Course Curricula: M.Sc. (Applied Statistics and Informatics)FIRST YEARSemester ICourse NameNo.Semester IILT P CCourse NameNo.LTPCCS101Computer Programming &Utilization20 26SI 402Statistical Inference3108SI 423Linear Algebra and Applications31 08SI 404Applied Stochastic Processes2106SI 417Introduction to ProbabilityTheory31 08SI 416Optimization2106SI 419Combinatorics21 06SI 418Advanced Programming & UnixEnvironment0033SI 425Basic Real Analysis31 08SI 422Regression Analysis3028SI 408Data Structures3108Total Credits1345 39Total Credits13 4 2 36SECOND YEARSemester IIICourse NameNo.Semester IVLT P CES 200/ Environmental StudiesHS 200 /Dept. Elective/Institute Elective--SI 505Multivariate Analysis31 0SI 503Categorical Data AnalysisElective IElective II3321 01 01 0SI 593Project I (Optional)--Total Credits- 6Course NameNo.SI 509SI 526LTPC8Time Series AnalysisExperimental DesignsElective III322111000866886Elective IVElective VProject II/Dept. Elective/Institute Elective22-11-00-6661150 38SI 598- 415 4 0 36Total CreditsElectives – Semester IIIElectives – Semester IVElective IElective IIIMA 419 Basic AlgebraSI 529 Applied AlgorithmsSI 512SI 534Finite Difference Methods for Partial differential EquationsNonparametric StatisticsMA 417 Ordinary Differential EquationsSI 507 Numerical AnalysisSI 513SI 532Theory of SamplingStatistical Decision TheoryMA 533 Advanced ProbabilityElective IIElective IV and VSI 525Testing of HypothesisSI 514Statistical ModelingSI 528SI 511SI 515BiostatisticsComputer Aided Geometric DesignStatistical Techniques in Data MiningSI 527SI 530SI 542Introduction to Derivative PricingStatistical Quality ControlMathematical Theory of ReliabilitySI 536Analysis of Multi-type & Big Data 3 0 0 6
COURSE CONTENTSCS 101 Computer ProgrammingAnd Utilization2026This course provides an introduction toproblem solving with computers using amodern language such as Java or C/C .Topics covered will include : Utilization :Developer fundamentals such as editor,integrated programming environment, Unixshell, modules, libraries. Programmingfeatures : Machine representation,primitive types, arrays and records, objects,expressions, control statements, iteration,procedures, functions, and basic i/o.Applications : Sample problems inengineering, science, text processing, andnumerical methods.Cohoon and Davidson, C Program Design:An introduction to Programming and ObjectOriented Design, 3rd Edition, Tata McGrawHill, 2003.Texts / ReferencesCunningham W.P. and Cunningham M.A.,Principles of Environmental Science,Tata McGraw-Hill Publishing Company,New Delhi, 2002.Nathanson, J.A., Basic EnvironmentalTechnology: Water Supply WasteManagement and Pollution Control, 4th Ed.Prentice Hall of India, New Delhi, 2002.Masters, G.M., Introduction toEnvironmental Engineering andScience, Prentice-Hall of India, SecondIndian Reprint, 2004.Davis, M. L. and Cornwell D. A.,Introduction to Environmental Engineering,2Texts / ReferencesBruce Eckel, Thinking in C 2nd Edition.G. Dromey, How to Solve It by Computer,Prentice-Hall, Inc., Upper Saddle River, NJ,1982.Polya, G., How to Solve It (2nd ed.),Doubleday and Co., 1957.ndEd., McGraw Hill, Singapore, 1998.Wright, R.T., Environmental Science:Towards a Sustainable Future, 9th Ed,Prentice Hall of India, New Delhi, 2007.Supplementary Reading Materials (SelectedBook Chapters and Papers)HS 200 Environmental Studies3003Social Issues and the environment, Publicawareness and Human rights, Indicators ofsustainability, Governance of NaturalResources - Common pool resources: issuesand management.Yashwant Kanetkar , Let Us C, AlliedPublishers, 1998.The Java Tutorial, Sun Microsystems.Addison-Wesley, 1999.ES 200 Environmental Studieshazardous waste management. Air Pollution:sources and effects, Atmospheric transport ofpollutants; Noise pollution; Global issues andclimate change: Global warming, Acid rain,Ozone layer depletion.3003Multidisciplinary nature of environmentalproblems; Ecosystems, Biodiversity and itsconservation; Indicators of environmentalpollution; Environment and human health;Utilization of natural resources andenvironmental degradation. Sustainabledevelopment; Environmental policy and law;Environmental impact assessment; Pollutionof lakes, rivers and groundwater. Principles ofwater and wastewater treatment; Solid andEnvironmentalethics,Religionandenvironment, Wilderness and DevelopingTrends, Environmental movements andActivism,SocialEcologyandBioregionalism, Environmental justice.Environmental economics, Trade andenvironment, Economics of environmentalregulation, Natural resource accounting,Green GDP.
