DEPARTMENT OF MATHEMATICShttp://maths.du.ac.in

Information Brochure

UNIVERSITY OF DELHI

CONTENTS

1. About the Department 1

2. Faculty Members and their Research 2

2.1. Faculty members and their expertise 2

2.2. Recent Publications of the Faculty Members 3

2.3. Research Grants 18

2.4. Conferences and Other Activities Organized 19

3. Courses/Admission/Students 23

3.1. M. Phil./Ph. D. Courses 23

3.2. Syllabus for M. Phil./Ph. D.Entrance Test 24

3.3. Ph.D./M.Phil. Students List 26

3.4. List of PhD awarded 30

3.5. M.A./M.Sc. in Mathematics 32

3.6. Syllabus For M.A. / M.Sc. Entrance Examination 35

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1. ABOUT THE DEPARTMENT

In University of Delhi, Department of Mathematics was started in 1947 and in 1957a post-graduate course in Mathematical Statistics was initiated. The department wastherefore renamed as Department of Mathematics and Mathematical Statistics. In1963 a two year postgraduate course in Operational Research was instituted underthis department. As such the department expanded considerably and so did its activ-ities. Consequently in December 1964 the Faculty of Mathematics was formed and inAugust 1973 the only department under the Faculty was divided into four departments,viz. Department of Mathematics, Department of Statistics, Department of OperationalResearch, and Department of Computer Science.

The impressive tradition of the Department of Mathematics derives its roots from theeast which predates the formation of the post graduate department. Encompassedwithin the tradition are names such as P.L. Bhatnagar, J.N. Kapur, A.N. Mitra, and B.R.Seth, all of whom distinguished themselves by their teaching and research and wholater carved out major roles for themselves on the Indian mathematical scenario eventhough they were not directly associated with the post-graduate department.

The post-graduate department was set up in 1947. It was fortunate to have Profes-sor Ram Behari as its first head. Prof. Ram Behari was an eminent mathematicianwho specialised in the important field of Differential Geometry. He can be creditedwith having started the tradition of research in Differential Geometry, one of the firstdisciplines in pure mathematics to have been pursued in the department. He guideda number of research scholars and established the high traditions of teaching in thedepartment. During his tenure, in 1957, the department also initiated an M.A./M.Sc.program in Mathematical Statistics and the department was designated as the Depart-ment of Mathematics and Mathematical Statistics.

In 1962, the department was given a formidable push when a distinguished mathe-matician, Prof. R.S.Verma, assumed the responsibilities of the head. It was entirelydue to his dynamism and academic breadth that research activities in the departmentblossomed in several directions such as Operational Research, Information Theory,Coding Theory, Space Dynamics and in Complex Analysis. The first masters programin Operational Research in the country was started in this department under his lead-ership. This was even before any university in the U.K. and in several other advancedcountries had done so. Since the activities and the courses in the department werenow so wide and varied the department was enlarged into the Faculty of Mathematicsat the initiative of Professor R.S.Verma.

In 1970, another distinguished mathematician, Prof. U.N.Singh, was appointed theHead of the Department and the Dean of the Faculty of Mathematics. He provided thedepartment with the requisite strength and depth in the core areas of mathematics. Hecreated strong research in Functional Analysis, Harmonic Analysis, and in OperatorTheory. During his stewardship of the department, several distinguished mathemati-cians from all over the globe began to visit the department regularly and the depart-ment can be said to have attained full maturity. He foresaw the need to have separatedepartments within the overall set-up of the Faculty of Mathematics and thus were

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created, in 1973, the Department of Mathematics, the Department of Statistics, theDepartment of Operational Research and the Department of Computer Science. TheFaculty of Mathematics was re-designated as the Faculty of Mathematical Sciences.

The Department currently offers M.A./M.Sc. courses and runs M.Phil., and Ph.D. pro-grams in Mathematics.

2. FACULTY MEMBERS AND THEIR RESEARCH

2.1. Faculty members and their expertise. The area(s) of expertise of the facultymembers of the department are given below.

Professors

Dinesh Singhdsingh@maths.du.ac.in

Banach Algebras, Complex Analysis,Functional Analysis

Bal Kishan Dassdassbk@rediffmail.com

Coding Theory, Combinatorics, InformationTheory, Discrete Maths, Applied Algebra

Tej B. Singhtbsingh@maths.du.ac.in

Algebraic Topology

Ajay Kumarakumar@maths.du.ac.in

Harmonic Analysis, Complex Analysis,Operator Algebras

R. K. Mohantyrmohanty@maths.du.ac.in

Numerical Analysis, Differential Equations,Fluid Dynamics/ Mechanics

V. Ravichandranvravi68@gmail.com

Complex Analysis

Associate Professors

Sapna Jainsapna@vsnl.com

Algebraic Coding Theory

Sachi Srivastavasachi srivastava@yahoo.com

Functional Analysis, Operator Theory, Ab-stract Differential Equations, Operator Al-gebras

C. S. Lalithacslalitha1@gmail.com

Mathematical Programming, OptimizationTheory

Vusala Ambethkarvambethkar@maths.du.ac.in

Computational Fluid Mechanics

Assistant Professors

Ratikanta Pandarkpanda@maths.du.ac.in

Analysis of PDE, Nonlinear FunctionalAnalysis

A. Zothansangaazothansanga26@yahoo.com

Functional Analysis

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Lalit Kumarlalitkvashisht@gmail.com

Theory of Frames, Functional Analysis

Anupama Panigrahianupama.panigrahi@gmail.com

Number Theory, Cryptography, InformationSecurity

Arvind Patelapatel@maths.du.ac.in

Fluid Dnamics, Computational Fluid Dy-namics, PDE

Kanchan Joshikanchan.joshi@gmail.com

Algebra: Non-Commutative Group Rings

Atul Gauragaur@maths.du.ac.in

Commutative Algebra

Hemant Kumar Singhhksinghdu@gmail.com

Algebraic Topology

Anuj Bishnoianuj.bshn@gmail.com

Field Theory and Polynomials

Sumit Nagpal (Ad-hoc)sumitnagpal.du@gmail.com

Complex Analysis

2.2. Recent Publications of the Faculty Members. The faculty members publishpapers in national and international journals. The following is a partial list of the publi-cations:

2014/Accepted

• Sumit Nagpal and V. Ravichandran, Construction of subclasses of univalentharmonic mappings, Journal of the Korean Mathematical Society, accepted.

• Sumit Nagpal and V. Ravichandran, A comprehensive class of harmonic func-tions defined by convolution and its connection with integral transforms andhypergeometric functions, Studia Universitatis Babes,-Bolyai Mathematica, ac-cepted.

• Rajni Mendiratta, Sumit Nagpal and V. Ravichandran, Second-order differen-tial superordination for analytic functions with fixed initial coefficient, SoutheastAsian Bulletin of Mathematics, accepted.

• V. Ravichandran, Radii of starlikeness and convexity of analytic functions satis-fying certain coefficient inequalities, Mathematica Slovaca, accepted.

• Sumit Nagpal and V. Ravichandran, Univalence and convexity in one directionof the convolution of harmonic mappings, Complex Variables and Elliptic Equa-tions, appeared online.

• Sumit Nagpal and V. Ravichandran, A subclass of close-to-convex harmonicmappings, Complex Variables and Elliptic Equations, Volume 59 (2014), no. 2,pp. 204-216.

• C.S. Lalitha, P. Chatterjee, Levitin-Polyak well-posedness for constrained qua-siconvex vector optimization problems, Journal of Global OptimizationDOI 10.1007/s10898-013-0103-9

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• Renu Chugh, Mukesh Singh, LK Vashisht, On Λ-type duality of frames in Ba-nach spaces, Int. J. Anal. Appl., 4 (2) (2014), 148-158.

• S. K. Kaushik, L. K. Vashisht and G. Khattar, Reconstruction property andframes in Banach spaces, Palest. J. Math. 3(1) (2014), 11-26.

2013

• B.K. Dass and Surbhi Madan, Repeated low-density burst error locating codes,Acta Universitatis Apulensis, No. 33 (2013), pp. 175-191.

• Sat Gupta, Samridhi Mehta, Javid Shabbir, B. K. Dass, Generalized Scramblingin Quantitative Optional Randomized Response Models, Communications inStatistics - Theory and Methods, Volume 42 (2013), Issue 22, pages 4034-4042.

• B. K. Dass, and Poonam Garg, A sufficient condition for the existence of a2-repeated low-density burst error correcting code, Tamsui Oxford Journal ofInformation and Mathematical Sciences, 29(2) (2013) 143-199.

• B. K. Dass, and Surbhi Madan, Blockwise repeated low-density burst error cor-recting linear codes, Italian Journal of Pure and Applied Mathematics, n. 30(2013), 87-100.

• T. B. Singh, Elements of Topology, CRC Press, Boca Raton, FL, 2013. xxii+530pp.

• R. Jain, Ajay Kumar, Spectral Synthesis for the Operator Space Projective Ten-sor Product of C*-algebras, Bulletin of the Malaysian Mathematical SciencesSociety (2), 36(4) (2013), 855–864.

• Ajay Kumar, Mukund Madhav Mishra, Powers of Sub-Laplacian on Step TwoNilpotent Lie Groups. J. Geom. Anal. 23 (2013), no. 3, 1559-1570.

• Ajay Kumar, Mukund Madhav Mishra, Green functions and related boundaryvalue problems on the Heisenberg group. Complex Var. Elliptic Equ. 58 (2013),no. 4, 547-556.

• Sapna Jain, K. P. Shum, Extended Varshamov-Gilbert-Sacks bound for linearLee weight codes. Algebra Colloq. 19 (2012), Special Issue No.1, 893-904.94B05

• Sapna Jain, Correction of two-dimensional solid burst errors in LRTJ-spaces.Proceedings of the International Conference on Algebra 2010, 597-603, WorldSci. Publ., Hackensack, NJ, 2012. 94B20

• R. M. Ali, Naveen Kumar Jain and V. Ravichandran, On the largest disc mappedby sum of convex and starlike functions, Applied and Abstract Analysis, Volume2013 (2013), Article ID 682413, 12 pages.

• R. Ali, M. M. Nargesi and V. Ravichandran, Convexity of integral transformsand duality, Complex Variables and Elliptic Equations, Vol. 58 (2013), no. 11,1569-1590.

• S. Nagpal, V. Ravichandran, Fully starlike and fully convex harmonic mappingsof order α. Ann. Polon. Math. 108 (2013), no. 1, 85-107.

• R. M. Ali, Saiful R. Mondal, and V. Ravichandran, Zero-free approximants toderivatives of prestarlike functions, Journal of Inequalities and Applications,Volume 2013 (2013), Art. 401.

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• S. S. Kumar, V. Kumar, V. Ravichandran and N. E. Cho, Sufficient Conditionsfor Starlike Functions Associated with the Lemniscate of Bernoulli, Journal ofInequalities and Applications, Volume 2013 (2013) Art. 176, 13pp.

• L. S. Keong, V. Ravichandran, S. Supramaniam, Bounds for the second Hankeldeterminant of certain univalent functions, Journal of Inequalities and Applica-tions, Volume 2013 (2013) Art. 281, 17pp.

• R. M. Ali, M. M. Nargesi, V. Ravichandran, Coefficient inequalities for starlike-ness and convexity, Tamkang Journal of Mathematics, Vol. 44 (2013), no. 2,149-162.

• Ali, R. M. ; Jain, Naveen Kumar ; Ravichandran, V. On the radius constants forclasses of analytic functions. Bull. Malays. Math. Sci. Soc. (2) 36 (2013), no.1, 23-38.

• L. S. Keong, V. Ravichandran, S. Supramaniam, Applications of differential sub-ordination for functions with fixed second coefficient to geometric function the-ory, Tamsui Oxford Journal of Mathematical Sciences, 29(2013), no. 2, 267-284.

• R. M. Ali, M. N. Mahnaz, V. Ravichandran, A. Swaminathan, Inclusion criteriafor subclasses of functions and Gronwall’s inequality, Tamsui Oxford Journal ofMathematical Sciences, 29(2013), no. 1, 61-75.

• S. Sivaprasad Kumar, Virendra Kumar, and V. Ravichandran, Subordinationand superordination for multivalent functions defined by linear operators, Tam-sui Oxford Journal of Information and Mathematical Sciences, Volume 29(2013),no. 3, 361-387.

• Rajni Mendiratta and V. Ravichandran, Livingston problem for close-to-convexfunctions with fixed second coefficient, Jnanabha, Volume 43 (2013), to appear.

• Q.H. Ansari, C.S. Lalitha and M. Mehta, Generalized Convexity, Nonsmooth In-equalities and Nonsmooth Optimization, Chapman and Hall/CRC Press, Taylorand Francis Group, Florida, USA, 2013, ISBN 9781439868201

• C.S. Lalitha, M. Dhingra, Optimization reformulations of the generalized Nashequilibrium problem using regularized indicator Nikaido-Isoda function,Journalof Global Optimization, 57(3) (2013) 843-861

• J. Dutta, C.S. Lalitha, Optimality conditions in convex optimization revisited,Optimization Letters, 7(2) (2013) 221-229

• C. S. Lalitha, Prashanto Chatterjee, Well-posedness and stability in vector op-timization problems using Henig proper efficiency. Optimization 62 (2013), no.1, 155-165.

