

ndconquerrelations,Solutionofrecurrencerelations,Solutionsbygeneratingfunctions.Integerpartition

s,Systemsofdistinctrepresentatives.

33 | P a g e

BooksRecommended:

1.J.H.vanLintandR.M.Wilson-ACourseinCombinatorics,2ndEd.,CambridgeUniversityPress,2001.

2.V.Krishnamurthy-Combinatorics, Theory and Application, Affiliated East-West Press 1985.

3.P.J.Cameron-Combinatorics,Topics,Techniques,Algorithms,CambridgeUniversityPress,1995.

4.M.Jr.Hall-Combinatorial Theory, 2nd Ed., John Wiley & Sons, 1986.

5.S.S.Sane-CombinatorialTechniques,HindustanBookAgency,2013.

6.R.A.Brualdi-IntroductoryCombinatorics,5thEd.,PearsonEducationInc.,2009.

4-InformationSecurity

Overview of Security: Protection versus security; aspects of securitydata integrity, data

availability, privacy;securityproblems,userauthentication,OrangeBook.Security Threats:

Program threats, worms,viruses, Trojan horse, trap door, stack and buffer over flow; system

threats- intruders; communicationthreats- tapping and piracy.Security Mechanisms:Intrusion

detection, auditing and logging, tripwire,system-call monitoring.

BooksRecommended:

1.C.PfleegerandS.L.Pfleeger-SecurityinComputing,3rdEd.,Prentice-HallofIndia,2007.

2.D.Gollmann-ComputerSecurity,JohnWileyandSons,NY,2002.

3.J.Piwprzyk,T.HardjonoandJ.Seberry-FundamentalsofComputerSecurity,Springer-

VerlagBerlin,2003.

4.J.M.Kizza-Computer Network Security, Springer, 2007.

5.M.Merkow and J.Breithaupt-

InformationSecurity:PrinciplesandPractices,PearsonEducation,2006.

34 | P a g e

SEMSTER- 1

Generic Electives/ Interdisciplinary

(04 Papers, 02 paper seach from two Allied disciplines)

(Credit: 06 each, Marks:100)

GE-I to GE-IV

GE-I: Calculus and Ordinary Differential Equations

Unit-I

Curvature, Asymptotes, Tracing of Curves (Cartenary, Cycloid, Folium of Descartes, Astroid,

Limacon, Cissoid & loops), Rectification, Quardrature, Volume and Surface area of solids of

revolution.

Unit-II

Sphere, Cones and Cylinders, Conicoid.

Explicit and Implicit functions, Limit and Continuity of functions of several variables, Partial

derivatives, Partial derivatives of higher orders, Homogeneous functions, Change of variables,

Mean value theorem, Taylors theorem and Maclaurins theorem for functions of two variables.

Maxima and Minima of functions of two and three variables, Implicit functions, Lagranges

multipliers. Multiple integrals.

Unit-III

Ordinary Differential Equations of 1st order and 1st degree (Variables separable, homogenous,

exactand linear). Equations of 1st order but higher degree.

Unit-IV

Second order linear equations with constant coefficients, homogeneous forms, Second order

equations with variable coefficients, Variation of parameters. Laplace transforms and its

applications to solutions of differential equations.

Books Recommended:

1. Advanced Higher Calculus (Vidyapuri Dr. Ghanasyam Sen & Others)

Ch- 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17

2. B. P. Acharya and D. C. Sahu-Analytical Geometry of Quadratic Surfaces, Kalyani

Publishers, New Delhi, Ludhiana. Ch. (2,3,4)

3. J. SinharoyandS.Padhy-A Course of Ordinary and Partial Differential Equations,

Kalyani

Publishers.Chapters:2(2.1to2.7),3,4(4.1to4.7),5,9(9.1,9.2,9.3,9.4,9.5,9.10,9.11,9.13).

BooksforReferences:

1. Shanti Narayan and P.K.Mittal-Analytical Solid Geometry, S. Chand & Company Pvt. Ltd.,

NewDelhi.

2. David V.Weider-AdvancedCalculus,DoverPublications.

35 | P a g e

3. Martin Braun-DifferentialEquationsandtheirApplications-MartinBraun,SpringerInternational.

4. M. D. Raisinghania- Advanced Differential Equations, S. Chand & Company Ltd., NewDelhi

5. G. Dennis Zill-A First Course in Differential Equations with Modelling Applications,

Cengage Learning India Pvt. Ltd.

MATH.-CG-I, SEM-I IS SAME AS MATH.-CC-I, SEM-I

GE-II:LinearAlgebraandAdvancedAlgebra

Unit-I

Vectorspace, Subspace, Spanofaset,

LineardependenceandIndependence,DimensionsandBasis.Linear transformations, Range,

Kernel, Rank, Nullity, Inverse of a linear map, Rank-Nullity theorem.

Unit-II

Matrices and linear maps, Rank and Nullity of a matrix, Transpose of a matrix, Types of

matrices.Elementaryrowoperations,Systemoflinearequations,Matrixinversionusingrowoperations

,DeterminantandRankofmatrices,Eigenvalues,Eigenvectors,Quadraticforms.

Unit-III

GroupTheory:Definitionandexamples,Subgroups,Normalsubgroups,Cyclicgroups,Cosets,Quotien

tgroups, Permutation groups, Homomorphism.

Unit-IV

RingTheory:Definitionandexamples,SomespecialclassesofRings,Ideals,Quotientrings,Ringhomom

orphism.Isomorphismtheorems.

Unit-V

Zerodivisors,Integraldomain,Finitefields,FinitefieldZ/pZ,FieldofquotientsofanIntegraldomain,P

olynomial ring, Division algorithm, Remainder theorem, Factorization of polynomials,

irreducible

andreduciblepolynomials,Primitivepolynomials,Irreducibilitytests,EisensteinCriterion.

BooksRecommended:

1.V.Krishnamurty,V.P.Mainra,J.L.Arora-AnintroductiontoLinearAlgebra,AffiliatedEast-

WestPressPvt.Ltd.,NewDelhi,Chapters:3,4(4.1to4.7),5(except5.3),6(6.1,6.2,6.5,6.6,6.8),7(7.4

only).

2. I.N Iterstein, Topics in Algebra

Ch-1(1.3 only), 2 (2.1 to 2.6;2.7 excluding application, 2.10), 3 (3.1 to 3.6, 3.9, 3.10)

BooksforReferences:

36 | P a g e

1. I.H.Seth-Abstract Algebra, Prentice Hall of India

Pvt.Ltd.,NewDelhi.Chapters:13,14,15,16, 17,18,19,20.

2.RaoandBhimasankaran-LinearAlgebra,HindustanPublishingHouse.

3.S.Singh-LinearAlgebra,VikasPublishingHousePvt.Ltd.,NewDelhi.

4.GilbertStrang-LinearAlgebra&itsApplications,CengageLearningIndiaPvt.Ltd.

5.Gallian-ContemporaryAbstractAlgebra,NarosapublishingHouse.

6.Artin-Algebra,PrenticeHallofIndia.

8.V.K.KhannaandS.K.Bhambri-A Course in Abstract Algebra, Vikas Publishing House

Pvt.Ltd.,NewDelhi.