2. K. Ross, Elementary Analysis: The Theory <strong>of</strong> Calculus, Springer Int. Edition, 2004.3. H. L. Royden, Real Analysis, 3rd edition, Prentice Hall <strong>of</strong> India, 1995.4. Terence Tao, Analysis-I <strong>and</strong> II, Second edition, Hindustan Book Agency, 2009.3. Discrete Mathematics (MA4003):3-1-0: 4 CreditsPrerequisite: NilSet theory: sets, relations, functions, countability; Logic: formulae, interpretations, methods <strong>of</strong> pro<strong>of</strong>,soundness <strong>and</strong> completeness in propositional <strong>and</strong> predicate logic; Number theory: division algorithm,Euclid's algorithm, fundamental theorem <strong>of</strong> arithmetic, Chinese remainder theorem, special numberslike Catalan, Fibonacci, harmonic <strong>and</strong> Stirling; Combinatorics: permutations, combinations,pigeonhole principle, inclusion <strong>and</strong> exclusion principle, partitions, recurrence relations, generatingfunctions; Graph Theory: paths, connectivity, subgraphs, isomorphism, trees, complete graphs,bipartite graphs, matchings, colourability, planarity, digraphs, Eulerian cycle <strong>and</strong> Hamiltonian cycle,adjacency <strong>and</strong> incidence matrices.Texts:1. K. H. Rosen, Discrete Mathematics & its Applications, 6th Ed., Tata McGraw-Hill, 2007.2. V. K. Balakrishnan, Introductory Discrete Mathematics, Dover, 1996.References:1. C. L. Liu, Elements <strong>of</strong> Discrete Mathematics, 2nd Ed., Tata McGraw-Hill, 2000.2. R. P. Grimaldi, Discrete <strong>and</strong> Combinatorial Mathematics, Pearson Education, 2002.3. R. C. Penner, Discrete Mathematics: Pro<strong>of</strong> Techniques <strong>and</strong> Mathematical Structures, World Scientific,1999.4. R. L. Graham, D. E. Knuth, <strong>and</strong> O. Patashnik, Concrete Mathematics, 2nd Ed., Addison-Wesley, 1994.5. J. L. Hein, Discrete Structures, Logic, <strong>and</strong> Computability, 3rd Ed., Jones <strong>and</strong> Bartlett, 2010.6. D. M. Burton: Elementary Number Theory. McGraw Hill, 2002.7. N. Deo, Graph Theory, Prentice Hall <strong>of</strong> India, 1974.4. Probability <strong>and</strong> Statistics (MA4004):3-1-0: 4 CreditsPrerequisite: NilProbability:-Axiomatic definition, Properties. Conditional probability, Bayes rule <strong>and</strong> independence <strong>of</strong>events. R<strong>and</strong>om variables, Distribution function, Probability mass <strong>and</strong> density functions, Expectation,Moments, Moment generating function, Chebyshev’s inequality. Special distributions: Bernoulli,Binomial, Geometric, Negative Binomial, Hypergeometric, Poisson, Uniform, Exponential, Gamma,Normal, Joint distributions, Marginal <strong>and</strong> conditional distributions, Moments, Independence <strong>of</strong>r<strong>and</strong>om variables, Covariance, Correlation, Functions <strong>of</strong> r<strong>and</strong>om variables, Weak law <strong>of</strong> largenumbers, P. Levy’s central limit theorem (i.i.d. finite variance case), Normal <strong>and</strong> Poissonapproximations to binomial.Statistics:-Introduction: Population, Sample, Parameters. Point Estimation: Method <strong>of</strong> moments, MLE,Unbiasedness, Consistency, Comparing two estimators (Relative MSE). Confidence intervalestimation for mean, difference <strong>of</strong> means, variance, proportions, Sample size problem, Test <strong>of</strong>Hypotheses:-N-P Lemma, Examples <strong>of</strong> MP <strong>and</strong> UMP tests, p-value, Likelihood ratio test, Tests formeans, variance, Two sample problems, Test for proportions, Relation between confidence intervals<strong>and</strong> tests <strong>of</strong> hypotheses, Chi-square goodness <strong>of</strong> fit tests, Contingency tables, SPRT, RegressionProblem:- Scatter diagram, Simple linear regression, Least squares estimation, Tests for slope <strong>and</strong>correlation, Prediction problem, Graphical residual analysis, Q-Q plot to test for normality <strong>of</strong>