• S.K. Kaushik, L.K. Vashisht and S.K.Sharma, Some results concerning framesassociated with measureable spaces, TWMS J. Pure Appl. Math., 4 (1) (2013),52-60.

• Lalit Kumar Vashisht, Geetika Khattar, On I-reconstruction property, Advancesin Pure Mathematics Vol.3 No.3(2013), Article ID:31227, 7 pages

• A Gaur, A Sharma, Maximal Graph of a Commutative Ring, International Jour-nal of Algebra 7 (12), 581-588

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2012

• B.K. Dass, R. Arora, Error Locating Codes Dealing with Repeated Burst Errors,Italian Journal of Pure and Applied Mathematics, Vol. 29 (2012) pp. 108-118

• B.K. Dass, P. Garg, Bounds for Codes Correcting / Detecting Repeated Low-Density Burst Errors, Discrete Mathematics, Algorithms and Applications, Vol.4, No. 4 (2012) 1250048 (14 pages)

• B. K. Dass and Rashmi Verma, Construction of m-repeated burst error correct-ing binary linear code, Discrete Math. Algorithm. Appl. 04, 1250043 (2012) (7pages)

• Samridhi Mehta , B. K. Dass , Javid Shabbir & Sat Gupta, A Three-Stage Op-tional Randomized Response Model, Journal of Statistical Theory and Practice,6 (3) (2012), 417-427

• Kumar, Ajay ; Rajpal, Vandana . Symmetry and quasi-centrality of the operatorspace projective tensor product. Arch. Math. (Basel) 99 (2012), no. 6, 519-529.

• H.K. Singh, T.B. Singh, The cohomology of orbit spaces of certain free cir-cle group actions, Proceedings of Indian Academy of Sciences, 122(1), 79-86(2012)

• R.K. Mohanty, V. Gopal, High Accuracy Arithmetic Average Type Discretizationfor the Solution of Two-space Dimensional Non-linear Wave Equations, Inter-national Journal of Modeling, Simulation, and Scientific Computing, Vol. 03, ID:1150005 (2012)

• R.K. Mohanty, R. Kumar, V. Dahiya, Cubic Spline Method for 1D Wave Equationin Polar Coordinates, ISRN Computational Mathematics, Vol. 2012, ID: 302923(2012)

• R.K. Mohanty and J. Talwar, Application of TAGE Iterative Methods for the So-lution of Non-linear Two Point Boundary Value Problems with Linear MixedBoundary Conditions on a Non-uniform Mesh, International Journal for Com-putational Methods in Engineering Science & Mechanics, to appear (2012)

• R.K. Mohanty, R. Kumar, Vijay Dahiya, Cubic Spline Iterative Method for Pois-son’s Equation in Cylindrical Polar Coordinates, ISRN Mathematical Physics,2012, ID: 234516 (2012)

• R.K. Mohanty, R. Kumar, Vijay Dahiya, Spline in Tension Methods for SingularlyPerturbed One Space Dimensional Parabolic Equations with Singular Coeffi-cients, Neural Parallel & Scientific Computations, 20, 81-92 (2012)

• R.K. Mohanty, M.K. Jain, B.N. Mishra, A Novel Numerical Method of O(h4)for Three-dimensional Non-linear Triharmonic Equations, Communications inComputational Physics, to appear (2012)

• J. Talwar, R.K. Mohanty, A Class of Numerical Methods for the Solution ofFourth-Order Ordinary Differential equations in Polar Coordinates, Advancesin Numerical Analysis, to appear (2012)

• R.K. Mohanty and N. Setia, A New Fourth Order Compact Off-step Discretiza-tion for the System of 2D Non-linear Elliptic Partial Differential Equations, EastAsian Journal of Applied Mathematics, to appear (2012)

• R.K. Mohanty, R. Kumar, Vijay Dahiya, Spline in Compression Methods for Sin-gularly Perturbed 1D Parabolic Equations with Singular Coefficients, Journal ofDiscrete Mathematics, to appear (2012)

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• R.K. Mohanty, V. Gopal, An Off-step Discretization for the Solution of 1-D MildlyNon-linear Wave Equations with Variable Coefficients, Journal of Advanced Re-search in Scientific Computing, 4(2), 1-13 (2012)

• Sapna Jain, K. P. Shum, Extended Varshamov-Gilbert-Sacks bound for linearLee weight codes. Algebra Colloq. 19 (2012), Special Issue No.1, 893-904.

• Sapna Jain, Correction of two-dimensional solid burst errors in LRTJ-spaces.Proceedings of the International Conference on Algebra 2010, 597-603, WorldSci. Publ., Hackensack, NJ, 2012.

• S. Nagpal, V. Ravichandran, Applications of Theory of Differential Subordina-tion for Functions with Fixed Initial Coefficient to Univalent Functions, AnnalesPolonici Mathematici, to appear (2012)

• R.M. Ali, N.E. Cho, S.S. Kumar, V. Ravichandran, First Order Differential Subor-dinations for Functions Associated with the Lemniscate of Bernoulli, TaiwaneseJournal of Mathematics, to appear (2012)

• R. M. Ali, N. E. Cho, N. Jain and V. Ravichandran, Radii of starlikeness andconvexity of functions defined by subordination with fixed second coefficients,Filomat, Vol. 26 No 3 (2012), 553-561.

• R.M. Ali, N. Jain, V. Ravichandran, Radii of Starlikeness Associated with theLemniscate of Bernoulli and the Left-half Plane, Applied Mathematics and Com-putations, 218, 6557–6565 (2012).

• R. M. Ali, N. E. Cho, O. S. Kwon, and V. Ravichandran, A First Order DifferentialDouble Subordination with Applications, Applied Mathematics Letters, 25, 268-274 (2012)

• R.M. Ali, L.S. Keong, V. Ravichandran, S. Supramaniam, Coefficient Estimatesfor Bi-univalent Ma-Minda Starlike and Convex Functions, Applied MathematicsLetters, 25, 344-351 (2012).

• R.M. Ali, A.O. Badghaish, V. Ravichandran, A. Swaminathan, Starlikeness ofIntegral Transforms and Duality, Journal of Mathematical Analysis and Applica-tions, 385(2), 808-822 (2012)

• V. Ravichandran, Geometric properties of partial sums of univalent function,Ramanujan Mathematics Newsletter, Vol. 22 No 3, 2012, pp. 208-221.

• C. S.Lalitha, Prashanto Chatterjee, Stability and scalarization of weak efficient,efficient and Henig proper efficient sets using generalized quasiconvexities, J.Optim. Theory Appl. 155 (2012), no. 3, 941-961.

• C. S. Lalitha, Prashanto Chatterjee, Stability for properly quasiconvex vectoroptimization problem. J. Optim. Theory Appl. 155 (2012), no. 2, 492-506.

• C. S.Lalitha, Guneet Bhatia, Levitin-Polyak well-posedness for parametric qua-sivariational inequality problem of the Minty type. Positivity 16 (2012), no. 3,527-541.

• V. Ambethkar, Mohit KumarSrivastava, Numerical study of an unsteady 2-Dincompressible viscous flow with heat transfer at moderate Reynolds numberwith slip boundary conditions. Int. J. Appl. Math. 25 (2012), no. 6, 883-908.

• Lalit Kumar Vashisht, On Retro Banach Frames of Type P, Azerbaijan Journalof Mathematics, 2(1), 79-86 (2012)

• Virender, A. Zothansanga, S.K. Kaushik, On almost orthogonal frames, Int. J.Math. Math. Sci. 2012, Art. ID 920607, 6 pp.

• R. K.Sharma, P. Yadav, and K. Joshi, Units in Z2(C2xD∞). Int. J. Group Theory1 (2012), no. 4, 33-41.

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2011

• Sahni, Niteesh ; Singh, Dinesh . Invariant subspaces of certain sub Hilbertspaces of $ Hsp 2 $ . Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), no. 4,56-59.

• Raghupathi, Mrinal ; Singh, Dinesh . Function theory in real Hardy spaces.Math. Nachr. 284 (2011), no. 7, 920-930.

• Jain, Ranjana ; Kumar, Ajay . Ideals in operator space projective tensor productof $ Csp * $ -algebras. J. Aust. Math. Soc. 91 (2011), no. 2, 275-288.(http://arxiv.org/abs/1106.3143)

• Dass, Bal Kishan ; Verma, Rashmi . Repeated low-density burst error detectingcodes. J. Korean Math. Soc. 48 (2011), no. 3, 475-486.

• Dass, Bal Kishan ; Garg, Poonam . On repeated low-density burst error detect-ing linear codes. Math. Commun. 16 (2011), no. 1, 37-47.

• Gupta, Sat ; Mehta, Samridhi ; Shabbir, Javid ; Dass, B. K. Some optimalityissues in estimating two-stage optional randomized response models. Amer. J.Math. Management Sci. 31 (2011), no. 1-2, 1-12.

• R.K. Mohanty, S. Singh, High Accuracy Numerov Type Discretization for theSolution of One Space Dimensional Non-linear Wave Equations with VariableCoefficients, Journal for Advanced Research in Scientific Computing, 3, 53-66(2011)

• R.K. Mohanty, M.K. Jain, D. Dhall, A Cubic Spline Approximation and Appli-cation of TAGE Iterative Method for the Solution of Two-Point Boundary ValueProblems with Forcing Function in Integral Form, Applied Mathematical Mod-elling, 35, 3036-3047 (2011)

• R.K. Mohanty, V. Dahiya, An O(k2 + kh2 + h4) Accurate Two-level Implicit CubicSpline Method for One Space Dimensional Quasi-linear Parabolic Equations,American Journal of Computational Mathematics, 1, 1-17 (2011)

• C. Grossmann, R.K. Mohanty, Hans-Georg Roos, Direct Higher Order Dis-cretization in Singular Perturbations via Domain Split - A Computational Ap-proach, Applied Mathematics and Computations, 217, 9302- 9312 (2011)

• R.K. Mohanty, M.K. Jain, B.N. Mishra, A New Fourth Order Difference Approxi-mation for the Solution of Three-dimensional Non-linear Biharmonic Equationsusing Coupled Approach, American Journal of Computational Mathematics, 1,318-327 (2011)

• R.K. Mohnaty, S. Singh, A New High Order Approximation for the Solution ofTwo-space Dimensional Quasi-linear Hyperbolic Equations, Advances in Math-ematical Physics, 2011, ID: 420608 (2011)

• R.K. Mohanty, D. Dhall, High Accuracy Arithmetic Average Discretization forNon-linear Two Point Boundary Value Problems with a Source Function in Inte-gral Form, Applied Mathematics, 2, 243-1251 (2011)

• R.K. Mohanty, V. Gopal, High Accuracy Cubic Spline Finite Difference Approxi-mation for the Solution of One-space Dimensional Non-linear Wave Equations,Applied Mathematics and Computations, 218, 4234-4244 (2011)

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• R.K. Mohanty, M.K. Jain, B.N. Mishra, A Compact Discretization of O(h4) forTwo-dimensional Non-linear Triharmonic Equations, Physica Scripta, 84, ID:025002 (2011)

• Sapna Jain, On a sufficient condition to attain minimum square distance inEuclidean codes. Algebra Colloq. 18 (2011), no. 3, 499-505.

• Sapna Jain, K. P. Shum, Construction of Lee weight codes detecting CT-bursterrors and correcting random errors. Algebra Colloq. 18 (2011), Special IssueNo.1, 847-856.

• N. E. Cho, O. S. Kwon, and V. Ravichandran, Coefficient, distortion and growthinequalities for certain close-to-convex functions, Journal of Inequalities andApplications, Volume 201, Article 100, 2011.

• R. M. Ali, R.Chandrashekar, L. S. Keong and V. Ravichandran, Convolutionsof meromorphic multivalent functions with respect to n-ply symmetric conjugatepoints, Applied Mathematics and Computations, Volume 218, Issue 3, (2011)Pages 723-728.

• A. O. Badghaish, R. M. Ali, and V. Ravichandran, Closure properties of opera-tors on the Ma-Minda Type starlike and convex functions, Applied Mathematicsand Computations, Volume 218, Issue 3, (2011), Pages 667-672.

• R. M. Ali, S. Nagpal, V. Ravichandran, Second-order differential subordinationsfor analytic functions with fixed initial coefficient, Bulletin of the Malaysian Math-ematical Sciences Society (2), Volume 34 (2011), No3, pp. 611-629.

• R. M. Ali, R. Chandrashekar, S. K. Lee, V. Ravichandran, and A. Swaminathan,Differential sandwich theorem for multivalent meromorphic functions associatedwith Liu-Srivastava operator, Kyungpook Mathematical Journal, Vol. 51 No 2(2011), 217-232.

• R. M. Ali, N. E. Cho, O. S. Kwon, and V. Ravichandran, Subordination andsuperordination for multivalent functions associated with the Dziok-Srivastavaoperator, Journal of Inequalities and Applications, Volume 2011 (2011), ArticleID 486595, 17 pages

• R. M. Ali, and V. Ravichandran, Integral operators on the classes of multiva-lent Ma-Minda starlike and convex functions, Mathematical and Computer Mod-elling, Volume 53 (2011) 581-586.

• R. M. Ali, R. Chandrashekar, V. Ravichandran, Janowski starlikeness for a classof analytic functions, Applied Mathematics Letters, Volume 24, Issue 4, April2011, Pages 501-505 .

