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![Page 1: collegeholkar.org. III-ilovepdf-compressed.pdf · 2.7,2.10-l ,2.10-2 & TB -2 Chapter VIII Linearfirnctiona1,boundedLinearfunctiona1,DualspaceSwitti@ Art. 2.8, 2.10-3 to 2.L0-7 & TB](https://reader033.vdocuments.site/reader033/viewer/2022042216/5ebdff04daba67009c03c837/html5/thumbnails/1.jpg)
Govt. (Autonomous) Holkar Science College, Indore O4I.P.)(Syllabus)
(Approved by Board of Studies of College)(2018- 1e)
Class :
Subject:
Paper:
Title:
&ot 8-tS
M.Sc. III Sem.
Mathematics
I (Compulsory)
Functional Analysis(Theory + CCE) 75+25 =100
Normed linear spaces, Pioperties ofNormal linear spaces, Branch Space & Example,T]NIT-I Convex Sets inNormal linear spaces. [TB-1: Art 3.r,3.2,2.2,2.3 &TB-2:
VIFinite Dimensional Normed linear spaces & Subspaces. Basic Properties of Finite
LINIT-II Dimensional Normed linear spaces. Equivalent norms, Riesz lernma andco -1: Art. 2.4,2.5 8.TB-2Quotient Space of normed linear spaoes and its completeness, Liner operato-isardtheir elemen ro l: Art.2.5 &TB -2Normed Linear operators & Bor:nded Linear operators & continuous operatots.[TB-1: Art. 2.7,2.10-l ,2.10-2 & TB -2 Chapter VIIILinearfirnctiona1,boundedLinearfunctiona1,DualspaceSwitti@Art. 2.8, 2.10-3 to 2.L0-7 & TB -2 chapter vIII up to tur.3.l
TB : TEXT BOOK
Text Books:
1. E- Kreyszig, Introductory Functional Analysis with applications, John Wiley & SonsNew York
.
2 . B.K. Lahiri, The world press private Limited calcutta ( w.B. )
Reference Books:
1. B. Cho$dhary and Sudarshan Nanda. Functional Analysis with applications, Wiley Eastem Ltd
2. G.F. Simmons, Introduction to To
JAdg$^.
![Page 2: collegeholkar.org. III-ilovepdf-compressed.pdf · 2.7,2.10-l ,2.10-2 & TB -2 Chapter VIII Linearfirnctiona1,boundedLinearfunctiona1,DualspaceSwitti@ Art. 2.8, 2.10-3 to 2.L0-7 & TB](https://reader033.vdocuments.site/reader033/viewer/2022042216/5ebdff04daba67009c03c837/html5/thumbnails/2.jpg)
GoW. (Autonomous) Holkar Science College, Indore (M.p.)
[semester wise svllabus (cBCS) f- M. s" Apprfrl"liul;?oard of studies of conege for session 20 1 8- 1 9r
Class :
Subject:
Paper:
Tiile:Max Marks:
lrI.Sc. Sem. IIIMathematics
1I ( Compulsory)Group: Advanced Special Functions(Theory + CCE) 75+25:10G
UN-'IT-I ;;, ffi,iJ"n',,1T,llTT.eflcn.lr".oto Jtr*li^^il^- f^_^^--r ?
ffi;ffi,l;;;;,;ffi;F'.rrler Tnf.-..rr"ai f^- F- D^r-^ -a '-r--)tI,esgn{e's duplication fornauia , Gauss murtiplication theorern.
N7-12, Art 15-20.
Sir,ple integral formffii-;'lIIT-II
The contiguous function relations. The hyper geometric diffbrentiaiSirnpie'iransformai:ons, Relation
Eleraentary series marripulations.functioa z and l-2.
{a,b,c, i ),eQualion.bew,eelr
Art 30-34, Arr 37-39.
saaischiitz''iheolem.A$ 44-46, Arr 49-53.
lLri 57 -64.Jontl
W: The flrncttonwruppte's t hesre:a, Dixon's Ttreorem..