Environment and development,and rehabilitation of people,climate change on economyVulnerability and adaptationchange.ResettlementImpacts ofand society,to climateTwo Dimensional Autonomous Systems andPhase Space Analysis: critical points, properand improper nodes, spiral points, and saddlepoints.Asymptotic Behavior: stability (linearizedstability and Lyapunov methods).Texts / ReferencesAgar, N., Life's Intrinsic Value, New York:Columbia University Press, 2001.Dasgupta, P. and Maler, G. (eds.), TheEnvironment and Emerging DevelopmentIssues, Vol. I, OUP. 1997.Guha, Ramachandra, “Mahatama Gandhi andEnvironmental Movement,” Debating onGandhi, in A. Raghuramaraju (ed.), NewDelhi: Oxford University Press, 2006.Guha, Ramachandra and Madhav Gadgil,Ecology and Equity: The Use and Abuse ofNature in Contemporary India, New Delhi:Penguin, 1995.Hanley, Nick, Jason F. Shogren and BenWhite, Environmental Economics in Theoryand Practice, New Delhi: MacMillan, 2004.Naess, A. and G. Sessions, “Basic Principlesof Deep Ecology,” Ecophilosophy, Vol.6,1984.Boundary Value Problems for Second OrderEquations: Green's function, Sturm comparision theorems and oscillations, eigenvalueproblems.Texts / ReferencesR. P. Agarwal and R. Gupta, Essentials ofOrdinary Differential Equations, TataMcGraw-Hill Publ. Co., New Delhi, 1991.M. Braun, Differential Equations and theirApplications, 4th Edition, Springer Verlag,Berlin, 1993.E. A. Coddington and N. Levinson, Theoryof Ordinary Differential Equations, TataMcGraw-Hill Publ. Co., New Delhi, 1990.L. Perko, Differential Equations andDynamical Systems, 2nd Edition, Texts inApplied Mathematics, Vol. 7, SpringerVerlag, New York, 1998.Redclift, M. and Woodgate, G. (eds.),International Handbook of EnvironmentalSociology, Edward Edgar, 1997.M. Rama Mohana Rao, Ordinary DifferentialEquations: Theory and Applications.Affiliated East-West Press Pvt. Ltd., NewDelhi, 1980.MA 417 Ordinary DifferentialEquationsD. A. Sanchez, Ordinary DifferentialEquations and Stability Theory: AnIntroduction, Dover Publ. Inc., New York,1968.3108Review of solution methods for first order aswell as second order equations, Power Seriesmethods with properties of Bessel functionsand Legendre polynomials.Existence and Uniqueness of Initial ValueProblems: Picard’s and Peano’s Theorems,Gronwall’s inequality, continuation ofsolutions and maximal interval of existence,continuous dependence.Higher Order Linear Equations and linearSystems: fundamental solutions, Wronskian,variation of constants, matrix exponentialsolution, behaviour of solutions.MA 419 Basic Algebra3108Review of basics: Equivalence relations andpartitions, Division algorithm for integers,primes, unique factorization, congruences,Chinese Remainder Theorem, Euler ϕfunction.Permutations, sign of a permutation,inversons, cycles and transpositions.Rudiments of rings and fields, elementaryproperties, polynomials in one and ls, Division algorithm, Remainder
Theorem, Factor Theorem, Rational ZerosTheorem, Relation between the roots andcoefficients,Newton'sTheoremonsymmetric functions, Newton's identities,Fundamental Theorem of Algebra, (statementonly), Special cases: equations of degree 4,cyclic equations.Cyclotomic polynomials, Rational functions,partial fraction decomposition, uniquefactorization of polynomials in severalvariables, Resultants and discriminants.Groups, subgroups and factor groups,Lagrange'sTheorem,homomorphisms,normal subgroups. Quotients of groups,Basic examples of groups (includingsymmetric groups, matrix groups, group ofrigid motions of the plane and finite groupsof motions).Cyclic groups, generators and relations,Cayley's Theorem, group actions, SylowTheorems.Probability measure, probability space,construction of Lebesgue measure, extensiontheorems, limit of events, Borel-Cantellilemma.Random variables, Random vectors,distributions, multidimensional distributions,independence.Expectation, change of variable theorem,convergence theorems.Sequence of random variables, modes ofconvergence. Moment generating functionand characteristics functions, inversion anduniqueness