• V. Ravichandran, and S. Sivaprasad Kumar Argument estimate for starlike func-tions of reciprocal order, The Southeast Asian Bulletin of Mathematics, Volume35, (2011) pages 837-843.

• R. M. Ali, R.Chandrashekar, S. K. Lee, V. Ravichandran, and A. Swaminathan,Differential sandwich theorem for multivalent analytic functions associated withDziok-Srivastava operator, Tamsui Oxford Journal of Mathematical Sciences,Volume 27 No 3 (2011), pages 327-350.

• R. M. Ali, Maisarah Haji Mohd, L. S. Keong, and V. Ravichandran, Radii ofstarlikeness, parabolic starlikeness and strong starlikeness for Janowski star-like functions with complex parameters, Tamsui Oxford Journal of MathematicalSciences, Volume 27 No 3 (2011), pages 253-267.

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• R. M. Ali, Mahnaz M. Nargesi, and V. Ravichandran, On Differential Subordina-tion of Linear Operators Satisfying a Recurrence Relation, Journal of Analysis,Vol 19 (2011), 61-70.

• R. M. Ali, V. Ravichandran, Uniformly Convex and Uniformly Starlike Functions,Ramanujan Mathematics Newsletter, Vol. 21 No 1, 2011, pp. 16-30.

• C.S. Lalitha, G. Bhatia, Stability of Parametric Quasivariational Inequality of theMinty Type, Journal of Optimization Theory and Applications, 148(2), 281-300(2011)

• Lalitha, C. S. ; Arora, R. Proximal proper saddle points in set-valued optimiza-tion. Topics in nonconvex optimization, 87-100, Springer Optim. Appl., 50,Springer, New York, 2011.

• Ambethkar, V. ; Singh, P. K. Effect of magnetic field on an oscillatory flow of aviscoelastic fluid with thermal radiation. Appl. Math. Sci. (Ruse) 5 (2011), no.17-20, 935-946.

• Ambethkar, V. Finite volume method for steady viscous incompressible flowwith heat transfer. Int. J. Appl. Math. 24 (2011), no. 2, 289-300.

• Tanvi Jain, Derivatives for antisymmetric tensor powers and perturbation bounds,Linear Algebra and its Applications, 435, 1111-1121 (2011)

2010

• Dinesh Singh, S. Lata, M. Mittal, A Finite Multiplicity Helson-Lowdenslager-deBranges Theorem, Studia Mathematica, 200(3), 247-266 (2010)

• B.K. Dass, R. Arora, Codes Correcting Repeated Burst Errors Blockwise, Ap-plied Mathematical Sciences, 4(49), 2405-2416 (2010)

• B.K. Dass, S. Madan, Repeated Burst Error Locating Linear Codes, DiscreteMathematics Algorithms and Applications, 2(2), 181-188 (2010)

• B.K. Dass, R. Arora, Codes Correcting Low-density Repeated Burst ErrorsBlockwise, Advances in Information Theory and Operations Research, VDMVerlag, 67-93 (2010)

• B.K. Dass, S. Madan, Syndromes of Shifts in Cyclic Codes, Information Theoryand Optimization Techniques in Scientific Research, VDM Verlag, 69-88 (2010)

• B.K. Dass, S. Madan, Blockwise Repeated Burst Error Correcting Linear Codes,Ratio Mathematica – Journal of Applied Mathematics, 20, 97-126 (2010)

• B.K. Dass, R. Arora, Error Correcting Codes Dealing with Repeated Low-densityBurst Errors, Ratio Mathematica – Journal of Applied Mathematics, 20, 67-96(2010)

• P. L. Q. Pergher, H. K. Singh and T. B. Singh, On Z2 and S1 free actions onspaces of cohomology type (a, b), Houston J. Math. 36 (2010), no. 1, 137–146.

• H. Begehr, A. Chaudhary, Ajay Kumar, Bi-polyanalytic Functions in the UpperHalf, Complex Variables and Elliptic Equations, 55, 305-316 (2010)

• A. Chaudhary, Ajay Kumar, Mixed Boundary Value Problems in the Upper HalfPlane, Journal of Applied Functional Analysis, 5, 209-220 (2010)

• Ajay Kumar, M.M. Mishra, Green’s Functions on the Heisenberg Group. Anal-ysis, International Mathematical Journal of Analysis and its Applications 30,147-155 (2010)

11

• R.K. Mohanty, A New High Accuracy Finite Difference Discetization for the So-lution of 2D Non-linear Biharmonic Equations Using Coupled Approach, Nu-merical Methods of Partial Differential Equations, 26, 831-944 (2010)

• R.K. Mohanty, On the Use of AGE Algorithm with a New High Accuracy Nu-merov Type Variable Mesh Discretization for 1D Non-linear Parabolic Equa-tions, Numerical Algorithms, 54, 379-393 (2010)

• R.K. Mohanty, Single Cell Compact Finite Difference Discretizations of OrderTwo and Four for Multi-dimensional Triharmonic Problems, Numerical Methodsof Partial Differential Equations, 26, 1420-1426 (2010)

• R.K. Mohanty, Application of AGE Method to High Accuracy Variable MeshArithmetic Average type Discretization for 1D Non-linear Parabolic Initial Bound-ary Value Problems, International Journal for Computational Methods in Engi-neering Science & Mechanics, 11, 133-141 (2010)

• Sapna Jain, High-density error correction/detection in Euclidean codes. J. Al-gebra Discrete Struct. 8 (2010), no. 1-2, 47-61.

• Sapna Jain, Singleton’s bound in Euclidean codes. Algebra Colloq. 17 (2010),Special Issue No.1, 741-748.

• Sapna Jain, Array codes in the generalized Lee-RT pseudo-metric (GLRTP-metric). Algebra Colloq. 17 (2010), Special Issue No.1, 727-740.

• Sapna Jain, K. P. Shum, Correction of CT burst array errors in the generalized-Lee-RT spaces. Acta Math. Sin. (Engl. Ser.) 26 (2010), no. 8, 1475-1484.

• R.M. Ali, A.O. Badghaish, V. Ravichandran, Multivalent Functions with Respectto n-ply Points and Symmetric Conjugate Points, Computers and Mathematicswith Applications, 60(11), 2926-2935 (2010)

• R.M. Ali, V. Ravichandran, N. Seenivasagan, Differential Subordination and Su-perordination of Analytic Functions Defined by the Dziok-Srivastava Linear Op-erator, Journal of Franklin Institute, 347(9), 1762-1781 (2010)

• R.M. Ali, M.M. Mahnaz, V. Ravichandran, K.G. Subramanian, Convolution Prop-erties of Classes of Analytic and Meromorphic Functions, Journal of Inequali-ties and Applications, 2010 Article ID 385728, 14 pages (2010)

• R.M. Ali, V. Ravichandran, Classes of Meromorphic ?-convex Functions, Tai-wanese Journal of Mathematics, 14(4), 1479-1490 (2010)

• R.M. Ali, V. Ravichandran, N. Seenivasagan, Differential Subordination and Su-perordination for Meromorphic Functions Defined by Certain Multiplier Transfor-mation, Bulletin of the Malaysian Mathematical Sciences Society, 33(2) 311–324 (2010)

• R.M. Ali, N. Jain, V. Ravichandran, Convolutions of Certain Analytic Functions,Journal of Analysis, 18, 1-8 (2010)

• C.S. Lalitha, G. Bhatia, Well-Posedness for Parametric Quasi-variational In-equality Problems with Set-Valued Maps and for Optimization Problems withParametric Quasivariational Inequality Constraints, Optimization, 59(7), 997-1011 (2010)

• C.S. Lalitha, A Note on Duality of Generalized Equilibrium Problem, Optimiza-tion Letters, 4(1), 57-66 (2010)

• C.S. Lalitha, A New Augmented Lagrangian Approach to Duality and ExactPenalization, Journal of Global Optimization, 46(2), 223-245 (2010).

12

• V. Ambethkar, A Numerical Study of Heat and Mass Transfer Effects on anOscillatory Flow of a Viscoelastic Fluid with Thermal Relaxation, Advances inTheoretical and Applied Mechanics, 3(8), 109-122 (2010)

• Kanchan Joshi, R.K. Sharma, Strongly Prime Radical of Group Algebras, Con-tributions in Algebra and Geometry, 51(2), 417-425 (2010)

2009

• Dinesh Singh, K. Davidson, V.I. Paulsen, M. Raghupathi. A Constrained Nevanlina-Pick Interpolation Problem, Indiana University Mathematics Journal, 58(2), 709-732 (2009)

• S.C. Arora, J. Bhola, Essentially Slant Toeplitz Operators, Banach Journal ofMathematical Analysis, 3(2), 1-8 (2009)

• B.K. Dass, P. Garg, On 2-Repeated Burst Codes, Ratio Mathematica – Journalof Applied Mathematics, 19, 11-24 (2009)

• B.K. Dass, R. Verma, Repeated Burst Error Detecting Linear Codes, RatioMathematica – Journal of Applied Mathematics, 19, 25-30 (2009)

• B.K. Dass, L. Berardi, R. Verma, On 2-Repeated Burst Detecting Codes, Jour-nal of Statistical Theory and Practice, 3(2), 381-391 (2009)

• A. Chaudhary, Ajay Kumar, Boundary Value Problems in the Upper Half Plane,Complex Variables and Elliptic Equations 54(5), 441-448 (2009)

• Ajay Kumar, R. Prakash, Mixed Boundary Value Problem for InhomogeneousPoly-Analytic Harmonic Equation, Proceedings of the 5th International ISAACCongress, Catania Eds. H. Begehr, F. Niolosi, World Scientific, Singapore,1149-1161 (2009).

• R.K. Mohanty, M.K. Jain, High Accuracy Cubic Spline Alternating Group Ex-plicit Methods for 1-D Quasi-linear Parabolic Equations, International Journalof Computer Mathematics, 86, 1556-1571 (2009)

• R.K. Mohanty, A Variable Mesh C-SPLAGE Method of AccuracyO(k2h1−1

+kh1+h31)

for 1-D Nonlinear Parabolic Equations, Applied Mathematics and Computa-tions, 213, 79-91 (2009)

• R.K. Mohanty, New Unconditionally Stable Difference Schemes for the Solutionof Multi-dimensional Telegraphic Equations, International Journal of ComputerMathematics, 86, 2061-2071 (2009)

• R.K. Mohanty, D. Dhall, Third Order Accurate Variable Mesh Discretization andApplication of TAGE Iterative Method for the Non-linear Two-point BoundaryValue Problems with Homogeneous Functions in Integral Form, Applied Math-ematics and Computations, 215, 2024-2034 (2009)

• S. Singh, D. Khattar, R.K. Mohanty, A New Coupled Approach High AccuracyNumerical Method for the Solution of 2D Non-linear Biharmonic Equations,Neural Parallel and Scientific Computations, 17, 239-256 (2009)

• D. Khattar, S. Singh, R.K. Mohanty, A New Coupled Approach High AccuracyNumerical Method for the Solution of 3D Non-linear Biharmonic Equations, Ap-plied Mathematics and Computations, 215, 3036-3044 (2009)

• Sapna Jain, Ki-Suk Lee, An upper bound on the number of parity checks forburst error detection and correction in Euclidean codes. J. Korean Math. Soc.46 (2009), no. 5, 967-977.

13

• Sapna Jain, Seul Hee Choi, Plotkin’s bound in codes equipped with the Eu-clidean weight function. Tamsui Oxf. J. Math. Sci. 25 (2009), no. 2, 207-223.

