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Tezpur University Statistics 
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Re: Tezpur University Statistics
As you want syllabus of Introductory Statistics subject of 4th Semester of Integrated M.Sc. in Mathematics Program of Tezpur University, so here I am giving detailed syllabus: Tezpur University Integrated M.Sc. in Mathematics Program ‘Introductory Statisticsn’ Syllabus MI 201 Introductory Statistics Unit1 Collection of data, methods of collections of primary data, presentation and classification of data. Unit2 Discrete and continuous variables, Frequency distributions, Graphical representation, cumulative frequency distribution and ogives. Unit3 Measures of location, the arithmetic mean of group data, properties of arithmetic mean, median and mode; other measures of location: quartiles, deciles and percentiles. Unit4 Measures of dispersion,Variance and standard deviation of ungrouped and grouped data, properties of standard deviation. Unit5 Elements of probability theory, classical definition of probability, axiomatic approach to probability, probability of a simple event, probability of composite event, addition rule, multiplication rule: conditional probability. Unit6 Probability Distributions: Binomial distribution, Properties of Binomial Distribution, Stirling approximation, Poisson Distribution, Properties of Poisson distribution. Moments of higher order, relation between mr and mr′, skewness and Kurtosis. Unit7 Correlation and regression: scatter diagram, coefficients of correlation, linear regression, fitting of regression line, the method of least squares, explained and unexplained variation, coefficient of variation, correlation and regression for grouped data. Unit8 Tests of significance, Null hypothesis and hypothesis testing; Chisquare distribution and tests related. Non parametric tests, ‘t’ tests – paired and student ‘t’ tests, ‘F’ test, critical difference at 0.01 and at 0.05. Textbook(s) 1. Medhi, J. Statistical Methods: An introductory Text, (New Age International (P) Ltd,, 2000). 2. Gupta, S.C. and Kapoor, V. K. Fundamentals of Mathematical Statistics, (S. Chand & Co., 2007). Reference book(s) 1. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. I, (Wiley, 2005). 2. Uspensky, J.V. Introduction to Mathematical Probability, (McGraw Hill, 2005). Here I am providing syllabus of other subjects of 4th Semester: MI 202 Probability and Mathematical Statistics (L3 T1 P0 CH4 CR 4) Unit1 Discrete sample space, Bayes’ formula, Discrete random variable, expected value of a random variable. Unit2 Standard probability distribution: Bernoulli, Binomial, Hypergeometric, Geometric, Poisson and Normal distribution. Unit3 Elements of Sampling theory: sampling with and without replacement. Unit4 Sampling distribution of the sample mean, sampling distribution of proportion, standard error. Textbook(s) 1. Medhi, J. Statistical Methods: An introductory Text (New Age International (P) Ltd, 2000). Reference book(s) 1. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. I (Wiley, 2005). MI 203 Linear Spaces and Complex Numbers (L2 T1 P0 CH3 CR 3) Unit1 Algebra of matrices; symmetric, skew symmetric, Hermitian and skew Hermitian matrices; elementary transforms, reduction to echelon and normal form. Unit2 System of linear equations, existence and uniqueness of solutions, rank of a matrix. Unit3 Definitions and examples of vector spaces, elementary properties of and as vector spaces, subspaces, operations on subspaces. Unit4 linear dependence and independence of vectors, basis and dimension of vector spaces. Unit5 linear mappings and their algebraic properties; eigenvalues and eigenvectors, characteristic equation, statement of CayleyHamilton theorem and its use in finding the inverse of a matrix. Unit6 Algebraic properties of complex numbers, geometrical interpretation of complex numbers, modulus and argument of complex numbers; exponential and trigonometric functions of a complex variable. Unit7 Theorems on limit and continuity of a function of complex variable, differentiability, analytic function, CauchyRiemann equations, Harmonic functions. Unit8 derivatives of elementary functions; contour integration, Cauchy’s integral theorem, Cauchy’s integral formula. Textbook(s) 1. Churchill R. V. and Brown, J. W. Complex variables and applications, (McGrawHill International edition, 2006). 2. Hoffman K. and Kunze, R. Linear Algebra, 2nd edition, (Prentice Hall, 2008). Reference book(s) 1. Dutta K. B. Matrix and Linear Algebra, (Prentice Hall of India, 2008). 2. Lang S. Linear Algebra, (SpringerVerlag, 2006). 