LI\{IT.IV
iivIT-'ri
Bessei fi:nctionrtrecurrence relatigF' A pure rocutrt,nc, reiarion. A generaring function" E3esso--i,sintegral Index haif an odd inteser.
Basic properties of 1Fl, fr***r,, flrsi fid o*ho
nrsi ibruluia. Kuramer's second forrcr-ria ,
crthogunaiity, An eq r-ii trr*i etru: i,
poiynoraiais, Expansion ct' j
orthogonal poiynomiais; simple se:s *i loly=ro*iuir,condidon ibr ,_ortsrgonalif,v, zeros *f' oitilogonai
noiynoroials. ?te Three-tenn reo-'r,=ence relarion.Ari 68-7S, Art Z8-83.
BcoS<s Resor$mended
i. R-ainvilie, E-D. ; speciar furiction, The rda;,ailia='Co.. New york 19?i "
-,?eferencSBooks
L"
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Govt.(Autonomous) Holkar Science Collegeo Indore O,I.P.)(Syliabus)
(Approved by Board of Studies of €ollege)(201 8- 1e)
20tg-ts
M.Sc. III Sem.
Mathematics
III (Optional)Advanc el F uzzy Mathem ati c s
(Theory + CCE) 7 5+25 :100
Class:
Subject:
Paper:Title:Max Marks:
LNIT-V
Fuzzy Versus Crisp Number System, Interval Sets, Representation of A Set Type of i
Sets, Subsets, Universal Set. Operations On Sets, Some irnportant Results on Venn ,
Diagrams Fuzzy Sets Fvzzy Set Definition Different types of Fuzzy Sets General i
Definitions and Properties of Fuzzy Sets. ;
Other Important Operations General Properties : Fuzzy Vs Crisp Some ImportantTheorems Extension Principal For Fuzzy Sets Fuzzy Compliments Further OperationsonFuzzv Sets.
UNIT.IIIAggregation Operations Extension Principle For Fvzzy Sets Surnmary.
IINIT.IV Extension for sets - The zadeh's extension principle.Fvzzy Numbers Algebraic Operations With Fuzzy Numbers Binary Operations WithFvzzy Numbers Binary Operations of Two Fuzry Numbers Some Special ExtendedOperations Extended Operations For L-R Representation of Fuzzy Sets Fuzzy
i fuithmetic Arithmetic operations on Fuzzy Numbers in the Form of a- Cut Sets.
Text Book:1. Fwzy Set Theory and its Application by F{.J. Zimrnermarul, Ailied Publication ltd. }Jew
Delhi, 199i2" Fuzzy Sets and FuzzyLogic by G. J. Kiir and B. Yuan Prentice- Hail of India, Nevr Deihi,
l tes
Book Recommended:Fuzzy Sets and uncertainty and Information by G.J. Kalia tina A. \olj.r- Prentice-Ha'' oflndia'
rr ) o"rt---:€i.,w Ldo\- f Jr.'-1$k" hK ^ ,$4 W,t,-V
',,4.r, e eL>-\ \ A CI- ,^.- , nr/ ^ \N\\ tJ A.,-o (
'\^' n--
t-norms and t-conoilns Definition Of Intersectiog and Union by Hamacher Yager'sUnion and Intersection of Two Fuzzy Sets as Definbd by Defined by Dubois and Prade
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Govt. (Model, Autonomous) Holkar science, college rndore (M.P.)