• R.M. Ali, L.S. Keong, V. Ravichandran, S. Supramaniam, The Fekete-SzegoCoefficient Functional for Transforms of Analytic Functions, Bulletin of the Ira-nian Mathematical Society, 35(2), 119-142 (2009)

• R.M. Ali, V. Ravichandran, L.S. Keong, Subclasses of Multivalent Starlike andConvex Functions, Bulletin of the Belgian Mathematical Society - Simon Stevin,16, 385-394 (2009)

• R.M. Ali, L.S. Keong, V. Ravichandran, S. Supramaniam, Convolution and Dif-ferential Subordination for Multivalent Functions, Bulletin of the Malaysian Math-ematical Sciences Society (2), 32(3), 351-360 (2009)

• M.H. Mohd, R.M. Ali, L.S. Keong, V. Ravichandran, Subclasses of Meromor-phic Functions Associated with Convolution, Journal of Inequalities and Appli-cations, 2009, Article ID 190291, 10pp (2009)

• R.M. Ali, V. Ravichandran, N. Seenivasagan, Differential Subordination and Su-perordination of Analytic Functions Defined by the Multiplier Transformation,Mathematical Inequalities and Applications, 12(1), 123-139 (2009)

• L.S. Keong, V. Ravichandran, S. Supramaniam, Coefficient Bounds for Mero-morphic Starlike and Convex Functions, Journal of Inequalities in Pure andApplied Mathematics, 10(3), 6pp (2009)

• V. Ravichandran, Criteria for Univalence of Integral Operators, Acta Universi-tatis Apulensis Inform., 17, 141-149 (2009)

• S.S. Kumar, V. Ravichandran, H.C. Taneja, Differential Sandwich Theorems forLinear Operators, International Journal of Mathematical Modeling, Simulationand Applications, 2(4), 490-507 (2009)

• C.S. Lalitha, R. Arora, Proper Clarke Epiderivative in Set-Valued Optimization,Taiwanese Journal of Mathematics, 13(6A), 1695-1710 (2009)

• C.S. Lalitha, G. Bhatia, On Well-Posedness for Variational Inequality Problemswith Generalized Monotone Set-Valued Maps, Numerical Functional Analysisand Optimization, 30(5–6), 548-565 (2009)

• C.S. Lalitha, G. Bhatia, Duality in ?-Variational Inequality Problems, Journal ofMathematical Analysis and Applications, 356(1), 169-178 (2009)

• C.S. Lalitha, M. Mehta, Characterizations of Solution Sets of Mathematical Pro-grams in Terms of Lagrange Multipliers, Optimization, 58(8), 885-1007 (2009)

• V. Ambethkar, Numerical Solutions of Heat and Mass Transfer Effects of an Un-steady MHD Free Convective Flow past an Infinite Vertical Plate with ConstantSuction and Heat source and sink, International Journal of Applied Mathemati-cal Mechanics, 5(3), 96-115 (2009)

• V.Ambethkar, Numerical Solutions of Magneto-hydrodynamic Flow Past a Sphereat High Reynolds Numbers, International Journal of Heat and Technology, 27(1),2009,

• Kanchan Joshi, R.K. Sharma, J.B. Srivastava, *-Prime Group Rings, Journal ofAlgebra and its Applications, 8(6), 797-803 (2009)

• R. Bhatia, Tanvi Jain, Higher Order Derivatives and Perturbation Bounds forDeterminants, Linear Algebra and its Applications, 431, 2102-2108 (2009)

• Atul Gaur, A.K. Maloo, The Theta ideal, Dense Submodule and the ForcingLinearity Number for a Multiplication Module, Contributions to Algebra and Ge-ometry, 50(2), 589-602 (2009)

14

2008

• S.C. Arora, J. Bhola, The Compression of a kth-order Slant Hankel Operator,Ganita, 59(1), 1-11 (2008)

• S.C. Arora, J. Bhola, Essentially Slant Hankel Operators, Bulletin of MalaysianMathematical Society, 31(2), 165-173 (2008)

• S.C. Arora, G. Datt, S. Verma, Multiplication and Composition Operators onLorentz-Bochner Spaces, Osaka Journal of Mathematics, 45(3), 629-641 (2008)

• S.C. Arora, G. Kalucha, Retraction of Quasihyponormal Toeplitz Operators J.Operator Theory, 59(1) 69-80 (2009), ” J. Opeartor Theory, 60(2), 445 (2008)

• S.C. Arora, J. Bhola, Generalized Essentially Slant Hankel Operators, Interna-tional Journal of Pure and Applied Mathematics, 47(2), 165-173 (2008)

• S.C. Arora, J. Bhola, kth Order Slant Hankel Operators, Mathematical SciencesResearch, 12(3), 53-63 (2008)

• S.C. Arora, G. Kalucha, Quasihyponormal Toeplitz Operators, J. Opeartor The-ory, 59(1) 69-80 (2009)

• B.K. Dass, R. Verma, Repeated Burst Error Correcting Linear Codes, Asian-European Journal of Mathematics, 1(3), 303-335 (2008)

• B. K. Dass, P. Garg, and M. Zannetti, Some Combinatorial Aspects of m-Repeated Burst Error Detecting Codes Journal of Statistical Theory and Prac-tice, Vol. 2, No. 4 (2008) pp. 707-711

• B.K. Dass, P. Garg, M. Zannetti, On Repeated Burst Error Detecting and Cor-recting Codes, Special volume of East-West Journal of Mathematics, 79-98(2008)

• Hemant Kumar Singh, Tej Bahadur Singh, Fixed point free involutions on co-homology projective spaces. Indian J. Pure Appl. Math. 39 (2008), no. 3,285-291.

• Ajay Kumar, R. Prakash, Neumann and Mixed Boundary Value Problem, Jour-nal of Applied Functional Analysis, 3, 399- 417 (2008)

• Ajay Kumar, R. Prakash, Dirichlet Problem for Inhomogeneous PolyharmonicEquation, Complex Variables and Elliptic Equations, 53, 643-651 (2008)

• R. Jain, Ajay Kumar, Operator Space Tensor Product of C*-algebras, Mathe-matische Zeitschrift, 260, 805-811 (2008)

• Ajay Kumar, M.M. Mishra, Polyharmonic Dirichlet Problem on the HeisenbergGroup. Complex Variables and Elliptic Equations, 53, 1103-1110 (2008)

• Vishnu Gupta, J. N. Chaudhari, Characterization of Weakly Prime SubtractiveIdeals in Semi Rings, Bulletin of the Institute of Mathematics Academia Sinica(NS) 3, 347-352 (2008)

• R.K. Mohanty, S. Singh, A New High Order Two Level Implicit Discretization forthe Solution of Singularly Perturbed Three Space Dimensional Non-linear Par-abolic Equations, International Journal of Numerical Analysis and Modelling, 5,40-54 (2008)

• R.K. Mohanty, A Two-level Implicit Non-uniform Mesh Cubic Spline Method ofO(k2h−11 + kh1 + h31) for the Parabolic Equation uxx = ϕ(x, t, u, ux, ut), NeuralParallel and Scientific Computations, 16, 449-466 (2008)

15

• R.K. Mohanty, N. Khosla, A.K. Ojha, Arithmetic Average Discretization and Two-step BLAGE Iterative Method for the Solution of Elliptic Partial Differential Equa-tions, Computing Letters, 4, 79-90 (2008)

• Sapna Jain, Row-cyclic codes in array coding. Algebras Groups Geom. 25(2008), no. 3, 287-310.

• Sapna Jain, Seul Hee Choi, Construction of m-metric array codes detecting andcorrecting CT-burst array errors. Asian-Eur. J. Math. 1 (2008), no. 4, 589-617.

• S. Jain, K.-S. Lee, A note on the correction of clustered errors with limitedintensity in Euclidean codes. J. Algebra Discrete Struct. 6 (2008), no. 1, 53-61.

• SapnaJain, An algorithmic approach to achieve minimum ?-distance at least din linear array codes. Kyushu J. Math. 62 (2008), no. 1, 189-200.

• Sapna Jain, On the generalized-Lee-RT-pseudo-metric (the GLRTP-metric) ar-ray codes correcting burst errors. Asian-Eur. J. Math. 1 (2008), no. 1, 121-130.

• Sapna Jain, Simultaneous random error correction and burst error detection inLee weight codes. Honam Math. J. 30 (2008), no. 1, 33-45.

• Sapna Jain, CT bursts-from classical to array coding. Discrete Math. 308(2008), no. 9, 1489-1499.

• Charles J. K. Batty, Ralph Chill, Sachi Srivastava, Maximal regularity for secondorder non-autonomous Cauchy problems. Studia Math. 189 (2008), no. 3, 205-223.

• Ralph Chill, Sachi Srivastava, Lp maximal regularity for second order Cauchyproblems is independent of p. Boll. Unione Mat. Ital. (9) 1 (2008), no. 1,147-157.

• R.M. Ali, V. Ravichandran, N. Seenivasagan, Differential Subordination and Su-perordination Associated with Schwarzian Derivatives, Journal of Inequalitiesand Applications, 2008, Article ID 712328, 18pp (2008)

• R.M. Ali, A. Badghaish, V. Ravichandran, Subordination for Higher-order Deriva-tives of Multivalent Functions, Journal of Inequalities and Applications, 2008,Article ID 712328, 18pp (2008)

• R.M. Ali, V. Ravichandran, N. Seenivasagan, Differential Subordination andSuperordination for Meromorphic Functions Defined by Liu-Srivastava LinearOperator, Bulletin of the Malaysian Mathematical Sciences Society (2), 31(2),193-207 (2008)

• R.M. Ali, K.G. Subramanian, V. Ravichandran, O.P. Ahuja, Neighbourhoods ofStarlike And Convex Functions Associated with Parabola, Journal of Inequali-ties and Applications, Volume 2008, Article ID 346279, 9pp (2008)

• C. S. Lalitha and Ruchi Arora, Weak Clarke Epiderivative in Set-Valued Opti-mization, Journal of Mathematical Analysis and Applications, 342(1), 704-714(2008)

• V. Ambethkar, Numerical Solutions of an Impact of Natural Convection on MHDFlow past a Vertical Plate with suction or injection, Journal of Korean Society ofIndustrial Applied Mathematics, 12(4), 201-222 (2008)

• Kanchan Joshi, R.K. Sharma, J.B. Srivastava, *-Prime and Strongly Prime Rad-icals of Group Algebras, Contemporary Mathematics (AMS), 456, 19-26 (2008)

• Tanvi Jain, R. A. McCoy, Lindelof Property of the Multifunction Space L(X) ofCusco Maps, Topology Proceedings, 32, 363-382, (2008)

• L. Hola, Tanvi Jain, R. A. McCoy, Topological Properties of the MultifunctionSpace L(X) of Cusco Maps, Mathematica Slovaca, 58(6), 763-780 (2008)

16

• Tanvi Jain, S. Kundu, Atsuji Completions vis-a-vis Hyperspaces, MathematicaSlovaca, 58(4), 497-508 (2008)

• Atul Gaur, A.K. Maloo, Maximally Differentially Graded Ideals in Zero Charac-teristic. Hiroshima Mathematical Journal. 38(1), 31-35 (2008)

• Atul Gaur, A.K. Maloo, Minimal Prime Submodules. International Journal of Al-gebra. 2(20): 953-956 (2008)

2007

• S.C. Arora, P. Dharmarha, On Joint Weighted Spectrum, Bulletin of CalcuttaMathematical Society, 99(5), 539-546 (2007)

• S.C. Arora, G. Datt, S. Verma, Weighted Composition Operators on Orlicz-Sobolev Spaces, Journal of Australian Mathematical Society, 83(3), 327-334(2007)

• S.C. Arora, G. Datt, S. Verma, Multiplication and Composition Operators onOrlicz-Sobolev Spaces, International Journal of Mathematical Analysis, 1(25-28), 1227-1234 (2007)

• S.C. Arora, S. Paliwal, On H-Toeplitz Operators, Bulletin of Pure and AppliedMathematics, 1(2) 141-154 (2007)

• S.C. Arora, R. Batra, On Slant Hankel Operators, Bulletin of Calcutta Mathe-matical Society, 99(1), 95-100 (2007)

• S.C. Arora, G. Datt, S. Verma, Weighted Composition Operators on LorentzSpaces, Bulletin of Korean Mathematical Society, 44(4), 701-708 (2007)

• S.C. Arora, G. Datt, S. Verma, Composition Operators on Lorenz Spaces, Bul-letin of Australian Mathematical Society, 76(2), 205-214 (2007)

• Hemant Kumar Singh, Tej Bahadur Singh, On the cohomology of orbit space offree Zp-actions on lens spaces. Proc. Indian Acad. Sci. Math. Sci. 117 (2007),no. 3, 287-292.

• H. Begehr, Ajay Kumar, Boundary Value Problems for Higher Order Inhomo-geneous Equations II, Analysis, International Mathematical Journal of Analysisand its Applications, 27, 359-373 (2007)

• Ajay Kumar, R. Prakash, Iterated Boundary Value Problems for the Inhomo-geneous Polyanalytic Equation, Complex Variables and Elliptic Equations, 52,921-932 (2007)

• Ajay Kumar, Operator Space Structure of Banach Spaces, Mathematics Stu-dent, 76, 239-248 (2007)

• R.K. Mohanty, S. Karaa, U. Arora, An O(k2 + kh2 + h4) Arithmetic AverageDiscretization for the Solution of 1-D Non-linear Parabolic Equations, NumericalMethods for Partial Differential Equations, 23, 640-651 (2007)

• R.K. Mohanty, S. Singh, A New Two Level Implicit Discretization of O(k2 +kh2 +h4) for the Solution of Singularly Perturbed Two Space Dimensional Non-linearParabolic Equations, Journal of Computational and Applied Mathematics, 208,391-403 (2007)

• R.K. Mohanty, An Implicit High Accuracy Variable Mesh Scheme for 1-D Non-linear Singular Parabolic Partial Differential Equations, Applied Mathematicsand Computations, 186, 219-229 (2007)

17

• R.K. Mohanty, Three-step BLAGE Iterative Method for Two-dimensional EllipticBoundary Value Problems with Singularity, International Journal of ComputerMathematics, 84, 1613 – 1624 (2007)

• R.K. Mohanty, The Smart-BLAGE Algorithm for Singularly Perturbed 2D Ellip-tic Partial Differential Equations, Applied Mathematics and Computations, 190,321-331 (2007)

• R.K. Mohanty, Stability Interval for Explicit Difference Schemes for Multi-dimen-sional Second Order Hyperbolic Equations with Significant First Order SpaceDerivative Terms, Applied Mathematics and Computations, 190, 1683-1690(2007)

• Sapna Jain, Ki-Bong Nam, Varshamov-Gilbert-Sacks bound for linear Lee weightcodes. Algebras Groups Geom. 24 (2007), no. 3, 349-360.

• S.Jain, K.-B. Nam, K.-S. Lee, Euclidean codes correcting random errors and si-multaneously detecting burst errors. J. Appl. Algebra Discrete Struct. 5 (2007),no. 3, 171-186.