theorems, continuity theorems,Weak and strong laws of large number,central limit theorem.Radon Nikodym theorem, definition andproperties of conditional expectation,conditional distributions and expectations.Texts / ReferencesrdDirect products, Structure Theorem for finiteabelian groups.P. Billingsley, Probability and Measure, 3ed., John Wiley & Sons, New York, 1995.Texts / ReferencesJ. Rosenthal, A First Look at RigorousProbability, World Scientific, Singapore,2000.M. Artin, Algebra, Prentice Hall of India,1994.D.S. Dummit and R. M. Foote, AbstractAlgebra, 2nd Ed., John Wiley, 2002.J.A. Gallian, Contemporary AbstractA.N. Shiryayev, Probability,Springer, New York, 1995.2nded.,K.L. Chung, A Course in ProbabilityTheory, Academic Press, New York, 1974thAlgebra, 4 ed., Narosa, 1999.K.D. Joshi, Foundations of DiscreteMathematics, Wiley Eastern, 1989.T.T. Moh, Algebra, World Scientific, 1992.S. Lang, Undergraduate Algebra, 2nd Ed.,Springer, 2001.rdS. Lang, Algebra, 3 ed., Springer (India),2004.J. Stillwell, Elements of Algebra, Springer,1994.SI 402 Statistical Inference3108Prerequisites : MA 411MA 438 (Exposure)Uniformly most powerful unbiased tests,Invariance in Estimation and ymptoticTheoryofEstimation, Asymptotic distribution oflikelihood ratio statistics.SequentialEstimation,Probability, Ratio Test.MA 533 Advanced Probability 3 1 0 8Texts / ReferencesSequential
G. Casella and R.L. Berger, StatisticalInference, Wadsworth and Brooks, 1990.E.L. Lehmann, Theory of Point Estimation,John Wiley, 1983.E.L.Lehmann,TestingStatisticalndHypotheses, 2 ed., Wiley, 1986.R.J. Serfling, Approximation Theorems ofMathematical Statistics, Wiley, 1980SI 404 Applied Stochastic Process 2 1 0 6Stochastic processes : description anddefinition. Markov chains with finite andcountably infinite state spaces. Classificationof states, irreducibility, ergodicity. Basic limittheorems. Statistical Inference. Applicationsto queuing models.Markov processes with discrete and continuous state spaces. Poisson process, pure birthprocess, birth and death process. Brownianmotion.Algorithms on arrays and matrices. DataStructures (Linked Lists and their variants,Stacks, Queues, Trees, Heaps and somevariants) and applications. Sorting, Searchingand Selection (Binary Search, Insertion Sort,Merge Sort, Quick Sort, Radix Sort,Counting Sort, Heap Sort etc. Medianfinding using Quick-Select, Median ofMedians). Basic Graph Algorithms (BFS,DFS, strong components etc.). Dijkstra'sShortest Paths algorithm, Bellman Fordalgorithm, All pairs shortest path problem Floyd Warshall's algorithm.Texts / ReferencesR. Sedgewick, Algorithms in C, AddisonWesley, 1992.T. Cormen, C. Leiserson, R. Rivest and C.Stein, Introduction to Algorithms, MIT Press,2001.M.A. Weiss, Data Structures and AlgorithmsAnalysis in C , Addison-Wesley, 1999.Applications to queuing models and reliability theory.Jon Kleinberg and Eva Tardos – AlgorithmDesign, Addison-Wesley, 2005Basic theory and applications of renewalprocesses, stationary processes. Branchingprocesses. Markov Renewal and semiMarkov processes, regenerative processes.SI 416 Optimization 2 1 0 6Texts / ReferencesU. N. Bhat, Elements of Applied StochasticProcesses, Wiley, 1972.V.G. Kulkarni, Modeling and Analysis ofStochastic Systems, Chapman and Hall,London, 1995.J. Medhi, Stochastic Models in QueuingTheory, Academic Press, 1991.R. Nelson, Probability, Stochastic Processes,and Queuing Theory: The Mathematics ofComputer Performance Modelling, SpringerVerlag, New York, 1995SI 408 Data Structures3108Toolsfor ns).Unconstrained optimization using calculus(Taylor's theorem, convex functions, coercivefunctions).Unconstrained optimization via iterativemethods (Newton's method, Gradient/conjugate gradient based methods, QuasiNewton methods).Constrained optimization (Penalty methods,Lagrange multipliers, Kuhn-Tuckerconditions).Introduction to Linear Programming.Texts / References:Bazaraa M.S., Sherali H.D., and Shetty C.M.,Nonlinear Programming: Theory andAlgorithms, 3rd Edition, Wiley, 2006.Beale E.M.L and Mackley L., Introduction toOptimization, John Wiley, 1988.