(Department of lligher Educationo Govt' of M'P')CfiolCE BASED CREDIT SYSTEM (CBCS)
Class: M.Sc. (Mathematics)Title: Theory of Linear OPerators -I
Syllabus(Session 2018-19)
Semester - III Paper IVMax Marks: 100 (Theory + CCE = 75 + 25)
T]1\[IT - ISpectral theory in finite dimensional normed space. Basic concept: Resolvent set and Spectrum'
Spectral properties of bounded linear operators. Properties of resolvent and spectrum'
( Art. No. 7.1 -7.4 from 1)
I]NIT - IIUse of complex analysis in spectral theory: Banach algebras. Properties of Banach algebras'
( Art. No. 7.5 - 7 .7 from 1)
UNIT - IIICompact linear operators on normed linear spaces and their p$perties.
( Art. No. 8.1 - 8.2frbm 1)
UNIT - rySpectral properties of compact linear operators on normed spaces. Operator equations' Theorem
ofFredholems tyPe.( tut. No. 8.3 - 8.5 from l)
UNIT - VTheorems of Fredholms type. Fredholm alternative and fredholm alternative theorem.
( Art. No. 8.6 - 8.7 from 1)
Text Book:1. E. Kreyszing: Introductory Fr:nction Analysis with applications, John-Wiley & Sons,
Ne)fs York, t978.\Reference Books:
Z. B. K. Lahiri : Elements of Fgnctional analysis, The word press Pvt. Ltd. Calcutta, 1998.
3. B. Choudhary and S. Nanda: Functional analysis with applications, \Viley Eastem, Ltd.,
4. N. Dunford & J.T. Schwartz:Linear operators - 3 part,Interqcience Wiley, New York,
1958 -71.wv'^'"'^'''
\ -/4 ootn-- frr\ Nlt-,- \ W . "o
-- r^ **vlzJw^6 v\
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Govt (Autonomous) Ilolkar Science College, Indore (M'P')(Syllabus)
[Semesier wise syllabus (CBCS) for M.Sc Approved by Board of Studies of College for session 2018-i9]
Class :
Subject:
Paper:Title:
Max Marks:
M.Sc. iII Sem.
Mattrematics
V (Optional)Analytic Number Theory
(Theory = CCE) 75+25:100
UNIT.I
lNIT.II
chlet Multipiication: Introduction , Definitions of the
Mobius function p(n), Eluer totient function i(n).A retration connecting !"r and i. The
product formal for 0 (n), The Dirichlet product of arithmetical functions. Dirichiet
lrrn.6.t and Mobins inversion formula.Tire Mangoidt fi:nction. Multiplicative functions.
Multiplicative functions and Dirichlet Multiplicatioqis. The big 'oh' notation, Euler's
Summation formul4 some elementary asymp'totic forrnulas.
Chap-art -2.1 -2.1 0, Chap -uk-Z .Z,Z .3,3 .4
Abei's identity for arithmetical fi:nctions"Construction of subgroups. The charactercharacters"
Theorem 4.2, Chap6-6.4-6.7
Dirichtet characters. Sums involving Diriciriet charasters, The non-vanishing
UNIT-III for reatr non principal X. Dirichlet theorem on primes, primes of fomr 4n-1 and
I Art 6.8-6.10, Chap 7-art7.t,
The plan of the proof of Diri theorem on primes. Distribution of primes in arithmetic
trN-IT,ry progression.Art - 7.3- 7.9"
Finite abeliangroup. The
groups & their characters;-orthogonaltty reiations for
oi i-{.1, X)4n+1.
I
i!t.:
-. UNIT.Yi:
i
Diiicirtet Series and Euler Products:- Defiaition and different types of Dirichiet series.
The half -piane of absolute convergence of a Dirictrlet series. Ttie function defineC bl a :
Dirichiet series, Uniqueness tJreorem. muitipiicatioa of Dirictriet series, Euler prociuet.
Chapli -art ii.1 - 11.5.
Book Recomme4ded:i.T"M. Apostol, Introduction to Analytic Number Theory, Narosa pub. Ho.use,1989.
W \W;)I#W {wt J*
-/
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Govt. (Model, Autonomous) Holkar Scienceo College Indore (M.P.)(Department of Higher Education, Govt. of M.P.)