• S. Jain, K.-B. Nam, K.-S.Lee, On some properties of Lee metric codes. J. Appl.Algebra Discrete Struct. 5 (2007), no. 2, 111-125.

• R. Aghalary, S.B. Joshi, R. N. Mohapatra, V. Ravichandran, Subordinationsfor Analytic Functions Defined by Dziok-Srivastava Linear Operator, AppliedMathematics and Computations, 187, 13-19 (2007)

• R. M. Ali, V. Ravichandran, N. Seenivasagan, Coefficient Bounds for p-valentFunctions, Applied Mathematics and Computations, 187, 35-46 (2007)

• R.M. Ali, V. Ravichandran, N. Seenivasagan, Sufficient Conditions for JanowskiStarlikeness, International Journal of Mathematics and Mathematical Sciences,2007, Article ID 62925, 7pp (2007)

• C.S. Lalitha, R. Arora, Conjugate Maps, Subgradients and Conjugate Dualityin Set-Valued Optimization, Numerical Functional Analysis and Optimization,28(7&8), 897-909 (2007)

• C.S. Lalitha, M. Mehta, Characterization of the Solution Sets of PseudolinearPrograms and Pseudoaffine Variational Inequality Problems, Journal of Nonlin-ear and Convex Analysis, 8(1), 87-98 (2007)

• C.S. Lalitha, M. Mehta, A Note on Pseudolinearity in Terms of Bifunctions, AsiaPacific Journal of Operational Research, 24(1), 83-91 (2007)

• V. Ambethkar, L. Rai, Numerical Solutions of an Unsteady Free ConvectiveOscillatory Flow through a Porous Medium, Aligarh Bulletin of Mathematcs,26(2), 1-21 (2007)

• Kanchan Joshi, R.K. Sharma, J.B. Srivastava: *-Prime Group Algebras, Com-munications in Algebra, 35(11), 3673- 3682 (2007)

• Arvind Patel, V. Saran, Self-similar Solution of Shock Propagation in RotatingMedium with Radiation Heat Flux, South East Asian Journal of Mathematicsand Mathematical Sciences, 5(2), 33-48 (2007)

• Arvind Patel, J.P. Vishwakarma, V. Chaube, Self-similar Solution of Shock Prop-agation in Non-ideal gas, International Journal of Applied Mechanics and Engi-neering, 12(3), 813-829 (2007)

• Tanvi Jain, S. Kundu, Boundedly UC spaces: Characterisations and Preserva-tion, Quaestiones Mathematicae 30, 247-262 (2007)

18

• R. A. McCoy, Tanvi Jain, S. Kundu, Factorization and Extension of Isomor-phisms on C(X) to Homeomorphisms on Hyperspaces, Topology and its Appli-cations, 54, 2678-2696 (2007)

• Tanvi Jain, S. Kundu, Atsuji Completions: Equivalent Characterisations, Topol-ogy and its Applications, 54, 28-38 (2007)

• Atul Gaur, A.K. Maloo, A. Parkash, Prime Submodules in Multiplication Mod-ules, International Journal of Algebra, 1(8), 375-380 (2007)

2.3. Research Grants. Some of the recent research grants received by the facultymembers are listed below:

• Prof. D. Singh, Linear Mapping Associated with Banach Spaces of Functions,DST, 1998-2003

• Prof. Ajay Kumar– Complex Analytic methods in PDE, Univ. Delhi, 2009-10– Harmonic analysis on nilpotent Lie groups, Univ. Delhi, 2010-11– Potential theory on stratified Lie groups, Univ. Delhi, 2011-12– Operator space tensor product of C*-algebras, Univ. Delhi, 12-13– Schur tensor product of operator spaces and harmonic analysis, R&D grant

from Univ. Delhi, 2013-14– DFG (German Research Foundation) collaboration with Indian National

Science Academy at Freie Universitat,Berlin,Germany. 2008– JSPS (Japan Society for Promotion of Science) collaboration with Indian

National Science Academy at Gunma University, Japan, 2012• Prof. B. K. Dass Repeated Burst Error Control Codes, R & Grant from Univ.

Delhi 2013-14• Prof. R. K. Mohanty

– High Order Off-step Discretization for Multi-dimensional Hyperbolic Equa-tions, Univ Delhi, 2012-13

– High Accuracy Approximation for Multi-dimensional Quasi-linear Hyper-bolic Equations, Univ. Delhi, 2011-2012

– Arithmetic Average Discretization for Multi-dimensional Non-linear WaveEquations, Univ. Delhi, 2010-2011

– Computational Methods for the Solution of Fourth Order Partial DifferentialEquations, Univ. Delhi, 2009-2010

– Parallel Numerical Algorithms for Non-linear Integro-Differential Equations,Univ. Delhi, 2008-2009

• Dr V Ravichandran– Geometric properties of harmonic univalent functions, Univ. Delhi, 2012-13– Linear operators associated with univalent and multivalent functions,2008-

09,2009-10– Radius Problems for Starlike and Convex Univalent FunctionsR&D grant

from Univ. Delhi, 2013-14– Co-investigator, On planar harmonic mappings and minimal surfaces, RU

Grant, Universiti Sains Malaysia, Dec 2011-Nov 2014• Dr Sapna Jain

– Cyclic Codes in Array Coding, NBHM, 2007-2010– R&D grant, Univ. Delhi, 2008, 2009, 2010

19

• Dr. Sachi Srivastava Quantum Dynamical semigroups, R&D grant from Univ.Delhi, 2013-14

• Dr C. S. Lalitha– Reformulations for Generalized Nash Equilibrium Problems, Univ. Delhi,

2012– Stability and Well-Posedness in Vector Optimization, Univ. Delhi, 2011.– Nonsmoothness and Well-Posedness in Optimization Univ. Delhi, 2010– Optimality and Well-Posedness Aspects of Vector Optimization Problems

Univ. Delhi, 2009– Optimisation and Nonsmooth Analysis, UGC Minor project, 2001-2003– Scalarization and Optimality of Vector-Valued Optimization, R&D grant from

Univ. Delhi, 2013-14• Dr V. Ambethkar

– R& D grants, Univ. Delhi, 2008-09, 09-10,10-11,11-12,12-13– Finite Volume method and its application to Navier-Stokes equations and

Heat Transfer, R& D grants, Univ. Delhi, 13-14• A Zothansanga Generalization of Frames in Hilbert Space and the Feichtinger

Conjecture, R & D grant from Univ. Delhi, 2013-14• Dr Lalit Kumar

– Frames , Atomic Decompositions and Riesz Bases in Banach Spaces,Univ. Delhi, 2010-11

– Expansions property of Frames in Banach Spaces, Univ. Delhi, 2011-12– Frames in Banach Spaces, Univ. Delhi, 2012-13– The Reconstruction Property in Banach spaces and their applications, R&D

grant from Univ. Delhi, 2013-14• Dr Anupama P R & D grant, Univ. Delhi, 2010-11• Dr Arvind Patel

– Shock Phenomena in Conducting and Non-Conducting Media, Univ. Delhi,2012-13

– Study of Shock Phenomena in non-ideal Gas, Univ. Delhi, 2011-12– Study of Shock Wave via Lie-Group Analysis,R&D grant from Univ. Delhi,

2013-14• Dr Atul Gaur

– Generalization of Radical formula for Modules, Univ. Delhi, 10-11– To study the Idealization of a Module, Univ. Delhi, 2011-12– Graph theoretic properties of commutative rings, Univ. Delhi, 12-13– Automorphism group and crossing number of maximal graphs, R&D grant

from Univ. Delhi, 2013-14

2.4. Conferences and Other Activities Organized.

Conferences/Workshops/Schools Organized

• Indo-French CIMPA research school (CRS) on Generalized Nash EquilibriumProblems, Bilevel Programming and MPEC, November 25-December 6, 2013

• National Seminar of Research Scholars in Mathematics, September 20-21,2013

• Instructional Schools for Lecturers On Group Theory, June 3-15, 2013

20

• The Legacy of Srinivasa Ramanujan - An International Conference (2012)• Advance Training in Mathematics (ATM) Schools in Real Analysis and Measure

Theory (2012)• Refresher Courses at CPDHE on Mathematics, Operations Research and Com-

puter Science (2012)• Workshop on Optimization and Statistics (2012)• Workshop on Maxima (2012)• Research Scholars’ Seminar (2012)• Advance Training in Mathematics (ATM) Schools in Geometric Complex Analy-

sis (2011)• Refresher Courses at CPDHE on Mathematics and Operational Research (2011)• National Meet on History of Mathematical Sciences (2010)• National Workshop on Differential Equations, Computing and Modelling (20th

-24th December 2010)• Training Programme on Optimization Theory and Apllications (Feb 10-14, 2010)• Advance Training in Mathematics (ATM) Schools in Real Analysis (2010)• Workshop on Mathematica (2010)• Research Scholars’ Seminar (2010)• Advance Training in Mathematics (ATM) Schools in Complex Analysis (2009)• Refresher Courses at CPDHE on Mathematics and its Applications (2009)• Workshop on Mathematica (2009)• Pre-ICM International Convention on Mathematical Sciences (2008)• Research Scholars’ Seminar (2008)• International Conference on Operator Theory and Related Areas (ICOTRA)

(2008)

Regular Seminars and colloquium Organized

• Prof. Garth Dales, Lancaster University, Finitely-generated maximal left idealsin Banach algebras, Friday January 31, 2014, 3:00pm at Seminar Room 115,Arts Faculty, DU South Campus. This talk will be followed by a 15 minute lectureby Prof. Dales on Ethics, code of practice and open access.

• Prof. K. B. Sinha, Jawaharlal Nehru Center for Advanced Research, Bangalore,Semigroups of linear operators, three lectures, January 15, 17, and 21, 2014,3:30 p.m.

• Prof. Om P. Ahuja, Kent State University, Ohio, Recent developments in har-monic univalent mappings and related functions, January 9, 2014, 3:00 p.m.

• Prof. James E. Jamison, University of Memphis, Some recent results on Her-mitian Operators on Banach spaces, December 23, 2013, 11.30 a.m.

• Prof. Jan Rychtar, University of North Carolina, USA , Math Biology Researchfor UNCG Under-graduate Students, December 12, 2013, 11.00 a.m.

• Prof. Sat Gupta, University of North Carolina, USA, Field Work Validation of Op-tional Unrelated Question RRI Models-Predictors of STD, December 12, 2013,12.00 noon.

• Prof. Shobha Madan, IIT Kanpur on 24th Oct. 2013• Prof. Francois Labourie, University of Paris 11, Orsay, on Margulis Space-times

November 7, 2013

21

• Prof. Ajay Kumar, University of Delhi on From Fourier Series to Harmonic Anal-ysis on August 30, 2013

• Prof. Indira Chatterji, University of Orleans on Some geometry and analysis ofhyperbolic groups on March 19, 2013

• Prof. Robert Tijdeman, Leiden University, The Netherlands on 14th Feb 2013• Prof. Kapil Paranjape, IISER, Mohali on The Shlafly Double-Six on January 17,

2013.• Paulsen, University of Houston, USA, Quantized Function Theory on January

10, 2012• S.K. Khanduja, Punjab University, India, Irreducibilty of Polynomials on March

13, 2012• Aparna Mehra, Indian Institute of Technology Delhi, India, Portfolio Optimization

on March 24, 2012• R.K. Sharma, Indian Institute of Technology Delhi, India, Discrete Log Problems

on March 24, 2012• Rajinder Bhatia, Indian Statistical Institute Delhi, India, Unity of Mathematics in

April, 2012• Inder K. Rana, IIT Mumbai, Integration on Abstract Measure Spaces in April,

2012• E.K. Narayanan, IISc.Bangalore, Integration on Locally compact Spaces in

April, 2012• P. Mohanty, IIT Kanpur, Abstract Lp spaces in April, 2012• Joydeep Dutta, IIT Kanpur, India, On Error Bounds for Variational Inequality

Problems on January 21, 2011• Adam Koranyi, Lehman College, City University of New York, USA, Homoge-

neous Operators on Hilbert Spaces, Some New Results on January 27, 2011• Didier Aussel, University of Perpignen, France, Gap Function for Variational and

Quasivariational Inequalities on January 28, 2011• Ram Murty, Queens University, Ontario, Canada, The Riemann Hypothesis and

Grimms Conjectureon February 18, 2011• Ajay Kumar, University of Delhi, India, Research Prospects for Young Researchers

and Abroad on March 12, 2011• P.K. Saxena, Director, SAG Group, DRDO, New Delhi, India, On Mathematics

in Defence Applications on March 12, 2011• K.B. Sinha, Indian Institute of Science, India, K reins and Other Higher Order

Operator on August 30, 2011• Ken Ross, University of Oregon, United States of America, Frequencies of First

Digits of Data on October 14, 2011• F. Gianessi, University of Pisa Italy, Variational Analysis and Design of Aircrafts

on November 28, 2011• Mati Abel, University of Tartu, Estonia, Generalization of the Liouvilles Theorem

and Their Applications in Theory of Topological Algebra on December 5, 2011• Mati Abel, University of Tartu, Estonia, On Splittings of Extensions of Rings and

Topological Rings on December 5, 2011• Sat Gupta, University of North Carolina, USA, Optimality Issues in Two-Stage