Chavatal V., Linear Programming. W.H.Reeman and Company, 1983.M. Woodroofe, Probability with Applications, McGraw-Hill Kogakusha Ltd., Tokyo,1975.Chong E.P.K. and Zak S.H., An Introductionto Optimization, 2nd Edition, Wiley-SI 418 Advanced Programming andUnix Environment0033Interscience Series in Discrete Mathematicsand Optimization, NY: Wiley, 2004.Joshi M.C. and Moudgalya K., Optimization:Theory and Practice, Narosa, New Delhi,2004.Nocedal Jorge and Wright Stephen J.,Numerical Optimization, 2nd Edition,Springer, New York, 2006.Ruszczy ́nski Andrzej, NonlinearOptimization, Princeton University Press,New Jersey, 2006.Vanderbei R.J., Linear ProgrammingrdFoundations and Extensions, 3 Edition,Springer, 2008.SI 417 Introduction to Probability Theory3108Axioms of Probability, Conditional Probability and Independence, Random variablesand distribution functions, Random vectorsand joint distributions, Functions of randomvectors.Expectation, moment generating functionsand characteristic functions, Conditionalexpectation and distribution. Modes ofconvergence, Weak and strong laws of largenumbers, Central limit theorem.Texts / ReferencesP. Billingsley, Probability and Measure, IIEdition, John Wiley & Sons (SEA) Pvt. Ltd.,1995.P.G. Hoel, S.C. Port and C.J. Stone,Introduction to Probability, Universal BookStall, New Delhi, 1998.J.S. Rosenthal, A First Look at RigorousProbability Theory, World Scientific. 2000.UNIX programming environment (filesystem and directory structure, andprocesses). Unix tools (shell scripting, grep,tar, compress, sed, find, sort etc). GraphicalUser Interface Programming using Java.Multithreaded programming in Java. Socketprogramming in Java.Texts / ReferencesEckel, Thinking In Java,http://www.bruceeckel.com/javabook.htmlB. Forouzan and R. Gilberg, Unix and ShellProgramming: A Textbook, 3rd ed.,Brooks/Cole, 2003.B.W. Kernighan and R. Pike, UnixProgramming Environment, PrenticeHall, 1984.SI 419 Combinatorics2106Prerequisites : MA 401, MA 402Basic Combinatorial Objects: Sets, multisets,partitions of sets, partitions of numbers, finitevector spaces, permutations, graphs etc.Basic Counting Coefficients: The twelve foldway, binomial, q-binomial and the Stirlingcoefficients, permutation statistics, etc.Sieve Methods: Principle of inclusionexclusion, permutations with restrictedpositions, Sign-reversing involutions, determinants etc.Introduction to combinatorial reciprocity.Introduction to symmetric functions.Texts / ReferencesC. Berge, Principles of Combinatorics,Academic Press, 1972.K.D. Joshi, Foundations of DiscreteMathematics, Wiley Eastern, 2000.
R.P. Stanley, Enumerative Combinatorics,Vol. I, Wadsworth and Brooks/Cole, 1986.SI 422 Regression Analysis3028Prerequisites: SI 417 Introduction toProbability TheorySimple and multiple linear regression models– estimation, tests and confidence regions.Check for normality assumption. Likelihoodratio test, confidence intervals andhypotheses tests; tests for distributionalassumptions. Collinearity, outliers; analysisof residuals, Selecting the Best regressionequation, transformation of responsevariables. Ridge's regression.Eigenvalues and eigenvectors: Algebraic andgeometric multiplicity of aneigenvalue. Bounds on eigenvalues. Rayleighquotients. Power method and QRmethod for finding approximate eigenvalues.Special matrices: orthogonal, unitary,hermitian, symmetric, skew-symmetric,Hadamard, Projection matrices.Diagonalization and the spectral theorem forsymmetric matrices.Least squares problem.Finite dimensional vector spaces over fields(with emphasis on R and C). Bases,Linear Transformations, and their matrixrepresentation.Texts / ReferencesLinear, bilinear and quadratic forms.B.L. Bowerman and R.T. O'Connell, LinearStatistical Models: An Applied Approach,PWS-KENT Pub., Boston, 1990Inverses, generalized inverse and MoorePenrose inverse.N.R Draper. And H. Smith., AppliedRegression Analysis, John Wiley and Sons(Asia) Pvt. Ltd., Series in Probability andStatistics, 2003.Partitioned matrices and applications.Kronecker products.D.C. Montgomery, E.A. Peck, G.G. Vining,Introduction to Linear Regression Analysis,John Wiley, NY, 2003Linear Algebra and Linear Models (3/E) byR.B. Bapat, Trim Series, 2012.A.A. Sen and M. Srivastava, RegressionAnalysis – Theory, Methods & Applications,Springer-Verlag, Berlin, 1990.SI 423 Linear Algebra and Applications3108Linear independence of vectors in Euclideanspace. Subspace and dimension. Innerproduct and Gram-Schmidtorthonormalization.Matrices: Null space. Row space and columnspace. Rank-Nullity theorem.Systems of linear equations: Elementary rowoperations. LU decomposition.Gaussian elimination. Rank and determinant.Cramer’s Rule.Books/References:Matrix Algebra: Theory, Computations andApplications in Statistics by J.E.Gentle, Springer, 2007Matrix Algebra Useful for Statistics, S. R.Searle, John Wiley, Hoboken, 2006Linear algebra and its applications (4thEdition) by G. Strang, Thomson, 2006Fundamentals of Matrix Computations byD.S. Watkins, 2nd ed., Wiley, New York,2002.SI 425 Basic Real Analysis3108Review of sequences and series of realnumbers. Tests for convergence of Series.Limit superior and limit inferior. Cauchysequences and completeness of R.