Semester wise Syllabus for post graduatesCHOICE BASED CREDIT SYSTEM (CRCS)
(With effect from the Academic year 201&"11I)
SyllabusClass - M.Sc. A{A (Semester-Il!Mathematics Modeling
Max Marks: 100 (Theory + CCE = 75+25)
Syllabus :
UNIT I:Simple situation requiring mathematicdl modeiling. Techniques, classification and characteristicsof mathematical models. Limitations of mathematics modellins.
;
UNIT II: qSefiing up first order differential equffions, qualitative solution, stabilewweity of solutions,growth and decay population models,.exponential and logistic population models.
UNIT lil:Comparfment models through system ef ODE. Mathematics models in medicine, arms race,battles and intemational trade in terms of system of ODE.
e"TINIT IV: i
Non-linear difference equations models for population growth probability generating function,fourth method of obtaining partial differentiai equation models. PDE model for a stochasticepidemic process with no removal. \4odel for traffic on a highway.-s..
USIIT V: 3General Communication networks, general weighted digraphs, 5nap-colorxing problems.
Reference Books:i. Kapoor JN: Mathematics models in biology and medicine EWP (1985)2. Mdtin Brann C.S Coleman , DA Drew (Eds) differential equation models.,?. C.L.Liu, Elements of discrete mathematics.4. A.M.Law and W.D Ketton, Simulation rnodeling and analysis, McGraw Hill Intl. Ed(Second
edition) 1991 $ >_+1D \M O"-h-'r (
\X-r$ '- ru v{**od."s. r,
^ 6/.t . r.r/u^ v
I
ffi,,$ G\ dtf \=ltv/'>-
(r" V\ )v
Subjecfi MathematicsPaper- Interdisciplinary Theory Paper
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-,3:iffi1'6"",181ffi:,i!;!TillJ,3'";i;iilii"';", ro* - ts
As recommended by central Board of studies and approved by the
Governor of M'P' Ma* n4"115731pro-tm 316 : 50
fffft Class
++'g{ Semester
frqq qW or qfrfir Title of SubjecV Group
gST Wi @. PaPer No.
srffi/ ffio- Compulsory/ OPtional Optional Gr-IV (i)
n and DeveloPment of
Operations Research, Characteristics of Operations Research'
u.* of Op.rations Researcho Uses anrtr
Limitations of operation Research, Linear programming Problerus''
Mathematical Formulation, Gnaptrical Solution Method'
: SirnPlex Method excePtional
I
I ."r.., artificial variable techniques ; Big M method, two phase Metho6I
i and Cyctic Problems, problem of degeneracy.
dualitY and theorem of dualitY'
Recommended Books :-1_ Kanti swarup, p.K. Gupta and Manmohan, operations Research,
Sultan Chand & Sons, New Delhi'Reference Books:-1- S.D, Sharma, OPeration Researcho
2- F.So l{iiler and b.J. Lieberrnan, Industrial Engineering serieso 1995
ffhis,book comes with a cD containing software)
i: - (
C. Hadley , Linear Prograrnrning, Narosa Publishing Elouse. 1995'
4- G. I{adley, Linear uod Dynamic programming, Addison \ileslerv
Reading Mass5- H.A. Tahao operations Research An introductiono Macmillan
Publishing co. Inc. New York6- prem Kumar Gupta and D.s. Hirao operation Reasearch, an
Introdution, S. Chand & Company Ltd. New Delhi'
1- I{.S. Kambo, Mathematiial Programming Techniques' Affilated East
- *w-est Pvt' Lt A -/' v-+
*-.. ^vxd {>v r1\'- h o r-\ nn/ \r n t"$t' \^l'y'.r\ \N\ nL{" \-N\'ffi^, & M q
M. Sc./iM.A Mathematics)
Operations Research-I
TUTTI]TV N
ation, GraPhical Solution Method'