Optional RRT Models on December 22, 2011

22

• Mary Crowe, Anna Tuck, Sat Gupta, University of North Carolina, USA, Non-Medical Use of Stimulant Medication by College Students: an Optional Ran-domized Response Technique on December 22, 2011

• Prajeneshu, Indian Agricultural Statistics, Pusa Road, New Delhi, India, Non-linear Growth Models and their Applications on December 22, 2011

• Vijaya Kumar Murty, University of Toronto, Canada, The Tau of Ramanujan onDecember 22, 2011

• Juan Enrique Martinez Legaz, University of Barcelona, Spain, On a SufficientCondition for Equality of Two Maximal Monotone Operators on August 23, 2010

• S.S. Khare, North-Eastern Hill university, Shillong, India, Taxi-Tab Geometry onNovember 18, 2010

• Jan Rychtar, Sat Gupta, Mary Crowe, University of North Carolina, USA, Inter-action with Faculty and Research Students on December 11-15, 2010

• M.S. Raghunathan, TIFR Mumbai, India, Mathematics that would Rather beScience? n December 22, 2010)

• M.S. Raghunathan,Kalyan Sinha, R. Adiga, Interaction with Faculty and Re-search Students on December 22-23, 2010

• K.R. Parthasarthy, Quantum Probability, Computing and Information on March13, 2009

• Daniel Wulbert, Locator Problem, on January 17, 2008• S.S. Khare, Introduction and Some Applications of Algebraic Topology, on Jan-

uary 22, 2007• James F. Glazebrook, Homotopy and Harmonic Maps, on February 11, 2008• Peter Zvengrowski , Applications of Homotopy Theory to Colouring Groups on

February 14, 2008• Peter Zvengrowski , Seifert Manifolds-I on February 15, 2008• Peter Zvengrowski , Seifert Manifolds-I on February 16, 2008• B.P. Duggal, Totally Hereditarily Normaloid Operators; Property b and Elemen-

tary Operators on February 27, 2008• D.N. Verma, Algebra is at the Heart of Mathematics and Classical Representa-

tion Theory is a Vital Key to Combinatorics on March 7, 2008• I.B.S. Passi, Group Theory and Related Areas during March 19-20, 2008• Sudesh K. Khanduja, Eisenstein-Schonemann Irredicibility Criterion from Valu-

ation Theory Point of View on April 23, 2008• K.B. Sinha, Introduction to Non-Commutative Mathematics I, II,III during April

29 to May 1, 2008• S.G. Dhani, Diophantine Approximation Via Dynamics on October 30, 2008• M.S. Narasimhan, Geometry and Partial Differential Equations on November 3,

2008• R. Parathasarthy, Quantum Probability, Computing and Information on Novem-

ber 14, 2008• Satya Deo Tripathi, Mapping Class GNnd non-metrizable Manifolds on Decm-

ber 12, 2008• Laszio Lovaszo, Large Networks and Their Challenge on December 22, 2008• H. Begher, Freie Universitat, Berlin, delivered a series of eight lectures on Com-

plex Analysis, Clifford Analysis, Boundary Value Problems during January 18to February 16, 2007

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• Kalyan Sinha, Endomorphisms of B(H), Product Systems and CCR Flows onOctober 5, 2007

• B.P. Duggal, Polaroid Operators and SVEP, on November 19, 2007• B.P. Duggal, Browder and WeylSspectra, on November 21, 2007• B.P. Duggal, Browder and Weyl Theorems, on November 23, 2007

3. COURSES/ADMISSION/STUDENTS

The department offers M. A./ M. Sc. courses and runs M. Phil. and Ph. D. program inMathematics. The Master degree programme is by course work while M. Phil and Ph.D. program includes course work as well as dissertation/thesis.

3.1. M. Phil./Ph. D. Courses. Twenty three seats are available for admission to M.Phil. programme including reserved seats as per the University norms. Admission toPh. D. programme depends on the availability of supervisors on yearly basis. The M.Phil. programme is governed by Ordinance VI – Master of Philosophy (M.Phil.) of Uni-versity of Delhi (available at http://www.du.ac.in/index.php?id=684). The Ph. D.programme is governed by the Ordinance VI-B – Doctor of Philosophy (Ph. D.) (avail-able at http://www.du.ac.in/fileadmin/DU/about_du/PDF/Phd_ordinance.pdf) ofUniversity of Delhi.

3.1.1. Duration of the programs. The duration of the M. Phil. course is one and a halfyears. For Ph. D course, the minimum duration is 2 years and the maximum durationis 4-5 years.

3.1.2. Eligibility. For M. Phil programme, the candidate should have good academicrecord with first or high second class Master’s Degree or an equivalent degree of a for-eign University in the subject concerned, or in an allied subject approved by the Deanof the Faculty of Mathematical Sciences and the Vice-Chancellor on the recommenda-tion of the Head of the Department.

For Ph. D. Programme, the candidate must have obtained a Master’s/M. Phil. degreeof the University of Delhi, or any other recognized University, or any degree recognizedas equivalent, in Mathematics or in an allied subject. She/he must have obtained eithera minimum of 50% marks or equivalent grade in the M. Phil. degree or a minimum of55% marks or equivalent grade in the Master’s degree.

As per University rules, for admission to the M.Phil and Ph. D. programmes, the SC/STcandidates shall be given 5% relaxation in the minimum eligibility marks.

3.1.3. Selection Procedure. Admission to the M. Phil. and Ph. D. programmes will bedone on the basis of the relative merit of students’ performance at undergraduate andpost-graduate examinations and the written test (of two hours duration). The merit listswill be prepared by taking into account 25% weight of marks scored in each of under-graduate and post-graduate examinations and 50% weight of marks scored in the test.

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The minimum qualifying marks for admission to Ph. D. programme is 60%. The Univer-sity/College teachers holding a permanent, temporary or adhoc positions and havingcompleted two years of service as teacher in a Department/Constituent Colleges ofthe University of Delhi and candidates having fellowships/scholarships instituted by theUniversity/national and international agencies under schemes approved/recognized bythe University (as well as certain other category (see the Ordinance) of students canbe directly registered to the Ph. D. programme.

3.1.4. Application Form and Syllabus for the Test. Applications will be invited by plac-ing an announcement in the department website every year. The application forms andthe syllabus for the test can be downloaded from the website at http://maths.du.ac.in.It can also be obtained from the office of the Department of Mathematics, University ofDelhi.

Separate applications for M. Phil. and Ph. D. programmes should be sent to the Head,Department of Mathematics, University of Delhi, Delhi 110 007. Each applicationshould be accompanied by a Demand Draft for Rs.600/- (Rupees six hundred only)(Rs. 300 for SC/ST/PH candidates) drawn in favour of The Registrar, University ofDelhi payable at Delhi/New Delhi.

3.2. Syllabus for M. Phil./Ph. D.Entrance Test.

Analysis. Finite, countable and uncountable sets, bounded and unbounded sets,Archimedean property, ordered field, completeness of R, extended real number sys-tem, limsup and liminf of a sequence, the ε−δ definition of continuity and convergence,the algebra of continuous functions, monotonic functions, types of discontinuities, in-finite limits and limits at infinity, functions of bounded variation, uniform continuity, dif-ferentiability, mean value theorem, sequence and series and their convergence, se-quence and series of functions, uniform convergence, Riemann integrable functions,improper integrals, their convergence and uniform convergence.

Euclidean space Rn, Bolzano-Weirstrass theorem, compact subsets of R, Heine-Boreltheorem, Fourier series, continuity and differentiability of functions from space Rn toR, partial and directional derivatives, Taylor’s series, implicit function theorem, line andsurface integrals, Green’s theorem, Stoke’s theorem. Elements of metric spaces, con-vergence, continuity, compactness, connectedness, Weierstrass’s approximation the-orem, completeness, Baire’s category theorem, Lebesgue outer measure, Lebseguemeasure and Lebsegue integration, Riemann and Lebesgue integrals.

Complex numbers, analytic functions, Cauchy-Riemann equations, Riemann sphereand stereographic projection, lines, circles, crossratio, Mobius transf ormations, lineintegrals, Cauchy’s theorems, Cauchy’s theorem for convex regions, Morera’s the-orem, Liouville’s theorem, Cauchy’s integral formula, zero-sets of analytic functions,exponential, sine and cosine functions, power series representation, classification ofsingularities, conformal mapping, contour integration, fundamental theorem of algebra,Riemann’s theorem on removable singularities, maximum modulus principle, Schwartzlemma, open mapping theorem, Casoratti-Weierstrass theorem.

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Banach spaces, Hahn-Banach theortem, open mapping and closed graph theorem,principle of uniform boundedness, boundedness and continuity of linear transforma-tions, dual spaces, embedding in the second dual, Hilbert spaces, projections, or-thonormal bases, Riesz representation theorem, Bessel’s inequality, Parseval’s iden-tity. Elements of Topological spaces, continuity, convergence, homeomorphism, com-pactness, connectedness, separation axioms, first and second countability, separabil-ity, subspaces, product spaces.

Algebra. Space of n vectors, linear dependence, basis, linear transformations, algebraof matrices, rank of a matrix, determinants, linear equations, characteristic roots andvectors.

Vector spaces, subspaces, quotient spaces, linear dependence, basis, dimension, thealgebra of linear transformations, kernel, range, isomorphism, linear functional, dualspace, matrix representation of a linear transformation, change of bases, reductionof matrices to canonical forms, inner product spaces, orthogonality, eigenvalues andeigenvectors, projections, triangular form, Jordan form, quadratic forms, reduction ofquadratic forms.

Groups, subgroups, normal subgroups, quotient groups, homomorphisms, cyclic groups,permutation groups, Cayley’s theorem, Symmetric groups, alternating groups, simplegroups. conjugate elements and class equations of finite groups, Sylow’s theorem,solvable groups, Jordan - Holder theorem, direct products, structure theorem for finiteabelian groups.

Rings, Ideals, prime and maximal ideals, quotient ring, integral domains, Euclidean do-mains, principal ideal domains, unique factorization domains, polynomial rings, chainconditions on rings, fields, quotient fields, finite fields , characteristic of field, field ex-tensions, elements of Galois theory, solvability by radicals, ruler and compass con-struction.

Differential Equations and Mechanics. First order ODE, singular solutions, initialvalue problems of first order ODE, general theory of homogeneous and non-homogeneouslinear ODE s , variation of parameters, Lagrange’s and Charpit’s methods of solvingfirst order PDEs, PDEs of higher order with constant coefficients.

Existence and uniqueness of solution dy/dx = f(x, y), Green’s function, Sturm - Li-ouville boundary value problems, Cauchy problems and characteristics, classificationof second order PDE, separation of variables for heat equation, wave equation andLaplace equation.

Generalized coordinates, Lagrange’s equation, Hamilton’s canonical equations, Varia-tional principle, Hamil ton’s principles and principles of least action, two dimensionalmotion of rigid bodies, Euler’s dynamical equations for the motion of rigid body, motionof a rigid body about an axis, motion about revolving axis.

Equation of continuity in fluid motion, Euler’s equations of motion for perfect fluids, twodimensional motion, complex potential, motion of sphere in perfect liquid and motion

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of liquid past a sphere, vorticity, Navier-Stoke’s equations of motion for viscous flows,some exact solutions.

3.3. Ph.D./M.Phil. Students List. List of Ph.D. Students currently on roll/ Super-visor(s)

• Preeti / Prof. Ajay Kumar• Sachin Sharma / Prof. R.K. Mohanty & Dr. Swarn Singh• Ankit Gupta / Dr. R.D. Sarma• Neetu Aneja / Dr. S.P. Tripathi• Kanika Sharma / Prof.. V. Ravichandran• Nitish Prajapati / Dr. Dinesh Khattar & Dr. Ayub Khan• Vishal Dhawan / Dr. Dinesh Khattar & Dr. Ayub Khan• Poonam Rani / Dr. Sanjay Kumar• Rajesh Singh / Dr. Purnima Gupta• Nidhi Malhotra / Dr. Bindu Bansal• Deepti Kaur / Dr. Swarn Singh & Dr. Vivek K.Aggarwal• Manish Chauhan / Dr. Raj Kumar• Monika Singh / Prof. Ajay Kumar & Dr. Pankaj Jain• Charanpreet Kaur / Dr. Binay K.Sharma• Devendra Tiwari / Prof. Ajay Kumar & Dr. Krishnendu• Shard Rastogi / Dr. Sachi Srivastava• Anuj Kumar / Dr. S.K. Sahdev• Riju Chaudhary / Dr. Pankaj• Konthoujam Somorjit Singh / Prof. T.B. Singh & Dr. H.K. Singh• Shah Jahan / Dr. Varinder Kumar• Jyoti / Dr. Promila Kumar• Neelima Ohri / Dr. Gopal Dutt• Rajni Arora / Dr. Swarn Singh• Anshika Mittal / Dr. Gopal Dutt• Sushil Kumar / Dr. V. Ravichandran• Niteesh Sahni / Dr. Dinesh Singh• Meetu Bhatia / Dr. Surjeet Suneja• Bhawna Kohli / Dr. Surjeet Suneja• Anu Aggarwal / Prof. Ajay Kumar• Seema Thakran nee Seema Rani / Dr. V.K. Tyagi Prof. B.K. Dass• Pritha Dass Gupta (nee Rekhi) / Dr. Atul Razdan• Pankaj Kumar Das / Dr. V.K. Tyagi Prof. B.K. Dass• Amita Sethi nee Goel / Dr. V.K. Tyagi Prof. B.K. Dass• Santosh Kumari / Dr. Pankaj Jain• Vinod Chauhan / Prof. R.K. Mohanthy• Ambika Tyagi / Dr. V.K. Tyagi• Megha Sharma / Dr. Surjeet Suneja• Jaspreet Kaur / Prof. T. B. Singh• Venu Gopal / Dr. L.M. Saha Prof. R.K. Mohanty• Tarannum Kaur Anand / Dr. Promila Kumar• Manju Kalra / Dr. Surjeet Suneja Dr. C. S. Lalitha• Pakhi Aggarwal / Dr. Pratibha Kumar, / Dr. Manish Kant Dubey (DRDO)