esiduals, Multiple regression, Analysis <strong>of</strong> Variance: Completely r<strong>and</strong>omized design <strong>and</strong> r<strong>and</strong>omizedblock design, Quality Control: Shewhart control charts <strong>and</strong> Cusum charts.Texts:1. Ge<strong>of</strong>frey R. Grimmett, David R. Stirzaker, Probability <strong>and</strong> R<strong>and</strong>om Processes, Oxford University Press,USA; 3 edition, 2001.2. Douglas C. Montgomery <strong>and</strong> George C. Runger, Applied Statistics <strong>and</strong> Probability for Engineers, Wiley,2006.3. Miller & Freund's Probability <strong>and</strong> Statistics for Engineers, 7th Edition, Pearson-Prentice Hall, 2005References:1. Sheldon M. Ross, A First Course in Probability, Prentice- Hall, Sixth Edition, 2001.2. Harold J. Larson: Introduction to Probability Theory <strong>and</strong> Statistical Inference. Wiley 1982.3. V. K. Rohatgi: An Introduction to Probability Theory <strong>and</strong> Mathematical Statistics. John Wiley & Sons1976.4. W. Feller, Introductopn to Probability Theory <strong>and</strong> its applications, Vol I, Wiley, 1968.5. A. M. Gun, M. K. Gupta, <strong>and</strong> B. Das Gupta: Fundamentals <strong>of</strong> Statistics.6. A. M. Gun, M. K. Gupta, <strong>and</strong> B. Dasgupta: Outline <strong>of</strong> Statistics.5. Computer Programming <strong>and</strong> Data Structures (MA4005):3-0-0: 3 CreditsPrerequisite: NilIntroduction - the von Neumann architecture, machine language, assembly language, high levelprogramming languages, compiler, interpreter, loader, linker, text editors, operating systems,flowchart; Basic features <strong>of</strong> programming (Using C) - data types, variables, operators, expressions,statements, control structures, functions; Advance programming features - arrays <strong>and</strong> pointers,recursion, records (structures), memory management, files, input/output, st<strong>and</strong>ard library functions,programming tools, testing <strong>and</strong> debugging; Fundamental operations on data - insert, delete, search,traverse <strong>and</strong> modify.Fundamental data structures - arrays, stacks, queues, linked lists; Trees, Binary trees, Searching <strong>and</strong>sorting - linear search, binary search, insertion-sort, bubble-sort, selection-sort; Introduction to objectoriented programming.Texts:1. E. Balagurusamy, Programming in ANSI C., Tata Mc graw Hill, 2004.2. A. Kelly <strong>and</strong> I. Pohl, A Book on C, 4th Ed., Pearson Education, 1999.References:1. H. Schildt, C: The Complete Reference, 4th Ed., Tata Mc graw Hill, 2000.2. B. Kernighan <strong>and</strong> D. Ritchie, The C Programming Language, 2nd Ed., Prentice Hall <strong>of</strong> India, 1988.3. B. Gottfried <strong>and</strong> J. Chhabra, Programming With C, Tata Mc graw Hill, 2005.4. Data Structures, Schum Series, Tata Mcgraw Hill, 1986.6. Computer Programming <strong>and</strong> Data Structures Lab (MA4101):0-0-3: 2 CreditsPrerequisite: NilProgramming laboratory will be set in consonance with the material covered in lectures <strong>of</strong> the course"Computer Programming <strong>and</strong> Data Structures". This will include assignments in a programminglanguage like C <strong>and</strong> C++ in GNU Linux environment.Texts:1. E. Balagurusamy, Programming in ANSI C., Tata Mc graw Hill, 2004.
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PHYSICS
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Books:1. A Handbook of Silicate Roc
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