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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:
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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.