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• Balram Kindra / Dr. D.S. Jaggi• Priyambada Tripathi / Dr. Ayub Khan• Neeru Kashyap / Dr. Anuradha Gupta• Praveen Kumar / Dr. Ayub Khan• Pooja Lauhan / Dr. Surjeet Suneja Dr. C. S. Lalitha• Naveen Kumar Jain / Dr. V. Ravichandran Prof. B.K. Dass• Mohit Kumar Srivastava / Dr. V. Ambethkar• Chandra Shekhar Nishad / Dr. Sobha Bagai• Rajni Kapoor / Dr. V. Ravichandran• Seema Bansal / Dr. Dinesh Khattar• Iffat Jahan / Dr. Naseem Ajmal• A. Zothan Sanga / Dr. S.K. Kaushik• Ajeet Singh / Dr. Ayub Khan• Amit Kumar / Prof. Ajay Kumar• Rashmi Gupta / Dr. Ratnesh R. Saxena• Sandhya Jain / Dr. Pankaj Jain• Prashanto Chatterjee / Dr. C.S. Lalitha• Samridhi Mehta / Prof. B.K. Dass Prof. Sat Gupta• Ram Parvesh Prasad / Dr. Ayub Khan Dr. V. Ambethkar• Deepak Kumar Porwal / Dr. Gopal Datt• Neha Bhatia / Dr. Anuradha Gupta• Naresh Kumar Kodam / Dr. Vagisha Sharma• Bikram Singh / Dr. Promila Kumar• Kapil Kumar / Dr. Navin Chandra• Mudita Upmanyu / Dr. Ratnesh R. Saxena• Rekha Aggarwal / Dr. Manjari Srivastava• Ritika Chopra / Dr. Ratnesh R. Saxena• Garima Virmani / Dr. Manjari Srivastava• Shailendra Kumar / Dr. B.K. Tyagi• Rimpi Pal / Dr. Ayub Khan Dr. V. Ambethkar• Bhavneet Kaur Bakshi / Dr. Rajiv Aggarwal• Monika Arora / Dr. Rajiv Aggarwal• Jyoti Talwar / Prof. R.K. Mohanthy Dr. Swarn Singh• Vinay Kumar / Dr. Beena R. Gupta• Khole Timothy Poumai / Dr. Manjari Srivastava• Manoj Kumar Rana / Dr. Davinder Singh• Shalu Sharma / Dr. S.K. Kaushik• Ravindra Kumar / Prof. R.K. Mohanthy• Sumit Nagpal / Prof. Ajay Kumar and / Dr. V. Ravichandran• Rashmi Sehgal / Dr. Alka Marwaha• Anu Chhabra / Prof. B.K. Dass Prof. Sat Gupta• Mamta Choudhary / Dr. Sunila Sharma• Rajesh Kumar / Dr. Sachin Vashistha• Dinesh Kumar / Dr. Sanjay Kumar• Gopal Datt / Dr. Sanjay Kumar• Sudha Rani Dehri / Dr. S.P. Tripathi• Saakshi Garg / Dr. Lalit Kumar• Rachna Choudhary / Dr. B.K. Tyagi

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• Rinku Sharma / Dr. Sachin Vashistha• Jitender Kumar / Dr. Sachin Vashistha• Meena Baweja / Dr. Ratnesh R. Saxena• Geetika Khattar / Dr. Lalit Kumar• Arvind Kumar / Dr. Pankaj Kumar Garg• Suman Panwar / Dr. S.K. Kaushik• Arti Sharma / Dr. Atul Gaur Prof. Bhavanari• Pooja Sharma / Dr. Anuradha Gupta• Shivani Dubey / Prof. Ajay Kumar• Nikita Setia / Prof. R.K. Mohanty• Swati / Dr. Navin Chandra• Sanjiv Kumar / Dr. Ratnesh R. Saxena• Tarun Lata / Dr. Vinod Tyagi• Vandana / Prof. Ajay Kumar• Uday Sharma / Dr. Shashi Aggarwal• Chavi Gupta / Dr. Shashi Aggarwal• Laxmi / Dr. Rajiv Aggarwal• Poonam Sarohe / Dr. Pratibha Kumar / Dr. Manish Kant Dubey (DRDO)• Sushil Yadav / Dr. Rajiv Aggarwal• Ashish Bansal / Prof. Ajay Kumar• Mansi Dhingra / Dr. C.S. Lalitha• Malti Chawla / Dr. Sunila Sharma• Geeta Nagrath / Prof. B.K. Dass Prof. Sat Gupta• Khushboo Bussi / Prof. B.K. Dass Dr. Dhananjoy Dey• Shashi Kant Pandey / Prof. B.K. Dass Dr. Prasanna R. Mishra• Neha Goel / Prof. B.K. Dass Dr. Indivar Gupta• Pranjali / Dr. Purnima Gupta Dr. B.D. Acharya• Subhash Chand / Dr. Vinod Tyagi• Jayanta Biswas / Dr. A.R. Prasannan• Rajeev Kumar / Dr. Arvind Dr. S.K. Pal• Madhu Kumari / Dr. Anupama Panigrahi and / Dr. S.K. Pal• Ajay Kumar / Prof. Dinesh Singh• Manoj Kumar / Dr. Anupama Panigrahi and / Dr. S.K. Pal• Harsh Vardhan / Dr. B.K. Tyagi• Manoj Singh / Dr. Arvind Patel• Bharti Sharma / Dr. Promila Kumar• Karuna Mamtani / Dr. Anuradha Gupta• Krishan Pal / Dr. Navin Chandra• Nikhil Khanna / Dr. Varinder Kumar• Chander Shekhar / Dr. S.K. Kaushik• Ritu Aggawal / Dr. Gopal Datt• Deepti Jain / Dr. Purnima Gupta Dr. B.D. Acharya• Rakesh Batra / Dr. Sachin Vashistha• Apeksha / Dr. V. Ambethkar• Anshika Mittal / Dr. Gopal Dutt• Rajni Arora / Dr. Swarn Singh• Neelima Ohri / Dr. Gopal Dutt• K. Somorjit Singh / Prof. T.B. Singh Dr. Hemant Kumar

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• Jyoti / Dr. Promila Kumar• Shahjahan / Dr. Varinder Kumar

M.Phil Students for the year 2013-14

Names of the students and their Supervisors

• Swati Anand• Noopur Matta• Shweta Gupta• Vivek Kumar Sinha• Soma Das• Amit Sharma• Swati Chhabra Seh-

gal

• Shiva Kapoor• Neha Sharma• Upendra Kumar

Singh• Harshita Shekhar• Alka• Rachna Shokhanda• Mohd Sarik Idrisi

• Soni• Mahendra Pratap

Pal• Reena• Neha Talpa• Nisha• Lakshmi Rani Ba-

sumatary

M.Phil Students for the year 2012-13

• Shelly Verma• Neha Ahuja• Prakriti Saxena• Vibha Anand• Salaj• Shweta Gandhi• Naveen Gupta

• Namita• Rachna Aggarwal• Karuna• Chhatra Pal• Sweeti Yadav• Poonam Verma• Abhay Kumar

• Manisha Saini• Tarachand Prajapati• Avinash Kumar• Rohit Kumar• Makhdoom Ahmed• Pravati Jodia

M.Phil Students for the year 2011-12

• Preeti• Mukta Garg• Nisha Bohra• Priyanka Sahni• Neha Mongia• Sulbha Kumar• Ruchi Bajargaan

• Ankit Gupta• Priyanka Yadav• Venu Bagri• Saloni Jindal• Kushal Lalwani• Himanshi Singh• Ravi Kumar Sagar

• Shahjahan• Sachin Sharma• Ajay Kumar Verma• Jay Kishore Sahni• Raj Kumar• Charan Singh

M.Phil Students for the year 2010-11

• Khushboo• Poonam Rathi• Vibhu Bansal• Tahir Nadeem• Japnit Kaur• Neeraj Kumar• Sonia

• Reema Agarwal• Chanpreet Kaur• Meenal Sambhor• Neelesh Kumar• Chandra Prakash• Konthoujam Sororjit

Singh

• Ashok Kumar Sah• Deepak Kumar• Tamanna Yadav• Braham Prakash• Pappu• Manoj Kumar• Rinkila Bhutia

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List of UGC-Non-NET Fellowship holders for the year 2012-13:

• Shelly Verma• Neha Ahuja• Prakriti Saxena• Vibha Anand• Salaj

• Shweta Gandhi• Rachna Aggarwal• Sweeti Yadav• Poonam Verma• Manisha Saini

• Tarachand Prajapati• Rohit Kumar• Makhdoom Ahmed

List of UGC-Non-NET Fellowship holders for the year 2011-12:

• Mukta Garg• Nisha Bohra• Neha Mongia

• Kushal Lalwani• Himanshi Singh• Ravi Kumar Sagar

• Shahjahan• Jay Kishore Sahni• Charan Singh

3.4. List of PhD awarded.

2012• Ranjana Jain under supervision of Ajay Kumar on Operator Space Tensor Prod-

ucts of C*-algebras and their Ideal Structure• Sumit Kumar Sharma under the supervision of R.K. Panda and S.K. Kaushik

on A Study of Atomic Decompositions in Banach Spaces• Surbhi Madan under the supervision of B.K. Dass on Bounds for Codes Locat-

ing Blockwise Correcting Repeated Burst Errors• Pramod Kumar under the supervision of Vishnu Gupta on On Armendariz Semir-

ings• Ritu Arora under the supervision of B.K. Dass on On Repeated Burst Error

Location/Correction Capabilities of Linear Codes• Satish Verma under the supervision of S.C. Arora on Weighted Composition

Operators on Banach Function Spaces2011

• Durgesh Kumar under the supervision of S.C. Arora and J.K. Kohli on FixedPoint Theorems in Symmetric Spaces and Uniform Spaces

• Raj Kumar under the supervision of S.K. Kaushik on On Frames in BanachSpaces And Their Conjugate Spaces

• Bharti under the supervision of L.M. Saha and R.K. Mohanty on Hyperbolicity,Energy Variability and Chaos in Nonlinear Dynamical Systems

• Neeti Goel under the supervision of R.K. Mohanty and Ayub Khan on ChaosControl in Various Problems of Dynamical Systems

• Jeetendra Kumar Aggarwal under the supervision of S.C. Arora and J.K. Kohlion Function Spaces and Variants of Continuity

• Varinder Kumar under the supervision of R.K. Panda and S.K. Kaushik on OnFrames of Subspaces for Banach Spaces

• Anita Kumari under the supervision of S.K. Bambhri on On R-Strong JordanIdeals in Rings and Ternary Rings2010

• Hemant Kumar Singh under the supervision of T.B. Singh on On the Cohologi-cal Structure of Orbit Spaces of Certain Tranformation Groups

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• Rashmi Verma under the supervision of B.K. Dass on A Study of RepeatedBurst Error Detecting and Correcting Codes

• Prem Pal Singh under the supervision of Ayub Khan and R.K. Mohanty• Ruchi Arora under the supervision of C.S. Lalitha and B.K. Dass on On Con-

strained Set Valued Optimization: Proper Efficiency, Conjugate Duality and Epi-derivatives

• S. Tahiliani under the supervision of S.C. Arora and S.P. Arya on ?-Open Setsin General Topology

• V. Shanta under the supervision of P.K. Jain on Some Aspects of Locally Con-vex Modules Over a Locally Convex Algebra

• Suket Kumar under the supervision of P.K. Jain on Boundedness of GeneralizedHardy Operators on Weighted Lebesgue-Type Spaces

• Poonam Garg under the supervision of B.K. Dass on On the Error Detecting /Correcting Codes

• Roopesh Tehri under the supervision of R.K. Mohnaty and L.M. Saha on Stud-ies on Chaos Control and Chaos Indicators in Dynamical Systems Chaos Con-trol in Various Problems of Dynamical Systems

• Ritu Narang under the supervision of S.R. Arora and B.K. Dass on VariousAspects of Multi-Level Programming Problems

• 1 Mukund Madhav Mishra under the supervision of Ajay Kumar on PotentialTheory on Stratified Lie Groups

• Guneet Bhatia under the supervision of C.S. Lalitha and B.K. Dass on Well-Posedness, Stability and Duality Aspects of Variational Inequality Problems2009

• Noopur Khosla nee Arora under the supervision of R.K. Mohanty on HighlyAccurate Variable Mesh Two Parameter Alternating Group Explicit Methods forthe Solution of boundary Value Problems

• Aparna Jain under the supervision of Naseem Ajmal on A Study of Lattices andCategories in fuzzy Group Theory Daulti Verma nee Rani under the supervi-sion of Pankaj Jain on Weighted Mean Inequalities in Certain Banach FunctionSpaces

