Page 132 - Academic Handbook FoS+29june

References:
1. G. Das and S. Pattanayak, Fundamentals of mathematics analysis, TMH Publishing Co., 2016
2. S.C. Mallik and S. Arora, Mathematical analysis, New Age International Ltd., New Delhi, 2012.
3. K. A. Ross, Elementary Analysis, The Theory of Calculus, Undergraduate Texts in Mathematics, Springer, Indian reprint,
2004.
4. S. Narayan, Elements of real analysis, S. Chand & Co. 2017.
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5. R. G. Bartle D.R. Sherbert, Introduction to Real Analysis, 3 edition, John Wiley and Sons Asia, Pvt. Ltd., Singapore, 2002.
6. C. G. Denlinger, Elements of Real Analysis, Jones & Bartlett, 2011.
7. W. Rudin, Real and Complex Analysis, McGraw Hill Series, 1987.

MA3203: METRIC SPACE [3 1 0 4]
Basic Definition: metric spaces, open spheres and closed spheres, neighbourhood of a point, open sets, interior points, limit points,
closed sets and closure of a set, boundary points, diameter of a set, subspace of a metric space, convergent and Cauchy sequences,
complete metric space, dense subsets and separable spaces, nowhere dense sets, continuous functions and their characterizations;
Isometry and Homeomorphism: Compact spaces, sequential compactness and Bolzano-Weierstrass property, finite intersection
property, continuous functions and compact sets. disconnected and connected sets, components, continuous functions and
connected sets.
References:
1. S. Shirali and Harikishan L. Vasudeva, Metric Spaces, Springer Verlag London, 2009.
2. B. K. Tyagi, First Course in Metric Spaces, Cambridge University Press, 2010.
3. K.C. Sarangi, Real Analysis and Matric Spaces, Ramesh Book Depot, 2016.
4. P.K. Jain and Khalil Ahmad, Metric spaces, Second Edition, Narosa Publishing House, New Delhi, 2003.
5. G.F. Simmons, Introduction to Topology and Modern Analysis, McGraw Hill, 1963.
6. E.T. Copson, Metric spaces, Cambridge University Press, 1968.
nd
7. S. Kumaresan, Topology of Metric Spaces, 2 edition, Narosa Publishing House, 2011.

DEPARTMENT SPECIFIC ELECTIVES
DSE – I & LAB
MA2240: STATISTICAL INFERENCE [2 1 0 3]
Estimation: Parametric space, sample space; Point Estimation: Properties of good estimator: Consistency, unbiasedness, efficiency,
sufficiency. Neymann factorization theorem, complete sufficient statistics, minimum – variance unbiased (MVU) estimators,
exponential family of distributions and its properties, Cramer- Rao inequality, minimum variance bound (MVB) estimators; Interval
Estimation: Confidence intervals for the parameters of various distributions, confidence intervals for difference of means and for
ratio of variances; Methods of Estimation: Method of maximum likelihood, methods of moments; Elements of Statistical Decision
Theory: Neyman theory of testing of hypotheses, simple and composite hypotheses, null and alternative hypotheses, two types of
errors, critical region, level of significance, power of the test, unbiased tests, Neyman- Pearson lemma, construction of most
powerful test, uniformly most powerful test, uniformly most powerful unbiased test; Tests of Significance: tests of significance
based on t, F and Chi-square distributions.
References:
rd
1. A.M. Goon, M.K. Gupta and B. Dasgupta, An Outline of Statistical Theory, Vol. II, 3 edition, World Press, Kolkata, 2005.
2. M Kendall, A. Stuart and J.K. Ord, Kendall's Advanced Theory of Statistics, Oxford University Press, 5th edition, 1991.
3. P. Mukhopadhyay, Applied Statistics, Books & Allied Ltd., 2011.
4. G. Casella, and R.L. Berger, Statistical Inference, Second Edn. Thomson Duxbury, 2002.
th
5. R.V. Hogg, and E.A. Tanis, Probability and Statistical Inference, 9 edition, Macmillan Publishing Co. Inc., 2014.
6. V. K. Rohatgi, Statistical Inference, John Wiley and Sons, 2003.

MA2230: LAB ON STATISTICAL INFERENCE [0 0 2 1]
The following practical will be performed using statistical software: Method of maximum likelihood, methods of moments,
minimum chi- square and modified minimum chi- square, computation of confidence intervals for the parameters of various
distributions, confidence intervals for difference of means and for ratio of variances, confidence interval for binomial proportion
and population correlation coefficient when population is normal.
References:
1. M. J. Crawley, Statistics: An Introduction Using R, Wiley, 2015.
rd
2. Gopal K. Kanji, 100 Statistical Tests, SAGE Publication, 3 edition, 2006.

MA2241: INVENTORY THEORY AND DYNAMIC PROGRAMMING [3 1 0 4]
Inventory Control: Different variables involved. Single item deterministic- economic lot size models with uniform rate, finite &
infinite production rates, with or without shortage-multiitem models with one constant; Deterministic Models with Price-Breaks: aii
units discount model and incremental discount model. Probabilistic single period profit maximization models with uniform demand,
instantaneous demand, with or without setup cost, dynamic inventory models, multi-echelon problems. Integrated approach to
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