Basic notions of Metric Spaces withemphasisonRn.Connectedness,Compactness, and Heine Borel Theorem.ContinuityandUniformcontinuity.Monotone functions and functions ofbounded variation.Derivatives. Mean Value Theorem andapplications.Riemann Stieltjes integral. Riemann'sCriterion for integrability. Improper integralsand the Gamma function.Sequences and series of functions. Uniformconvergence (proofs should be omitted).Functions of several variables: Directionalderivative, partial derivative, total derivative,Mean Value Theorem, Taylor's Theorem andapplicationsto Maxima/Minimaandconvexity. Double and triple integrals.Statement of Fubini’s Theorem and change ofvariable formula (withoutproofs) withillustrations.Texts/References:T. M. Apostol, Mathematical Analysis, 2nded., Narosa Publishers, New Delhi, 2002.R. G. Bartle and D. R. Sherbert, Introductionto Real Analysis, 4th ed., John Wiley, NewYork, 2011.S. R. Ghorpade and B. V. Limaye, A Coursein Calculus and Real Analysis, Springer(India), New Delhi, 2006.R. R. Goldberg, Methods of Real Analysis,4th Edition, Oxford and IBH Publishing Co.,New Delhi.K. A. Ross, Elementary Analysis: The Theoryof Calculus, 2nd ed., Springer (India), NewDelhi, 2013.SI 503 Categorical Data Analysis3108Two-way contingency tables: Table structurefor two dimensions. Ways of comparingproportions. Measures of associations.Sampling distributions. Goodness-of-fit tests,testing of independence. Exact and largesample inference.Models of binary response variables. Logisticregression. Logistic models for categoricaldata. Probit and extreme value models. Loglinear models for two and three dimensions.Fitting of logit and log-linear models. Loglinear and logit models for ordinaryvariables.Regression: Simple, multiple, non-linearregression, likelihood ratio test
Chavatal V., Linear Programming. W.H. Reeman and Company, 1983. Chong E.P.K. and Zak S
2021-2022 Graduate Degree Curricula DEGREE CURRICULA NOTES A student is responsible for knowing when his/her required courses are offered. General Remarks Each degree curriculum in this document is provided as a reference showing all course requirements. All degrees leading to USCG licensure also require passing the relevant license exams.
Course Curricula : M.Sc. Mathematics) First Semester Second Semester Course Name L T P C Course Name L T P C CS101 Computer Programmin
Course Curricula: M.Sc. (Mathematics) First Semester Second Semester Course Name L T P C Course Name L T P C CS101 Computer Programming
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Computer Science Curricula 2013 Curriculum Guidelines for Undergraduate Degree Programs in Computer Science December 20, 2013 The Joint Task Force on Computing Curricula
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Assessment Instrument – A tool used to evaluate, measure, and document the academic readiness, learning progress, skill acquisition, or educational needs of a student. Comprehension – The ability to extract, construct and apply meaning from text. Core Curricula – Core Curricula is a Comprehensive Tier 1 instruction curricula that includes: a.
ENDS content in their programs' curricula 34 4.7 Average values per region regarding ENDS importance to DH programs' curricula 35 . (DH) programs' curricula across the United States. Methods: The emails of 336 entry-level DH program directors were obtained from the American Dental Hygienists' Association (ADHA) website, and a web-based .