• Monika Mehta nee Sethi under the supervision of C.S. Lalitha and B.K. Dasson On some Aspects of Variational Inequality Problems in Terms of Bifunctions

• Veena Sharma under the supervision of V. Shrikant and B.K. Dass on A Studyof Ciphers Through Classification and Clustering Methods

• Gopal Datta under the supervision of S.C. Arora on Multiplication and compo-sition Induced Operators on Lorentz Spaces

• Preeti Dharmaraha nee Dhingara under the supervision of S.C. Arora on AStudy of Weighted Weyl Spectra of Operators

• Khundrakpam Binod Mangang under the supervision of P.P. Hallan and S.C.Arora on Linear and Non-Linear Stability of Equilibrium Points in Robes Re-stricted Three Body Problem

• Narender Kumar under the supervision of D. Bhatia and B.K. Dass on VectorOptimization Involving n-Set Functions

• Reena Kapoor under the supervision of S.R. Arora on Various Techniques forLinearzing Binary Non-linear Programming Problems

• Sudha Arora nee Jairath under the supervision of S.R. Arora on Some Aspectsof Facility Location Problems

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• Nisha Gupta under the supervision of S.K. Kaushik and Ajay Kumar on A Studyof Banach Frames and Related Concepts in Banach Spaces

• Ritu Gupta under the supervision of S.R. Arora on On Multi-Level and Multi-Objective Programming Problems Using Goal and Fuzzy Programming

• Arun Chaudhary under the supervision of Ajay Kumar on Complex BoundaryValue Problems in Unbounded Regions

• Anuradha Sharma nee Gaur under the supervision of S.R. Arora on Some As-pects of Multi-level and Integer Programming Problems

• Jyoti Bhola under the supervision of S.C. Arora on Generalized Slant HankelOperators2008

• Lalit Kumar under the supervision of P.K. Jain on A Study of Frames in BanachSpaces

• Vani under the supervision of S.K. Suneja on The Study of Optimality and Du-ality in Vector Optimization Problems

• Sachin Vashshta under the supervision of J.K. Kohli on Fixed Point Theoremsin Metric Spaces and Probabilistic Metric Spaces

• Dhiraj Kumar Singh under the supervision of Prem Nath and B.K. Dass on OnSome Functional Equations in Information Theory

• Neenu Gupta under the supervision of B.B. Chakraborty and L.M. Saha onRegular and Chaotic Motions in Stellar Pulsations2007

• Ravi Shankar under the supervision of S.R. Arora on Various Techniques forSolving Non-Linear Set Covering Problem

• Swarn Singh under the supervision of R.K. Mohanty on New Highly AccurateDiscretization for the Solution and the Estimates of (du/dn) for singularly Per-turbed Non-Linear Multi-Dimensional Elliptic and Parabolic Partial DifferentialEquations

3.5. M.A./M.Sc. in Mathematics. Students have been admitted to the M.A./M.Sc.program during 2013-14 either directly (Mode I) or through an entrance test (ModeII). Applicant graduated under 10+2+3 scheme or any equivalent scheme are eligiblefor admission. There are 308 seats in North Campus and 62 in South Campus forM.A./M.Sc. programme in Mathematics. Seats are also available in Non-CollegiateWomen’s Education Board (NCWEB).

The distribution of seats under various categories of students in both North Delhi Cam-pus (NDC) and South Delhi Campus (SDC) are given in table on the other side.

Mode I: Direct Admission. 50% seats shall be filled on the basis of merit list drawn inorder of preference separately at North Delhi Campus, South Delhi Campus and NonCollegiate Women’s Education Board (for female candidates only) from the followingcategories of the candidates.

(1) B.A.(Hons)/B.Sc.(Hons) Examination in Mathematics of Delhi University withatleast 60% marks in Mathematics.

(2) B.A.(Hons)/B.Sc.(Hons) Examination in Mathematics of other Universities rec-ognized by Delhi University with atleast 75% marks in Mathematics.

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NDC SDC

General Category Mode-I 78 16

Mode-II 77 15

OBC Category Mode-I 42 8

Mode-II 42 8

SC Category Mode-I 23 4

Mode-II 23 4

ST Category Mode-I 12 4

Mode-II 11 3

NDC SDC

Supernumery Seats

PW Mode-I 04 1

Mode-II 05 1

Sports Mode-I 07 2

Mode-II 08 1

CW Mode-I 07 2

Mode-II 08 1

(3) B.A.(Hons)/B.Sc.(Hons) Examination in Mathematics of Delhi University withatleast 50% marks in Mathematics

(4) B.A.(Hons) / B.Sc.(Hons) Examination in Mathematics of other Universities rec-ognized by Delhi University with atleast 65% marks in Mathematics.

Under Mode I, the minimum requirement for SC/ST candidates will be 40% marks inB.A.(Hons) /B.Sc.(Hons) Examination in Mathematics in each of above four categories.

Admission at all the campuses for Mode-I shall be made, independently, from amongstthe candidates registered at the respective Registration Centres, in order of merit andupto the number of seats available in the Colleges falling within the jurisdiction.

Separate applications are to be filled for different campuses. Candidates desirous ofseeking admission on the basis of merit (Mode I) in NDC, SDC and NCWEB shallbe required to register their names with the following Registration Centre as per theschedule prescribed for the purpose:

(1) Room No. 01, New Academic Block, Department of Mathematics, Faculty ofMathematical Sciences, University of Delhi, North Delhi Campus (NDC), Delhi-110007.

(2) South Delhi Campus (SDC), Benito Juarez Road, New Delhi-110021(3) Non-collegiate Women’s Education Board (NCWEB), University of Delhi - Delhi-

110007.

Registration form for registration to M.A./M. Sc. will be available at the respective Reg-istration Centres (NDC/SDC/NCWEB). These forms duly filled in accompanied with allthe relevant certificates (original and self-attested copies thereof in person only) shallhave to be submitted at the respective registration Centres. The original certificateswill, however, be returned to the candidates immediately after verification but attestedcopies thereof will be retained along with the form. No registration form which is incom-plete and not supported by all the required documents will be accepted. Consequentupon the acceptance of their registration forms the candidates will be issued registra-tion slips as a token of their having been registered for provisional admission. Theseslips will have to be produced at the time of collection of Provisional Admission, Slip,

34

if selected for admission. The candidates are, therefore, advised to retain the regis-tration slip carefully. However, the registration will be valid for the current academicsession only.

Mode II: Admission Through Entrance Test. The remaining 50% seats be filledon the basis of merit in an entrance test. Any candidate who has obtained Bachelordegree in any subject and has studied qualified at least 3 courses each of one yearduration or 6 courses each of one semester duration in Mathematics securing at least45% marks in aggregate will be eligible to appear in the Entrance test.

Any candidate appearing in the final year examination of Bachelor’s degree of the samecalendar year shall also be eligible to appear in the entrance test, however, he/she willbe considered for admission if he/she fulfils the other requirements of admission.

The qualifying marks in the entrance test for a candidate belonging to General categoryshall be 40%. Any seat remaining vacant under this mode of admission will be filled inaccordance with the mode 1. If a student qualifies for admission through both modes,he/she will be granted admission through Mode I.

The candidates belonging to other categories will be provided relaxations/ reservationsas per University rules in both the modes of admission.

The entrance examination shall be of three hours duration. The question paper shallbe of 300 marks, comprising of three sections: Analysis, Algebra, Applied Mathematicswith weightage of 100 marks each. The questions would be of short answer descriptivetype testing the ability and understanding of the subject.

The fee for the entrance examination would be Rs. 800/- for students of general cate-gory and Rs. 400/- for students belonging to SC/ST/PH categories payable by a bankdraft drawn in favour of the Registrar, University of Delhi, Delhi 110007 payable atDelhi.

The entrance examination would be held sometimes in June/July every year and wouldbe duly notified on the University/ Department website along with the syllabus andother details of the examination.

Registration form for registration under mode-2 in the NDC/SDC/ NCWEB wiJl be avail-able in Room No. 0], Faculty of Mathematical Sciences, New Academic Block, Univer-sity of Delhi, Delhi-l10007. These forms duly filled in accompanied with all the relevantcertificates (original and self-attested copies thereof in person only) shall have to besubmitted at the Faculty office North Delhi Campus along with a Bank Draft for Rs.800/- (General/OBC) and Rs. 400/- (SC/ST/PH) as per eligibility conditions. The bank-draft may be drawn in favour of Registrar, University of Delhi, De1hi-ll0007 payable atDelhi along with a self-addressed envelope of 9”x4” size affixing postage stamp of Rs.12/-

The Office of the Faculty of Mathematical Sciences will prepare Admission Lists forstudents selected for admission separately. The first admission list will be notifiedat the New Academic Block, Registration Centre probably in the 4th week of June

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2012. Second and subsequent lists, if necessary, will be notified as early as possible,thereafter.

A copy of each admission list will also be sent to the Principal of each College con-cerned and also to the other Registration Centre (SDC/ NCWEB) for display, etc. Can-didates whose names appear on the admission list (NDWB) will be issued provisionaladmission slips from the office of the Faculty of Mathematical Sciences after notifi-cation of first admission Iist. A candidate after collecting the admission slip will seekadmission to the allotted College offering the concerned subject and attached to theNorth Delhi Campus.

Candidates who will be issued provisional admission slips will be required to completethe admission.fomalities including payment of necessary fees, etc. in a College allottedwithin three days of the issue of admission slips. The admission slips will be retainedby Colleges and the counterfoils returned to the Faculty office, duly signed and rub-ber stamped by the Principals of respective Colleges after a student has been dulyadmitted there. The names of those candidates who fail to complete the admissionformalities or fail to surrender the admission slip in any College within the stipulatedperiod shall be removed from the admission list without any further reference to themand seats thus vacated will be offered to other candidates in order of merit (Mode- Iand Mode- II)

After the college have intimated the number of seats vacant, second and sub-sequentadmission lists of candidates selected for their provisional admission equal to the num-ber of seats vacant each time, will be notified by the Faculty from time to time. Thestudents in their own interest are advised to look up at the Notice Board outside theFaculty Office or website: http:// maths.du.ac.in for any notification issued from time totime relating to admissions.

There would be no minimum age bar for post-graduate course under the Faculty ofMathematical Sciences, [Ee. Res. No. 120 (7) dt 27.12.2007].

3.6. Syllabus For M.A. / M.Sc. Entrance Examination. Analysis. Elementary settheory, finite, countable and uncountable sets, real number system as a complete or-dered field, Archimedean property, supremum, infimum.

Sequence and series, convergence, limsup, liminf, Bolzano Weierstrass theorem, HeineBorel theorem.

Continuity, uniform continuity, intermediate value theorem, differentiability, mean valuetheorem, Maclaurin’s theorem and series, Taylor’s series, Sequences and series offunctions, uniform convergence.

Riemann sums and Riemann integral, improper integrals, monotonic functions, typesof discontinuity, functions of several variables, directional derivative, partial derivative.

Metric spaces, completeness, total boundedness, separability, compactness, connect-edness.

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Algebra. Divisibility in Z, congruences, Chinese remainder theorem, Euler’s φ-function.

Groups, subgroups, normal subgroups, quotient groups, homomorphisms, cyclic groups,permutation groups, Cayley’s theorem, Class equations, Sylow theorems.

Rings, fields, ideals, prime and maximal ideals, quotient rings, unique factorizationdomain, principal ideal domain, Euclidean domain, polynomial rings and irreducibilitycriteria.

Vector spaces, subspaces, linear dependence, basis, dimension, algebra of lineartransformations, matrix representation of linear transformations, change of basis, in-ner product spaces, orthonormal basis. eigenvalues and eigenvectors of matrices,Cayley-Hamilton theorem.

Applied Mathematics. Existence and Uniqueness of solutions of initial value prob-lems for first order ordinary differential equations, Singular solutions of first order ordi-nary differential equations, System of first order ordinary differential equations, Generaltheory of homogeneous and non-homogeneous linear ordinary differential equations,Variation of parameters, Sturm Liouville boundary value problem, Green’s function.

Lagrange and Charpit methods for solving first order PDEs, Cauchy problem for firstorder PDEs, Classification of second order PDEs, General solution of higher orderPDEs with constant coefficients, Method of separation of variables for Laplace, Heatand Wave equations.

Numerical solutions of algebraic equations, Method of iteration and Newton-Raphsonmethod, Rate of convergence, Solution of systems of linear algebraic equations usingGuass elimination and Guass-Seidel methods, Finite differences, Lagrange, Hermiteand Spline interpolation, Numerical integration, Numerical solutions of ODEs usingPicard, Euler, modified Euler and second order Runge-Kutta methods.

Velocity, acceleration, motion with constant and variable acceleration, Newton’s Lawsof Motion, Simple Harmonic motion, motion of particle attached to elastic string, motionon inclined plane, motion of a projectile, angular velocity and acceleration, motionalong a smooth vertical circle, work, energy and impulse, Collision of elastic bodies,Bodies falling in resisting medium, motion under action of central forces, central orbits,planetary motion, moment of inertia and couple, D’Alembart’s principle.

Equilibrium of particle and a system of particles, Mass centre and centres of gravity,Frictions, Equilibrium of rigid body, work and potential energy.