3. Spiegel M. R. Theory and Problems of Complex Variables, Schum’s Outline Series, (McGrawHill, 2000). MI 204 Mathematical Methods and Partial Differential Equations (L2T1 P0 CH3 CR 3) Unit 1 Partial differential equations: What are partial differential equations (PDEs), and where do they come from? Flows, vibrations and diffusions. Solutions of first order PDEs: Charpits method, Jacobi method. Unit 2 Secondorder linear equations and their classification. Initial and boundary conditions, with an informal description of wellposed problems. D'Alembert's solution of the wave equation. Duhamel's principle for one dimensional wave equation. Separation of variables: application of the method to simple problems in Cartesian coordinates for one dimensional wave and heat equations. Unit 3 Calculus of variation: Variational problems with fixed boundariesEuler’s equation for functionals containing first order derivative and one independent variable. Extremals. Functionals dependent on higher order derivatives. Functionals dependent on more than one independent variable. Variational problems in parametric form. Invariance of Euler’s equation under coordinate transformation. Variational problems with Moving boundariesFunctionals dependent on one and two functions. One sided vatiations. Sufficient conditions for an extremum  Jacobi and Legendre conditions. Unit 4 Special Functions: Series solution of differential equations. Power series method. Bessel and Legendre equations. Bessel and Legendre functions and their properties. Convergence. Recurrence and generating functions. Textbook(s) 1. Rao, K. S. Introduction to Partial Differential Equations, 2nd Edition (Prentice Hall of India, 2007). 2. Gupta, A. S. Calculus of Variation with Applications, (Prentice Hall of India, 1997). 3. Gelfand, I. M. and Fomin, S. V. Calculus of Variation, (Dover Publications, 2000). Reference book(s) 1. Andrews, G.E., Askey, R. A. and Roy, R. Special Functions, (Cambridge University Press, 1999). 2. Sneddon, I. N. Elements of Partial Differential Equations, 4th ed., (Dover, 2006). MI 205 Algebra (L2 T1 P0 CH3 CR 3) Unit1 Relations, Equivalence relations, Mapping and binary operations Unit2 Groups, subgroups, cosets, Lagrange’s theorem, Subgroup generated by a set, cyclic groups permutation groups, normal subgroups, quotient groups. Unit3 Polynomials, Euclid’s Algorithm, greatest common divisor, unique factorization of polynomials over a field F of numbers (statement only), Fundamental theorem of Algebra (statement only), roots and their multiplicity, Irreducible polynomials over Q, R, C. Unit4 Relationship between roots and the coefficients, Fundamental theorem of symmetric polynomial (without proof), Evaluation of symmetric functions of roots. Rational roots of polynomials with integral coefficients. Unit5 Descartes rule of sign, Strum’s theorem (statement only) Solution of cubic equation, Cardon’s method and solution of biquadratic equation. Textbook(s) 1. Gallian, J. A. Contemporary Abstract Algebra, Narosa, 1995. 2. Mapa, S. K. Higher Algebra, Asoke Prakashan, Calcutta, 2006. Reference book(s) 1. Herstein, I. N. Topics in Algebra, 2nd Edition (Wiley Eastern Limited, 1998). 2. Fraleigh, J. B. A First Course in Abstract Algebra, (Narosa, 1995). 3 Barbeau, E. J. Polynomials, (Springer 2003). MI 206 Integral Equations and Transforms (L3 T1 P0 CH4 CR 4) Unit 1 Elementary idea of Improper Integrals, their convergence, Beta and Gamma fnctions, their properties. Integral as a function of parameter (excluding improper integrals). Continuity and derivability of an integral as a function of a parameter. Unit 2 Linear integral equations of the first and second kind of Fredholm and Volterra type: Definitions of integral equations and their classification. Eigen values and Eigen functions. Integral equations of second kind with separable kernels. Reduction to a system of algebraic equations. Method of successive approximations. Iterative scheme for integral equations of the second kind. Unit 3 Integral Transform Methods: Fourier Series, Generalized Fourier series, Fourier Cosine series, Fourier Sine series, Fourier integrals. Fourier transform, Laplace transform. Inverse Transform: Inverse Laplace and Fourier Transform, Solution of differential equation by Laplace and Fourier transform methods. Unit 4 Tensor: Transformation of coordinates, summation convention, kronecker delta. Definition of tensors, covariant, contravarient and mixed tensor, symmetric and antisymmetric tensors, outer and inner product of tensors, contraction, quotient law. Textbook(s) 1. Parashar, B.P. Differential and Integral Equations, 2nd ed., (CBS Publishers, 2008). 2. Mikhlin, S. G. Linear Integral Equations, (Hindustan Book Agency, 1990). 3. Spain, B. Tensor Calculus, (Radha Publishing House, 2000). Reference book(s) 1. Kanwal, R. P. Linear Integral Equation. Theory and Techniques, (Academic Press, 1991). 2. Poularikas, D. The Transforms and Applications, (CRC Press, 1996). 
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